SECRET 

REF ID:A70315 

Register No. 11 

WAR DEPARTMENT 

OJ'FICi: OF THE CHIEF SIGNAL OFFICER 

WASHINGTON 

ANALYSIS 

OF A 

MECHANICO-ELECTRICAL 

CRYPTOGRAPH 

PART II 

!Declassified and approved for release by NSA on 12-17-2013 pursuant to E.O. 1352§ 
REF ID:A70315 

SBCHBf' 

Register N'! 11 

WAR DEPARTMENT 

OFFICE OF THE CHIEF SIGNAL OFFICER 

WASHINGTON 

ANALYSIS 

OFA 

MECHANICO-ELECTRICAL 

CRYPTOGRAPH 

PART II 1--·-· - Dl!P _.CAT-~---,"·i I A copy r:f this c;ocumsrd i 

i is cat;ioged in t·-.e i 

;_!4SAJ.e!;_'1nical library J 

TECHNICAL PAPER 

01' 

SIGNAL INTELLIGENCE SECTION 

WAR PLANS AND TRAINING DIVISION 

1JNITED STA.TBS 

GOVEBNllENT PRINTING Ol'l'ICB 

w A!IBINGTON I 1981 
REF ID:A70315 

TABLE OF CONTENTS 

Section Pa.-

I. Introductory reJll&l"ks ___ ------- _ ---- _ --- _ ------- _ --- _________________ --- ____ ---- _ ------ 1 

II. Description of machine and its operation------------------------------------------------- 2-11 

III. Cryptographic analysis of the machine---------------------------------------------------- 12-22 

IV. Synoptic tables--- _ ---------------- ____ ---- ________________________ ------------ _____ --- 23-47 

Appendix 

I. IDBtructioDB--------------------------------------------------------------------------- 49-IO 

II. Basic ciphel'-text sequences ____ ----------- _ -------------- _ --- _ ---- ____ ------------------- 51-82 

III. First interval data-cipher-text relationships ________________________________ ----------____ 63-88 

IV. Basic plain-text sequences _________________________________________________ ------------- 89-100 

V. First-interval data-plain-text relationships_--------_------ ____ -- ____ -- __ -- ____ ---- _______ 101-126 

VI. Summary of results ___________ ---- ______________________________________________________ 127-129 

(Ill I 
REF ID:A70315 

ANALYSIS OF A MECHANICO-ELECTRICAL CRYPTOGRAPH 

PART II 

SECTION I 

INTRODUCTORY REMARKS 

PafBll'Bph Nature of investigation ______________________________________________________________ ----_________ 1 

1. ll'ature of investigation.-In April 1932, there was submitted to the Chief Signal Officer 

a modified form of the Hebern Cipher Machine with a view to testing it for its cryptographic 

security.1 It was desired that the test be of the utmost severity, exceeding in severity what 

could be expected from an attack under the most favorable conditions. 

With this in view, there was fumished, v.ith the mo.chine, 55 messages \\ith plain text and 

110 messages without the equivalent plo.i.n text; also the genera.I system employed in setting 

up message indicators. (See Appendix I.) 

1 This test was made at request of the Code and Signal Section, Office of Naval Communications, 

Navy Department. The test was conduct.cd by Mr. F. B. Rowlett, Dr. S. Kullback, and Dr. A. Sinkov, under 

the supervision of Mr. W. F. Friedman, Chief of Signal Intelligence Section. 

(1) 
SECTION II 

DESCRIPTION OF MACHINE AND ITS OPERATION 

l'aragmph 

General description___________________________ 2 

Motion of the wheels-------------------------- 3 Ratchet cradle_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ 4 

Functions of LAW and RAW__________________ 5 

Paralll'BPh 

DetailPcl 11f:11dy of a particular dog setting________ 6 

Study of cryptographic action__________________ 7 

Action of pm1sible dog settings ____ .. _____ . _ _ _ _ _ 8 

2. General de~crip~on.-The 1932 model of the Hebern Cipher Machine consists of a 

keyboa.i:<l, a set of five cipher wheels, a set of five pawls for controlling the angular displacements 

of the cipher w~eels, ~n an-ang~ment for governing the tLCtion or the pawls, a mechanical drive 

for angularly displacmg the cipher wheels, and an automatic printer. This model requires 

a current supply of 110 volts direct current. 

. 3. Motion of ~e wheels.-~.,rom a cryptographic standpoint, the essential difference between 

this and the previous model rests almost entirely on the difference in the type of cipher-wheel 

BACK DOQ 

AWP2 

RATCH£T CRADLE. 

R-••~---~::::=t.f:~ijt:~:j:::l~~~==!!:f:;J__rRONTDOQ BAR. 

AWPI IPHER WHEEL PAWLS. 

ROLLER 1 

BS2 CW3 

CW2 

EXTENSION OF BENCH MARK. 

FIGURE 1 

B NCH MARK 

RFS 

displ~eme.nt utilized by the two machines. (See W. F. Friedman, A11al71sis of a MechanicoElectrical. Ory1Jtograpl&, Part I, Technical Publication S. I. S., 1934.) In the earlier model the displacements of ~he cipher ~heels are definitely fixed and invariable, being similar to the mo~ements 

of t~e wheels 1n a recordmg meter. Only the fifth (or extreme right-hand) wheel steps forward 

contmu.ously once per ?epression on the keyboard; the first wheel steps forward once per 26 

d~presmons; and the nnddle wheel steps forward once per 650 depressions. Wheels 2 and 4 8.re 

d1spln.c:eablc only by hnnd, and not. automatically. In t.h~ 1932 model the an-angement is no longer 

meU:rhke-any tw~ of the five cipher wheels (depending upon the action selected) may move 

con~~ously, a third wheel moves one step per 26 depressions on the keyboard, and the two 

rema:mmg wheels move one step after 650 depressions on the keyboard. 

. 4. Batchet cradle.-The accompanying diagram, figure 1, shows the mechanical means 

which causes the wheels to move forward. 

(2) 

3 

This menns consists of n. mchet rradle upon whirh u.re mounted two dog bars co.rrying thr<.~e dogs, 

five ciphcr-wheC'l 1ut'wls, three oluminum-v.-111:'<.'1 pa.wls, nnd nn arrangement (not shown in the 

diagrn.m) for releasing nll the pnwls \r-hilc the whrcls nrP. being sP.t. '!'he nction of the dogs ie 

controlled by two nluminum wh~.els, LA '\oV r.ncl RAW, which 11re mountl'd on the left.-llft.nd side 

of the machine in n line \\ith nnd on nn ext!>m1ion of the i;:hnft upon which revolve the cipher 

wheels. LAW nnd RAW, however, move independently of the ripher whcl'ls. 

The front dog bu.r has two dogs mounted upon it nnd provides five 1tctive positions which 

are designated by the first 5 ll'tters of the nlphnhet, A, B, C, D, E, as is shown in fiJ?ure 1. The 

back dog ba.r ho.sonly one dog mounted upon it, and ulso provides five active positions designated 

by the Iii.St 5 letters of the o.lphnbl't, V, W, X, Y, 11nd Z. 

The construction of the two nluminum wheels, LAW and RAW, is identic1tl o.nd is such 

that the periphery of each of the two wheels is divided into two bands. The left-hand band of 

en.ch whel'l has 26 t<.•<.•t.h, earh tooth bring deeignnted by u letter of the alphabet. The righthand band is smooth throughout the entire circumforence of the wheel except for a notch 

which extends from the letter Y to the lotter Z. 

The five cipher-wheel pawls, CWPl to 5, ore mounted upon a shaft which is located underneath the two dog ho.rs. Enl'h pawl hns two notches on it (not shown in fig. 1), one situated 

for acting in association with a dog on the front bn.r, the other situated for n.cting in association 

wit11 a dog on the re11.r bo.r. Since the dogs are individu11lly slidable on their bars, tl1e five 

pawls mn.y act independently. When a dog situated either on the front or the rear bar is in 

position, the pawl immedi1ttely beneath it is withdrawn Crom its active position and is prevented 

from stepping the cipher wheel forward, except in those special cases when the action of the 

dog is neutralized by the action or either the LAW or RAW, as will now be discussed. 

5. Functions of LAW and RAW.-The three aluminum-wheel pawls, AWPl, AWP2, and 

A WP3, are mount.ad upon an extension of the shaft holding the cipher-wheel pawls. The first 

aluminum-wheel pawl, AWPl, acts each time a key is depressed and moves tho LAW forward 

one space; that is its only function. The action or A WP2 is controlled by the LAW in the 

following manner. On the left side of AWP2 there is a projection upon which is mounted a. 

small roller, designated roller 1 in the sketch. This roller normally rests upon the smooth 

band on the right-hand side of the LAW 1md, when such is the case, A WP2 is out of action. 

However, when the LAW moves tot.he position where roller 1 falls into the notch in the righthand hand, AWP2 acts in two ways: (1) It engages the RAW and moves it forward one space; 

(2) A WP2 is connected to the back-dog bar by a lever, and the arrangement is such that the 

action of the hack dog is neutralized when roller 1 of AWP2 has dropped into the notch. This 

allows the cipher-'11.·bucl pawl that is temporarily associated with the back dog to engage its 

cipher wheel and mo,·e it forward one space. The roller of the A WP is so pla.cecl that when 

the peripheral letter I on the LAW is at the bench mark, A WP2 engages the R.A. W, and the 

cipher-wheel pawl that is tP.mporarily associated with the back dog engages its cipher wheel. 

Since the notch in the right-hand band on LAW must present itself to roller 1 om·e per complete 

revolution of LAW, and since this will he.ppen once per 26 depressions on the keyboard, it 

follows that thP ripher-whee>l pawl tho.t is temporarily asso<'iated with the dog on thu 1·ear bar 

will step the a.ssorintcd cipher wheel forward one step per 26 depressions on the keyboard. 

AWP3 acts both upon the RAW and the front-dog bar. On the right-hand side of the 

A WP3 there is a roller (roller 2) similar to that on A WP2. Roller 2 rests upon the smooth 

band of the RAW, except when the RAW is so set that its pe1ipheral letter I is at the bench 

mark. At this point roller 2 drops into the notch and allows A WP3 to enge.go the RAW and 

also neutralize tht~ action of the front dogs, allowing the two cipher-wheel pawls temporarily 

associated with these dogs to engage the proper two cipher wheels. 
6. Detailed study of a particular dog setting.-The consequences of the forP.going arrangement of dogi!, pawls, and ratchets can now be made <'!leo.r. Suppose the two front dogs are. set 

into positions B and D, and the rear dog into position V, as shO\vn in figure 1. Ta.king tho 

elements of tho dog-a.l'tion setting BDV in alphabetical order, B men.ns that, in general, CW2 

will not ho allowed to step forward; D means that CW4 n.1110 wiJJ not he allowed to l-ltep forward. 

Hence, there remain CW1, CW3, and CW5 free to step forwa1·d so far as the front dogs a.re 

concerned. But since the dog on the rco.r bar is set at V, and this will affect CW1, it follows 

that only CW3 and CW5 are free to step f01wa.rd for each depression of a key, so far as the 

dogs on both front and rear bars are concerned. Further, whenever the dog on the rear bn.r, 

now set at V, is neutralized by the o.c.·tion of roller 1 and AWP2, the result will be that CWI 

will be allowed to step forward; and whenever the dogs on tho front bar, now at B and D, are 

simultaneously neutralized by the action of roller 2 and AWP3, t.hen CW2 and CW4 will be allowed to step forward. 

The foregoing explanation of dog action and wheel displac!ements will now be set forth in 

connection \Vith detailed observations on the actual sequence of events and results. It should 

be obsel'Ved at this point that th('I wheels 1110.y be inserted in the machine in either a diroct 01· a 

reversed position, the two cases yielding entirely different results. As a consequence, any 

single wheel may be made to serve the part of two if the reversed posit.ion be included. The 

lotter d or r will be written alter the number of the wheel (as below) to distinguish between 

these two cases. Thus CWld and CWlr will mean cipher wheel 1 in the direct and reversed 

positions respectively. It should also be observed in this connection that the letters on the 

periphery of a direct wheel pl'Ogress in reverse order as the wheel moves forward whereas the 

progression is normal for a reversed wheel. Let us suppose that the wheels are brought to the following initial setting: 

LAW RAW CW1d CW2d CW3d CW4d CW5d 

H I A A A A A 

Let the dog action be BDV. The foilowing represent the successive settings of the wheels as 

the keys of the keyboard are depressed: 

';:! • 

"" 0 

---lat 

2d 

Cl .s3 h ~== ,!!lc:I << ..:I p: 

1 H I 

2 GH 

3 FH 

4 EH 

5 DH 

6 CH 

7 BH 

8 AH 

9 ZH 

10 YH 

11 XH 

12 WH 

13 VH 

14 UH 

15 TH 

16 SH 

17 RH 

18 QH 

19 PH 

20 0 H 

21 NH 

22 MH 

2a LH 

24 KH 

25 J H 

26 I H 

27 HG 

28 GG 

29 FG 

30 EG 

31 DG 

32 CG 

33 BG 

34 AG 

35 ZG 

36 YG 

37 XG 

38 WG 

39 VG 

40 UG 

41 TG 

42 S G 

43 RG 

44 Q G 

45 PG 

46 0 G 

47 NG 

48 II G 

49 LG 

ao KG 

61 JG 

52 I G 

5 

'fARLE 1.-SuccessirJe settings of all wheels 

[Initial aettiup;, HI -AAAAA · dog artion, BDVJ I 

- "'~ ... .,, ! ~==~a:~ I t.i tJ t.i 0 t.> 

A A A A A 

AZ Z Z Z 

AZYZY 

AZXZX 

AZWZW 

AZVZV 

AZUZU 

AZTZT 

AZ S ZS 

AZRZR 

AZ Q Z Q 

AZPZP 

AZ 0 Z 0 

AZ NZ N 

A Z 14 Z M 

AZLZL 

AZKZK 

AZ J Z J 

AZIZ I 

AZHZH 

AZGZG 

AZ F Z F 

AZ E Z E 

AZ DZ D 

AZ CZ C 

AZBZB 

ZZAZA 

zzzzz 

z z y z y 

zzxzx 

zzwzw 

z z v z v 

zzuzu 

Z Z T Z T 

zzszs 

ZZRZR 

z z Q z Q 

ZZPZP 

z z 0 z 0 

ZZNZN 

Z Z II Z M 

ZZLZL 

ZZKZK 

ZZJZJ 

Z Z I Z I 

ZZHZH 

ZZGZG 

ZZFZF 

ZZEZE 

ZZDZD 

z z c z c 

ZZBZB 

! 

a 

53 

.. 

79 

05 

31 

57 

83 

4th 

5th 1 

8th 1 

7th 1 

8th 1 

9th 2 09 

10th 2 35 

11th 2 

12th 2 

13th 3 

14th 3 

15th 3 

16th 3 

17th 

18th 

19th 

20th 

21st 

22d 

23d 

61 

87 

13 

39 

65 

91 

417 

443 

469 

495 

521 

547 

573 

24th 

25th 

28th 

599 

625 

626 

7 

8 

9 

630 

1 

2 

3 

4 

5 

8 

7 

8 

9 

840 

1 

2 

3 

4 

5 

6 

7 

8 

9 

650 

1 

2 

3 

I I 

I 

I ~ I 

I 

~it:!:;;[!:;:;: ... j~ ot:Goo tJ 

HF Y ZAZA .. ..... HE XZAZA 

HD WZAZA 

HC VZAZA 

HB UZAZA 

HA I T ZAZA 

I HZ S ZAZA 

Hy RZAZA 

HX QZAZA 

H 'R PZAZA 

HV OZ AZ A 

HU NZAZA 

HT!llZAZA 

HS LZAZA 

HRiKZAZA 

HQ J ZAZA 

HP I ZAZA 

H 0 HZAZA 

HN GZAZA 

HM FZAZA 

HL EZAZA 

HK DZAZA 

HJ CZ AZ A 27th 

G J c z z z z 

F J CZYZY 

EJ czxzx 

DJ c z' z w 

c J c z v z v 

BJ czuzu 

AJ CZ T Z T 

z J czszs 

y J CZRZR 

XJ CZQZQ 

'J c z p z p 

VJ c z 0 z 0 I 

u J CZNZN 

T J C Z II Z II 

s J CZLZL 

RJ CZKZK 

QJ CZJZJ 

p J CZ I Z I 

0 J CZHZH 

NJ CZGZG 

II J CZFZF 

L J CZEZE 

KJ CZDZD 

J J c z c z c 

I J CZBZB 

HI BZAZA 28th 

GH BYZYZ 

FH BYYYY 

--· Cl 

o .. -.! 

~E! 

::!Cl 

::.::i 

== --= == < ;~;;; ..:I=: tJt.itJOt.; 

4 EH BYXYX 

5 DH'BYWYW 

6 CH BYVYV 

7 BH BYUYU 

8 AH BY TY T 

9 ZH BYS Y S 

660 YH BYRYR 

1 XH BYQYQ 

2 WH By p y p 

3 VH BY 0 Y 0 

4 UH BYNYN 

5 TH BYllYll 

6 SH BY LY L 

7 IR H BYKYK 

8 Q H By J y J 

9 pH B Y I Y I 

670 0 H BYHYH 

1 NH BYGYG 

2 II H BYFYF 

3 LH BYEYE 

4: KH BYD YD 

5 J H BY CY C 

6 I H BY BY B 

7 HG AYAYA 

8 GG AYZYZ 

D FG AYYYY 

680 EG AYXYX 

1 DG AYWYW 

2 CG AYVYV 

3 BG AYUYU 

4 AG A YT YT 

5 ZG A Y SYS 

6 YG AYRYR 

7 XG A y Q y Q 

8 WGIAYPYP 

9 VG A Y 0 Y 0 

890 UG AYNYN 

1 T G A Y II Y II 

2 S G AYLYL 

3 RG AYKYK 

4: QG A y J y J 

5 PG A YI YI 

8 0 G AYHYH 

7 NG AYGYG 

8 II G A Y FY F 

9 LG AYE YE 

700 KG AYDYD 

1 JG A Y CY C 

2 I G AYBYB 

3 HF ZYAYA 

4: GF ZYZYZ 

5 FF ZYYYY 

8 

. In figure 2 the lett~ indicated are the letters at the bench mark. The notch in the LA. W 

which controls the motion of the 11 26" wheel comes into play when the letters opposite the 

bench mark pass from I to H. Therefore, for each line of the diagram the "26" wheel remains 

stationary. The 11 1" wheels move, of course, from column to column but remain fixed in any 

~le column. The RAW is so constructed that no matter what the position of LA. W RAW 

will move from I to H after one depression instead of after. 26 depressions, as is the cas~ in all 

other letters on RAW. The movement of RAW from I to H induces the movement of the 

"650" wheels. For the block of 650 outlined, the motion then is as follows: The 11 1 " wheel 

moves. for e"'?h letter; the 11 26" wheel moves in passing from line to line; the 11 650" wheels 

move in p8.SS1ng from block to block. 

The fi~. illustrates the most general complete block. A message may, of course start 

anywhere within the block.1 ' 

The diagramm~tic scheme of the motions of the wheels enables one to find readily the 

length of cycle reqmred for the wheels to return to their original relative setting. 

Since the "650" wheels move before the "26" wheel has made a complete revolution the 

"650" wheels and. the "26" wheel will be in the same relative setting after 1 +J's revolutio:..S of 

the 11

26" wheels, 1.e., on line ~8. The 11 1 " wheels must move one space to catch up to the 

other wheels. The letters which come from the same relative settings are therefore 27 lines 

of 26 apart and one column over to the right; that is, the length of this cyclic period is 703 

letters [(27X26)+1J. 

The impo~to.nce of a thorough_ understanding of figure 2 is, that if it is possible to determine 

~ti~ when in the course of enc1pherment of a mes!ilage the "650" wheels were displaced "t 

~ po881ble to determine the exact initial settings of LAW and RAW (save for the two exc~;. tional cases referred tO in footnote 1 below). · 

7. Study o~ Cl'J'ptographic a?tion.-We may now proceed with a discussion of an actual 

example of enc1pherment. Let it be assumed for t}Jis example that the initial setting is as 

follows: 

{ ~ce-c~-c Permutation of wheels: j ~ ~ ~ B ~ ~ ~~~~~~~~-

Alignment of wheels: A A A A A A A 

Dog action: BDV 

Switch lever setting: "CODE" 

[The above aetting ia that depicted in figure 1 ] 

F1ouu 3 

The machine is ready for operation at the instant the current is tumed on. Let it be 

assumed that the message begins 

RELIA BLERE PORTS INDIC ATETH ATJAP ANESE 

FORCE SHAVE ADVAN CEDON CHINE SEFOR TIFIC 

ATION SINTH EWOOS UNGAR EA ... 1 There are two exceptiona to the aituation depicted in figure 2. If the control wheela were aet originally 

at HH, the first block would contain 651 lettera, although thereafter the motion would be as in figure 2 If 

the control wheela were aet origWally at BI (in which fJ ia not H), the "650" wheels would move after the.firat 

letter waa enciphered and thereafter the motion would conform to figure 2. 

9 

When the encipherer depresses the key R, two switches are closed. One of these controls the 

printing circuit and the other the mechanical. device which steps the wheels forward. In the 

printing circuit, the current leaves the contact corresponding to key R, passes to the letter R 

on the RFS · 1 from R on the RFS it goes through the cipher wheels to E on the Ll~S; from E on 

the LFS th~ circuit goes to the solenoid corresponding to E in the back of the printer where it 

is translated into a mccl1anical action, and the letter Eis printed. 

While the cipher letter is being printed, the magnet controlling the mechanical device is 

energized and causes the motor to move the ratchet cradle downward and back to its original 

position. When the cradle has reached its lowest point, CWP3, CWP5, and A WPl engage 

their respective wheels and step them forward on the upward thrust. The machine is now in 

position to encipher the second letter of the message. The setting for the second letter will be 

ZA-AAZAZ. The enciphering operation is the same for the following 18 letters. However, at 

the encipherment of the nineteenth letter, the LAW will be so set that I is at the bench mark, 

and the roller of AWP2 will fall into the notch on the periphery, causing the RAW to move 

forward. The action of the back dog will be neutralized during this instant, and the cipher 

wheel pawl governed by it will be permitted to act. Since the ho.ck dog is set at V, CWPl will 

be liberated and CWl will move forward one step accompanied by CW3 and CW5. At tl1e 

,,.,w, of the encipherment of this letter the setting is 

S! ~BB~~ HZ ZAHAH 

F1oua:m 4: 

For the next 26 letters, CW3 and CW5 will move forward continuously and, with theenci· 

pherment of the forty-fifth letter, the action described immediately above will be duplicated. 

From this point on, the RAW and CWl will move forward one step with each 26 letters. 

However, after 17X26+18 letters have been enciphered from the initial setting, the alignment 

of the wheels will have become 

s~ ~BB~~ JJ JAJAJ 

F1GUBll 5 

•In the earlier model of the machine when the awltch ia at the "direct" or enciphering poaition, the keyboard is connect.eel to the LFB. In the 1932 model, however, the reverae of thia ia true. The current flowa from 

the key contact to the RFB, through the cipher wheels to the LFB, and from the LFB to the proper aolenoid 

of the printer. For the RFS, LFB, and wiring of the wheels, see pagea 12 and 13. 
10 

When the key corresponding to the next plain-text letter is depressed, the CWP3, CWP5, and 

AWPl will engage their respective wheels o.nd move them forward to the setting 

j! 8~8~~ IJ JAIAI 

FIGURll 6 

On the next letter, the roller of A WP2 will fall into the notch of LA. W and will cause RA. W 

and CW! to move forward with CW3 and CW5. The setting is 

j! B~B~~ HI I AH AH 

F!ouu 7 

Now for the next letter the roller of A.WP3 will fall into the notch of RAW and the CWP2 

and CWP4 will be liberated so that they may engage CW2 and CW 4. The A WP3 will also 

engage the RAW, moving it forward along with cipher wheels 21 31 4, and 51 and the LAW giving 

== ...:irr: :g~~!;g PS .......... u~ 

GH IZGZG 

F1ouu 8 

for the encipherment of the next letter. Now CW2 and CW5 will not move forward again until 

the RAW has been rotated to I. It will be noted in the case considered above, that the 

RAW on reaching J moves forward two spaces for one revolution of the LAW. This particular 

setting of the RAW is tho only one which allows such a motion. 

8. Action of possible dog settings.-The displacements of cipher wheels in the example thus 

far studied corresponded to those for a BDV setting of the dogs. What would happen for other 

settings? The following table shows the displacements for each of the 50 possible settings of 

the three dogs: 

11 

TABLE IL-Showing cipher-wheel di11placemcnl.s for au dog settings 

Moving per depre&- Moving 1111r 26 depres- MO\"IDll per 000 depres-1 Setting or SloD sl.ons sinus 

dop 1 2 3 4 5 1 2 3 4 5 1 2 3 4 5 

ABV 3 4 5 1 1 2 I 

" 3 4: 5 2 1 2 

x 4: 5 3 1 2 

y 3 5 4: 1 2 

z 3 4: 5 1 2 

ACY 2 4 5 1 1 a 

" 4: 5 2 1 a 

x 2 4: 5 3 1 3 

y 2 5 4: 1 3 

z 2 4: 5 1 3 

MJV 2 3 5 1 1 4: 

" a 5 2 1 4: 

x 2 5 a 1 4: 

y 2 a 5 4: 1 4: 

z 2 a 5 1 4: 

AEV 2 a 4: 1 1 5 

" 8 4: 2 1 5 

x 2 4 3 1 5 

y 2 8 4 1 5 

z 2 3 4: 5 1 5 

BCV 4: 5 1 2 3 

" 1 4: 5 2 2 3 

J: 1 4 5 3 2 3 

y 1 5 4 2 3 

z 1 4 5 2 3 

BDV 3 5 1 2 4 

" 1 8 5 2 2 4 

x 1 5 3 2 4 

y 1 3 5 4 2 4 

z 1 3 5 2 4 

BEV 3 4 1 2 5 

" 1 3 4 2 2 5 

x 1 4: 3 2 5 

y 1 3 4 2 5 

z 1 3 4: 5 2 5 

CDV 2 5 1 3 4 

" 1 5 2 3 4: 

x 1 2 5 a 3 4: 

y 1 2 5 4 3 4: 

z 1 2 5 3 4 

CEV 2 4 1 3 5 

w 1 4 2 3 5 

x 1 2 4 3 3 5 

y 1 2 4: a 5 

z 1 2 4 5 a 5 

DEV 2 3 1 4 5 

w 1 3 2 4 5 

x 1 2 3 4 5 

y 1 2 a 4 4 5 

z 1 2 3 5 4: 5 

Not all the settings shown in table II, however, were used m the test messages, as will 

be noted from a careful reo.ding of the instructions set forth in Appendix I. Informally, it 

was stated that a limited number was employed, but the ho.sic principles followed in tbe selection 

of settings actually used were not disclosed. 
SECTION III 

CRYPTOGRAPHIC ANALYSIS 01' THE MACHINE 

Pl.rllll'8pb Preliminary preparation ___ --- __ _ __ _ _ _ _ _ ____ _ 9 

Claaaifioation of messages____________________ 10 

Pmqnpb 

Index of monoalphabeticity__________________ 14 

Conversion of "V" measages_________________ 11 

Application to Serial No. 210 ________ .,_______ 15 

Relation between alphabets in different blocks_ 16 

General observations on "V" messages________ 12 R.dsum6----------------------------------- 17 Application message_________________________________ of principles to a suspected "V" 13 

9. Preliminary preparation.-The first step in the analysis is, of course, to record the exact 

wiring of the LFS, RFS, and the various cipher wheels, so that the mi~ed-alphabet sequences 

may be transcribed upon sliding strips which may be employed in tracing through the exact 

paths followed by the electric current in encipherment or decipherment. 1 The wiring of the 

six cipher wheels was kindly furnished by the Navy Code and Signal Section, to eliminate the 

small amount of labor that would be involved in this determination. The wiring of the LFS 

and the RFS was determined in collaboration with a representative of the Navy Code and Signal 

Section, with a simple testing circuit including a voltmeter. The wiring of the foregoing elements is as shown below: 

Cipher wheel ld 

Right A B C D E F G H I J K L M N 0 P Q R S T U V W X Y Z 

Left NBIVLAPJWRUFDGSECHOQZTMYXK 

Cipher wheel 2d 

Right A B C D E F G H I J K L M N 0 P Q R S T U V W X Y Z 

Left KRVFDLWICXPAYNMTBJZOHSEGUQ 

Cipher wheel 3d 

R~t ABCDEFGHIJKLMNOPQRSTUVWXYZ 

Left RVUQNJSDXIALOKMFECYBZWPHTG 

Cipher wheel 4d 

Right A B C D E F G H I J K L M N 0 P Q R S T U V W X Y Z 

Left C S X T M Q N L Y 0 E I F W A H P B G R U K J D Z V 

Cipher wheel 5d 

R~t ABCDEFGHIJKLMNOPQRSTUVWXYZ 

Left J 0 R X Q E G I S C F N A U Z M H V Y L K D B T W P 

• See Section III of Part I. 

(12) 

13 

Cipher wheel 6d 

Right ABCDEFGHIJKLMNOPQRSTUVWXYZ 

Left CGKUPFWOSXQEZJIBLHTRDNAMVY 

Bench 

mark RFS (right fixed sequence) 

l 

YLVRZXCPFOIQAMJBNSEKDGHTUW 

Bench 

mark LFS Oeft fixed sequence) 

l 

TEGDNSXUPQYVHAMBKRFJLZIWOC 

FIGU:U 9 

The foregoing alphabets of the cipher wheels, for purposes of analysis, must be converted 

into their reciprocals (see par. 8 of Part I), and are then as follows: 

NALi 

MALi 

NA.I.,. 

MALa 

NA.La 

MA.La 

ABCDEFGHIJKLMNOPQRSTUVWXYZ 

FBQMPLNRCHZEWASGTJOVKDIYXU 

ABCDEFGHIJKLMNOPQRSTUVWXYZ 

LQIEWDXUHRAFONTKZBVPYCGJMS 

ABCDEFGHIJKLMNOPQRSTUVWXYZ 

KTRHQPZXJFNLOEMWDAGYCBVISU 

NALa ABCDEFGHIJKLMNOPQRSTUVWXYZ 

MAL. ORAXKMSPLWVHEGJQFTBDUZNCIY 

NA.La ABCDEFGHIJKLMNOPQRSTUVWXYZ 

MALa MWJVFKGQHAUTPLBZECIXNRYDSO 

NAL. ABCDEFGHIJKLMNOPQRSTUVWXYZ 

MAL. WPAULFBRONCQXVHEKTISDYGJZM 

FIGUBll 10 

The foregoing alphabets are now transcribed upon sliding strips and made ready for use. 

10. Ola1Biflcation of me11ages.-In what follows we shall refer to and classify messages 

according to the final letter of the dog-action setting, V, W, X, Y, or Z. By a "V" message, for 

uample, we mean one in which the dog-action setting is 919-V; by a "Z" message we mean one 

in which the setting is (Ji{J1Z. 

In respect to the foregoing classification, the types of messages which lend themselves most 

r8adny to study belong to the "V" or "Z" classes, for reasons which will now be explained. 

We first take up "V" messages. · 

· 11. Conversion of "V" mes1ages.-Suppose that the cipher wheel in position l1 has been 

determined, together with its initial setting and motion. It is then possible to convert the 

message into a new cipher from which the e1fect of the LFS and the first cipher wheel has been 

removed. In fact, if the motion and identity of any number of consecutive cipher wheels begin1 We number the wheel positions from left to right. 

'11838--811--2 
14 

Ding from the left have been completely determined, the effect of the LFS and these wheels 

may be removed from the particular message so that only the remaining cipher wheels have any 

effect in producing the converted messo.gc. 

To illustrate, suppose it is known that a. particular cipher letter Q representing EP was obtained 

with CWld set at Fin position 1. The permutation and settings of the remaining wheels are 

temporarily of no consequence. Then, since Q on the LFS is opposite position 10 on BSl, the 

current must have come from the tenth letter on MALl, viz, S. The S of NALl is opposite 

position 14 on BS2, and it may therefore be concluded that the current producing the letter Q 

in question passed through the fourteenth conte.ct of the second bakelite separator. This 

information may be diagrammatically represented as follows: 

BS2.------- 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 

NALL----- F G H I J K L II N 0 p Q R § T u v w :x: y z A B c D E 

' I 

MALL _____ L N R c H z E w A G T J 0 v K D I y x u F B Q II p 

l 

BBl-------- 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 

LFB-------- T E G D N s x u P i Y V H A II B K R F J L Z I W O C 

F1ouu 11 

H the successive contacts of BS2 were identified by means of a normal sequolice, position 

14 would correspond to letter N, and the current could be said to have come from Non BS2. 

In other words, the action of the last four cipher wheels, i.e., those in positions 2, 3, 4, and 5, 

may be considered to have resulted in a replacement of E., by N0 • 

If the setting of the second wheel were also known, the conversion, i.e., the elimination of 

the cipher wheel in position 2, could be carried over to BS3. 

Of course, the foregoing applies to a single letter only. But, if the left-end wheels were 

known not only as to identity and position but also as to motion, then the motion could be 

taken account of and the conversion carried through for the entire message. 

Returning then to a consideration of a "V" motion in connection with the foregoing reasoning; suppose it possible to determine the first cipher wheel and its initial setting. Then, since 

a "V" motion means that the cipher wheel in position 1 steps forward once every 26 letters, a 

complete conversion to BS2 can be carried out. Moreover, no difficulty can arise in connection 

with the exact place in the message where this cipher wheel steps forward, because the initial 

setting of the first wheel gives the initial setting of the left control wheel and hence determines 

just where each line of 26 letters begins.1 

If the converted message is written out in lines of 26 letters, then in each column we have 

letters which have been enciphered with the last four cipher wheels in exactly the Mme position; 

hence all letters within the same column belong lio the same monoalphabet. It is thus seen 

that a "V" message whose first wheel is known, when correctly converted, becomes a polyalphabetic substitution cipher of 26 alpha.bets. The latter may be recognized or detected by 

the usual tests based upon repetitions and the normo.l appearance of monoalphabetic distributions. 

12. General observations on 11V" me11ages.-A method of attack is thus indicated. If a 

message is suspected to be in a "V" motion, a conversion can be carried through for every possible 

wheel in every possible bench-mark setting. The co1'7'ICI assumption 'Will yield a message arranged. 

in 16 al.phabets, which may be recognized by the usual external phenomena. Since there are 

six wheels, each of which may assume two positions and 26 settings on _each wheel, the total 

a See Appendix I, instructions issued with Hebern, par. 2 (c) (2). 

15 

number of trials necessary for any single message is 6X2X26=312. For each of these trials the 

converted message must he .tested to determine whether or not it is now in the form of a set of 

26 monoalphabets from left to right in the successive columns. 

Naturally, for such tests the length of the message is very important, for unless there are 

enough elements in a frequency distribution it is very difficult to tell whether we are dealing 

with a random or a polyalphabetic distribution. Consequently, we should make our tests 

first upon the longest message we can find and then, if no "V" message is indicated, try the next 

longest message, and so on. Accordingly, Serial No. 183, with 1,420 letters, the longest in the 

set of 110 cipher messages, was the first one selected for experiment The results were negative, 

i.e., the tests indicated that the message was not a "V" message. Since the steps followed are 

the same as in a successful test, the details in connection with this negative experiment can be 

omitted in favor of those in connection with a successful experiment. 

13. Application of principles to a suspeo'8d 11V" me11age.-Consider the second longest 

message, Serial No. 210, with 1,325 letters. 

This message begins as follows: 

OCRYP HWKON QCPJI MUNDK GZLYY JLFZG 

Let us assume that CWld occupies position 1. Let us further assume that the initial 

bench-mark setting for CWl is A, so that 19 letters will be enciphered before CWl moves. 

Then the conversion equivalents (to eliminate LFS and CWl) for the first line of cipher text 

are obtained by setting MAL1-NAL1-BS2 against the LFS so that A on NALl is opposite T 

of LFS (the initial or bench-mark setting). 

The diagram of sliding-strip alphabets for the conversion is as follows: 

BS2 ______ A BCD EFG HI J KL MN 0 P QR STU V W X Y Z 

{

NALl ____ A B C D E F G H I J K L M N 0 P QR S TU V W X Y Z 

ldA.Ll ____ F B Q 11 PL N RC HZ EWA SGT J 0 V K DI Y XU 

LFS ______ T E G D N S X U P Q Y V H A II B K R F J L Z I W 0 C 

CWl 

F1ouu 12 

By tracing en.ch cipher letter back from LFS to BS2 on the foregoing diagram, we get the 

following conversion equivalents: 

1 2 a ~ & a ' s o ro u a o u u H u a " 

Cipber------------------- 0 C R Y P H W K 0 N Q C P J I M U N D 

Conversion equivalents ____ X U J Z C W Y T X P H U C V I S R P M 

F10UB111 l8 

To obtain the equivalents for the second line of cipher text, we must now shift MALl-NALl 

one interval forward, to take into account the fact that CWl has stepped forward one interval. 

BS2 remains stationary. The die.gram of alphabets for this conversion is as follows: 

BS2 ______ A BCD EFG HI J KL 11 N 0 P QR STU V W X Y Z 

{

NALL ___ Z A B C D E F G H I J K L II N 0 P Q R S T U V W X Y 

MALL ___ U F B Q II P L N R C H Z E W A S G T J 0 V K D I Y X 

J..FS ______ T E GD NS XU P Q Y V HA II BK RF J L Z I W 0 C 

CWl 

FIGUBll 14 
16 

The conversion equivalents for the second line are then as follows: 

123<(687891011 

Cipher ____________ ------- K G Z L Y Y J L F Z G 

Conversion equivalents ____ H C L W I I P W K L C 

FIGll'Bll IS 

To obtain the equivalents for the third line of cipher text, NALi-MALi is displaced one 

more interval (forward) to the right, and so on. 

· · 14. Inda of monoalpha.beti.oity.-When this has been done for the whole message, the 

columns of conversion equivalents are examined from the point of view of their possible monoalphabeticity. Of course, one could study the columns for repetitions of single letters within 

oolumns, as well ··as for repetitions of digraphs, trigraphs, and polygraphs. But this would 

require much time and the compilation of m&DY frequency distributions. A better way is to 

try to establish. monoalphabeticity by statistical methods. For this purpose we me.y set up, 

theoretically, or by calculation on actual. plain text, an index of monoalphabeticity with which 

a calculation for unknown text should agree within limits of variation due to chance. The plain 

text should be arranged in horizontal lines and the frequency distributions for individual columns 

then prepared; :in order to have accurate results, the number of columns and the number of 

mements in each column should be fairly large. 

In each distribution the sums of the squares of the frequencies should be found. The 

index itself and the limits of variation should then be obtained by :finding the mean and standard 

deviation for all frequency distributions. For a monoalphabet of T letters the mean of the sum 

of the squ~ of the absolute frequencies is, theoretically, given by 8"=0.066 7'2+0.934 T. (For 

a more complete statistical discussion of monoa.lphabeticity, see S. Kullback, 8tati8tical Methods 

'" OryptaiMlyria, Technical Pliblication of the Signal Intelligence Section, 1934.) 

To apply these results to the problem in hand however, a slight modification is necessary. 

The foregoing index applies to the case where a frequency distribution contains T letters and 

is llridl71 m.onoalphabetic. In our problem, however, we can never expect these two conditions 

to obtain, because, firstly, at a maximum. there can be only 25 letters in each monoalphabet 

. (for after 25 lines have been enciphered. the "650" wheels move and consequently the twentymth letter in the column belongs to a different alphabet than do the first 25 letters); secondly, 

we do not know where this "650" break occurs in the message. It may occur after the very 

first line, or after the second, third . • .. line. Consequently, it can easily happen that in taking 

only 26 let~. per column we may be assimilating 10 letters of one monoalphabet with 16 of 

another, or 11 of one and 15 of another, and so on, so that the inde."t for pure monoalphabeticity 

would never be closely approximated. We may, however, be sure of one thing: If we should 

11 

take columns of 36 letters, the number of letters that ma.y fe.ll in the respective alphabets can 

be only as follows: 

TABLJll III 

First Seeond Third caae First Seaond Third 

Cme alphabet alphabet alphabet alphabet alphabet alphabet 

1 0 25 11 14 13 23 0 

2 1 25 10 15 H 22 0 

3 2 25 9 16 15 21 0 

4 3 25 8 17 16 20 0 

5 4 25 7 18 17 19 0 

6 s 25 6 u 18 18 0 

7 6 25 5 20 19 17 0 

8 7 25 4 21 20 16 0 

9 8 25 3 22 21 15 0 

10 9 25 2 23 22 14 . 0 

11" 10 25 1 24 23 13 0 

12 11 25 0 25 24 12 0 

13 12 24 0 26 25 11 o· 

The worst possible~ for our p~rposes are those in which three difterent aiphabets enter. 

The best possible cases are those in which only two alphabets en~. . . 

We may, however, assume theoretically that th~e ten eases m which. t?~ 36 letters fall 

into three different alphabets would not distort the index for monoalphabetic1ty v~ m~ch, 

since the letters falling in one alphabet (25) are much more numerous than those falling mto 

each of the two other alphabets. In fact, the index may perhaps not be disto~d any more 

in those cases than in the ones where the distribution is 18 in e~ alphabet! or 17 m one and ~9 in the other or 16 in one and 20 in the other. Consequently, if we consider that the case m 

which the I~tters are divided equBlly between two alphabets is perhaps the worst for our purposes, even then we have only bialphe.beticity to deal with. . . . 

Our problem is therefore now one not of strict monoe.lp~abetimty but of app~~ate 

bialphabeticity. What is the index for tho.t? Actual calculati~ns upon several dJStnbutions 

of sets of 36 letters in two dift'erent alphabets gave an average index of 94 for the sum of the 

squares of occurrences of letters for the case where the 36 letters were evenly divided between 

two alphabets. . · · 'bl 

For our purposes, therefore, we may assume an index of 94 to be the IllllllDlUm pemllSSl e 

in studying columns of 36 letters. . . 15. Application to Serial Bo. 910.-When the catculation~ perte.ining to thi~ mdex of 

bialphabeticity were applied to the various conversions of Sena.I No. 210, ~rding. ~ the 

different cipher wheels, the calculation applicable to the case ":hei;e CW2r was m po8ltio~ 1, 

with Hat the bench-mark setting gave, for the first five colwμns, mdices that seemed conclUSlve. 

Thus: 

[Index 112] 

FIGUBB 16.-Diatribution for column I 

and similar results for the columns 2, 3, 4, and 5. 
18 

. The message WBB accordingly completely converted and transcribed. In this transcription we may place the very first letter of the message under H of the LAW sequence, since under 

the specifications it is known that the initial setting of LAW and the cipher wheel in pasition 

1 must coincide. Note the repetitions that appear: 

Fxauu 17.-Berial no. 110, conW1Tted 

FROM: NAVAL STATION GUAM 

TO: OPNAV 3 MARCH. 1932 

INDICATOR: 1003 EHHBE VGBKL 

H 2 a t 11 • 7 a 11 10 11 12 1a 1t 111 1e 11 18 111 211 21 22 23 11 26 211 GFEDCBAZYXWVUTSRQPONMLKJI 

1 ~FGBRPSYKCNFRVHTXCEYWJUBBV 9 2 WHVMBNHOSURJRQSZFDIJUDUKYH 10 3 P V B I X P I Y 0 X N Y B A S 0 Z I P W B Y C Z I H 11 4 IFBIKLCZQRRFOKAMMESTJDCJBG 12 5 VCEMRNJPOORFQCKSDEMMVLBQ!...B 13 6 VGUMLBMXAANNYCVTNAFNBLKMMR 14 7 PFRMRTLCWKOBCEUSHPEIBXSMGS 15 8 DSFWBPSUNPKHMNWPKLNWENALIQ 16 g KGEEANJYKJKARDSGNSRUWEQUHR 17 10 PCHEAXLZLIVBOCUISDNYCZTXGI 18 11 JCPHASPOOAUQLGV~UICGGJYR 19 12 QFIMLBMBXWEFFGAYYDKTBYTXWB 20 13 IGUMZNJKEWPHFEVCSQGTBXUXMQ 21 14 PGUDIXQYZVLLBCBJXRUUOQBZFS 22 15 DBQMIKZEZOOBBXAAFWNBCQIXBV 23 16 GFEMAXLUNJPKUUFGDBKUSGQLSV 24 17 IMTUFNXVLAORLXCIXOWTBEBXOD 25 18 GGFERPRPLJUARWKIJAEI1L!SKJJ 26 19 PYFHFDSONMTBOGHSVTMECYWWHR 1 20 CCUBIFDRPWAGHJSNWWNTCRIMHU 2 21 LHTNBBWEOLKLIWA.Q....LQJIWJLYAD 3 22 GCENIMVVAIUAHTAJVJHJPCQLHR 4 23 QBVRASPMSCKFMOAZDGVUIRTXMI 5 24 SHTSMLZFQWNWQWCEVGECBYTOBQ 6 25 L 7 

19 

FIGUBE 17.-Serial no. SlO, con11erted--Continued 

FROM: NAVAL STATION GUAM 3 MARCH. 1932 

TO: OPNAV 

INDICATOR: 1003 EHHBE VGBKL . -·-

1 2 3 4 5 8 7 8 11 10 11 12 13 14 15 Ill 17 18 111 20 21 22 28 24 211 28 

H G F E D C B A Z Y X W V U T S .R Q P 0 N M L K J I 

25 D F F R L G 0 D U Q N L J S C K W R Z L D Z K J S 7 

26 QVLLAPAZLKQGAIOPUVFWGUGVCK 8 

27 JOERUSFZGIJLNVMSQGPJLOMWCX 9 

28 NPEHXXBILCQQXISXMVOMZHXACK 10 

29 J Y P C D S D K Q R H A K I K U I H I A F R W T K I 11 

30 P G G Y 0 Z Q B 0 K S W B I C L U il S 0 J G 0 P I 12 

31 I T Y D L H S Q E N C Z P W S Q J H X Y F F W Y S ! 13 

32 .QJTVUFWSTPYGBZMFZK!._!PBXAIP 14 

33 UDPZOFEVNIZRMFRFBKKXHKPNUU 15 

34 TXCREZGIUNYCQWSCFEZSOQRUVA 16 

35 TVUVENDHTUOVRTSQMJKZRQWLHI 17 

36 TXCRUBPQAUNYXYICKODSOWGAWI 18 

37 BWRXJGSMLGCLAZSUI..JLEJLUMEDY 19 

38 AGKDAXWCJHHDDVMSUL.[MHZDYVP 20 

39 LWEUOBQMLGCLAZSUUGPMSUYCOG 21 

40 E N P C I B G I i'"8 Q Q X M K F !..JLE H P M M D D G 22 

41 OQEKNNGIUERJBQCISJIXZNDLYI 23 

42 WDGXZNSBOMQUPORFUVOZLUCDOL 24 

43 WDPCSCSOLGUXAZNAJEF.§_QFWLIK 25 - - - - 44 ATFDLNSJLNYGLECIIPBZCQPVBX 26 

45 WGLEWGEKXZNQREYMYJWTDKCAVI 1 

46 QVHUURHHOMNEHITCFEBLERNDQX 2 

47 XJHCRPFKVGNABASXPOAQMUAFGE 3 

48 TJTXXKzgGUBHBGKYBKBMOMWDII 4 

49 DTPCPCYSTIOZPJTQXEFUDUZWFK 5 - - 50 XJHCLXDQOJQDUWSISKPSORRWVI 6 

51 SK 7 

51 JPDBJRVESOXXPVAPOBTRFPO 7 

16. Relation between alphabets in different blocks.-It is clear that all the 51 letters in 

any one column of this converted cryptogram cannot belong to the same monoalphe.bet. At 

most, only 25 of them can do so. There may be two or three monoolphabe!'& involv:_ed ~ e~ 

column, depending upon where the "650" breaks occur. Thus, we may outline the distribution 

of the 51 letters as follows: 
20 

TABLll IV 

Number of letters Inc ... "8111" br-.t CIOOUnl OD 

111111 l'ln& Seoond Third J'onrth alphabet alphabet alphabet alphabet 

1 1, 26, 51 0 25 25 1 2 2, 27 1 25 25 0 3 3, 28 2 25 24: 0 4: 4, 29 3 25 23 0 5 5, 30 4: 25 22 0 6 6, 31 5 25 21 0 7 7, 32 6 25 20 0 8 8, 33 7 25 19 0 9 9, 34: 8 25 18 0 10 10, 35 9 25 17 0 11 11, 36 10 25 16 0 12 12, 37 11 25 15 0 13 13, 38 12 25 14: 0 14: 14:, 39 13 25 13 0 15 15, 4:0 14: 25 12 0 16 16, 41 15 25 11 0 17 17, 42 16 25 10 0 18 18, 43 17 25 9 0 19 19, 4:4: 18 25 8 0 20 20, 4:5 19 25 7 0 21 21, 4:6 20 25 6 0 22 22, 47 21 25 5 0 23 23, 48 22 25 4: 0 24 24, 4:9 23 25 3 0 25 25, 50 24: 25 2 0 

The question now arises· Can tell ti · break or breaks ? Why. we exac y or even approxunately where the u 650 II 

occur not use the repetitions of digra hs d · hs ~pie, note the long repetition on lines 37 and 39. obvio~sl an th~p as a test? For 

lino 38 or 39, nor, for that matter, on line 37 after the repetiu.!~ 111.G break ~ot occur ~n ~reak occur between lines 27 and 37' because the trigraph VMS is common io" th~ lin: can t~ e 

it looks as though the. break cannot occur between lines 26 and 28, because the digr~ hi~' :,:n: ~ thtwo 1;fues. .we may now study repetitions within the first half of the:~ g w e middle, lines 25-26, and try to localize the section where the break m b ' 

ay e. 

21 

By a careful study of what repetitions do appear, we are led to believe that the break occurs on 

line 25 and we may tentatively block out the message as shown herewith: 

Linea 1to25 

Linea 26 to 50 

Line 51 

I I 

FIOUBlll 18 

H the foregoing is correct, then the second letter of the message indicator (VgBKL) equals IP. 

(Refer, in this connection, to fig. 2.) 

The following two points in procedure should be carefully observed since they are of frequent 

application in the solution of the messages submitted. 

(1) The method of message indicators is essentially a polyalphabet of five alphabets. 

As a result, if the letter D in the indicator DMSCH enciphers F P• then tl.D. initial D in any other 

indicator will also represent F P· Similarly the determination of the equivalent of n.ny letter in a 

given indicator gives the equivalent of that same letter in the same position in any other indicator. 

· (2) The initia.l setting of a wheel determines whether it is to be inserted in a direct or 

reversed position. Hence, if it has once been determined that CWl origino.lly set at F is direct, 

then any other whetfl. set at F must also be direct. 

We have before us now not one but two independent problems, each involving 26 mixed 

alphabets, with but 25 letters in each alphabet. (The single letter at the beginning of the 

message and the last line can be of very little help.) The difficulties of reaching a solution 

under these circumstances require no further comment. 

H we could relate the two blocks in some way, perhaps the difficulties could he reduced. 

Why not take advantage of the "703 11 cycle mentioned in paragraph 6, if possible? 

Under the conditions of the system we know that after 703 letters have been enciphered 

the five cipher wheels have returned to their original positions relative to one another. The 

only change that has occurred in the setting of the machine between the 2d and the 705th 

letters is that the five cipher wheels have, as though they were permanently :fixed on the horimntal abaft, been displaced one step forward between the LFS and the RFS. This is equivalent to a forward step of ell the paths which the electric current traces out between the 

wheels. Consequently, if on the 2d depression a current enters the wheels from the RFS at 

Y, for example, and emerges from the wheels at Ton the LFS, on the 705th depression a cur-
22 

rent entering the wheels from the RFS at L (the letter that follows Y on the RFS) must emerge 

from the wheels at E (the letter that follows T) on the LFS. Since all letters 703 intervals 

apart are related in the same manner, we can use this fact to advantage. But, first we must 

take into account the fa.ct that our tra.nscribed message represents the conversion text, not 

the original cipher text. How are sequent letters of the LFS .related in the converted text? 

Obviously, tho method of establishing the conversion text indicates that if T, of the original 

text is replaced by Z in the conversion te.'tt, then E, of the original text will be replaced by A 

in the conversion text, since T is follo\Ved by E on the LFS, and Z is followed by A on the BS2 

sequence. (The reader should refer to the sliding strips with CW2r set at H in position 1.) 

Now refer to the second letter of the conversion text. It is F, and there are five of them 

in column 2 of the first block. Whatever IJ0 the letter F represents, it is the same for all five 

occurrences. Suppose for a moment that IJ=E. If the letter G which follows Fon the bakelite 

separator were the 705th letter of the converted text, its plain-text equivalent would be K, 

because K follows E on the LFS. But one can say even more. Since the conversion has 

produced monoalphabets in the columns of each block, any G, in the third column of the 

second block would have tbe so.me value as a Ge in position 705. There are two G's in this third 

column; if the assumption IJ=E is correct, then both of these letters must represent K. Such a 

result is not very likely o.s we would not expect K0 to occur two times in but 25 letters, hence 

the assumption IJ=E is not a good one. If IJ=T0 , then G=U0 , which is again unlikely. Thus, 

we examine all the possibilities and pick out these as most likely: 

F=00 F=Ap F=N0 F=Sp 

G= I 0 G=M., G=S0 G=Ep 

FIGUBB 19 

Enough has been indicated to show the procedure. Were the message long enough, say 

about 600 words, then there would be a.ve.ile.ble at least four blocks of "703" cycles for comparison and check on assumed values and there is hardly any doubt but that such a message 

could be solved within a reasonable length of time. One could tabulate the frequencies of A. 

in the first alphabet of block I; the frequencies of Ba in the second alphabet of block II; the 

frequencies of Ca in the third alphabet of block III; and so on. Suppose A. represents Ep; then 

B., C, . . • would represent l<p, D0, • • • in sequence. The weight assigned to a particular 

&ITangement is given by the product of the frequency of each cipher letter and its corresponding 

plain-text letter. If A. is assumed to represent T0, then a different set of pie.in-text letters and 

consequently a new total frequency would be obtained. The correct result will be theoretically 

determined as that one which yields the greatest weight. Letters obtained on this basis can 

then be inserted in the message. Here, however, we have only two such blocks; sufficient material is not at hand to permit of solution within a reasonable length of time. However, it must 

be stated that an earnest attempt was made to solve this cryptogram on the basis of the observable repetitions and the "703" phenomenon but without success. It seemed necessary to 

elaborate better methods of attack if the problem were to be solved at all. 

17. Msumi5.-Let us set down the difficulties in their broad outlines. First, there are 

those connected with the determination as to whether a given cryptogram is in a "V" motion. 

We saw that long messages are necessary for this determination and that the process may involve 

a maximum of 312 different trials, each quite lengthy. Next there come the difficulties of 

determining just where the "650" break occurs in a message that has been found ·to be in a "V" 

motion. Then there come the difficulties involved in attempts to solve a polyalphabetic substitution cipher of 26 nonrelated, random-mixed alphabets, or, at most, of two related sets of 

such alphabets. 

Let us see if we can eliminate some of the diffi.culti.ee of the first sort and facilitate the discovery of "V" messages. 

SECTION IV 

SYNOPTIC TABLES 

P1r111raph 

Conaideration of "W" messages __ ------------ 24 

Fir1t interval data, plain-test relationsbipe____ 25 

Parqr&ph 

"V" JD11111111P11 with known plain ten---------- 18 

First-interval data, cipher-text relationahips___ 19 

Application of first-interval data to a known "'V" Application of plain-text relatioD11hips to mes20 1&gea with kno"ft"D plain text---------------- 28 

21 Application of plain-text relatlonllbip1 to mes- 22 1&ge& with unknown plain tm.t_____________ 27 

1De1111&18--------------------------------- Statlstlcal atudy of "V" me1111&geB------------

B.6euln6----------------------------------- Application of Btatiatioal method to an unknown 

'Dlm''P (Serial No. 189)------------------ 28 

18. "V" meas1.1es with known. pla.in iut.--Suppose we make the ~roblem more easy by 

studying cert.a.in phenomena in a known "V" message with known plom text. Let the mes--

sage indicator (enciphered) be llCDDU. 

lP O F F I C E R C 0 N S I D E R E D F A I R L Y R E L 

10 C F R Y H G U Y G K I E N Z U N W W I B L I II R J Y 

~ IABLEATTACHEDTOYOUNGMARSHA 

00 TPCNIYVSXXQDDHOLMIFYVBMYGL 

3p L S H E A D Q U A R T E R S S T A T E S T H A T II A 

30 SMVSGBEDDHOYGARDDYVAHXATHK 

~ NCHURIANFORCESAREBEINGMOVE 

40 BUCOJQBHNNSQLZCYQDCINGXKKZ 

FIGUBll 20 

Let us now etudy certain plain-cipher relationships, in connection with ?ur sliding alphabets. Consider Hp in line 3P, column 3 and Hp in. lin~ 4P, colu~ ~; the pl~-text letters are 

the same, the cipher equivalents, different. This difference in c1~her eqmvalents for. two 

similar letters in the so.me column is occasioned solely 1 by the d1Splacement of the cip?er 

wheel in position 1, for the cipher wheels in positions 2 to 5 are in exactly the ~e setting 

in the two cases (since we are dealing with a known "V" message). The same 1B the case 

with the following pairs in the same lines: 

Sp (line 3P, column 14)==Aa 

S0 (line 4P, column 14)=Z, 

Ep (line 3P, column 19)==V, 

Ep (line 4P, column 19)=C. 

FIGUBll 21 

1 We &11UID.e the "850" break not to ooour in the firBt four lines of the meuage. 

(23) 
24 

. The qu~ii:on ari~es: C~ we find by experiment with the various cipher wheels (or their 

equivalent sli~~ strips) which wheel will produce the cipher equivalents indicated above, 

under the conditions noted there? Consider the case of the two plain-text letters Hin lines 

3P and 4P. '!he current corresponfilD:g to H., in both cases entered the cipher wheels from 

the tw~ty-third contact of the RFS; its po.th through the cipher wheels in positions 5 4 3 

and 2 lS _unlmown, but whatever it is, it left the cipher wheel in position 2 at exactly th~ s~m~ contac~ m b?~ cas_es, so that ~he contact on BS2 from which the current entered the cipher 

':heel m pom~on 1 ~ ~e same m both cases. Now consider what happens at the LFS and the 

mpher _wh~el m p0B1tion 1 (for both cases). The only reason the cipher equivalent for ae 

first .H IS different from that for the second H is that the cipher wheel in position 1 has advanced 

one mterval, and the current entering it from BS2 in the first instance emerges from the cipher 

wheel at Von the LFS, in the second instance, e.t C. 

We may take one of the ~di~ alphabets, say CWl, and place it in position 1, between 

the LFS and BS2; we may arbitrarily set CWld at A. We then locate Von the LFS and trace 

the path of the current from V, through NALl-MALl, to a contact on BS2, making note of 

the latter. We then advance CW~ one interval and repeat the operation, beginning with C 

on th~ ~S. I~ the contact ~ which the ~ond tracing leads (on BS2) is different from ·that fi? whic:h it led m. the first tracing, then obviously CWld cannot be the correct wheel for position 1 if the setting must be A. If CWld is correct it is not at the correct setting and we 

must try an?th~ s~tting. H, however, the two paths lead to the same contact on BS2, then 

we have an md1ce.tion that CWl may be the correct wheel for position 1. We say "may be" 

because, unless we c":11 get some further corroboration, this coincidence of exits from CWl 

for both cases ~ay Bllilply be accidental and not causal. Therefore, we should try another 

co.se. where the cipher letters are different for identical plain-text letters in the same two lines 

but m another column, e.g., SP in column 14, yielding A, in the first encipherment z in th~ second. We replace NALl-MALl in its A setting against LFS and BS2 and trac~ the pa.th 

of the current from A. on LFS to BS2; slide the o.lphabet one interval forward and trace the 

path from z. on~ to ~S2. _If a.gain the current leads to the same contact for 1both encipherments, ~ corroboration .19 ?btamed for CWl at the setting and position indicated; if not, then 

we con~der the first commdence to be purely accidental, and proceed with further tests of the 

same kind. 

These ~ests would require muclt time if carried out exactly as indicated above, but we may 

v_ery ~terially_ s??~ten the work b~ constructing certain synoptic tables which will, by inspection, nel~ pos.8lbilities for correct cipher wheels and at the same time give the exact setting. 

19. Jlrst-mternl data, cipher-text relationships.-Consider CWld set at A in position 1 

and suppose the plain-text letter being enciphered is E. ' 

LFS __________ T E G D N S X U P Q Y V H A 11 B K R i J L Z I I O C 

MALl--------F B Q II P L N R C H Z E I A S G T J b V K D I y X U . I 

NAL1--------A B C D E F G H I J K L II N 6 P Q R S T U V I X y z 

881 __________ 1 2 3 4 5 6 7 8 9 10 11 12 13 14 1! 16 17 18 19 20 21 22 23 24 25 26 

t 

[4 iJlt.ervening wheels] 

RFS _________ y L V R Z X C P F 0 I Q A II J B N S ~ K D G H T U I 

1 

FIGUBll 22 

25 

The current leaves Eon the RFS and passes through the wheels in positions 2, 3, 4, 5. The exact 

path is not known; it depends on the identity o.nd relative position of the intervening wh~ls. Suppose the path traced leads to position 15 on BSl opposite 0 on NALL Then the resulting 

cipher letter is F. After 26 letters have been enciphered, the wheels will be in the following 

position: 

LFB-------- T 

MALl------ U 

E G D N S X b P Q Y V H A 

F B Q 11 P L ~ R C H Z E W 

11 B K R F J L Z I I 0 C 

A S G T J 0 V K D I Y X 

I 

l!f AL1------ Z A B C D E F G 

:881-------- 1 2 3 4 5 6 7 8 

H I J K L 11 N 0 P Q R S T U V I X Y 

9 10 11 12 13 14 1! 16 17 18 19 20 21 22 23 24 25 26 

t 

[4 intervening wheels) 

RFB-------- Y L V R Z X C P F 0 I Q A II J B N S ~ K D G H T. U W 

FIGUBE 23 

If in this position E is again enciphered, the po.th traced by the current will again lead to position 

15 on BSl, because the four intervening wheels are in tho so.me position as before. Since now, 

position 15 on BSl is opposite Non NALl, the resulting cipher letter is U. 

These results indicate that for CWld set o.t A, the cipher digraph FU corresponds to a plaintext repetition at an interval of 26 letters or interval 1 down a column. We obtained this 

cligraph by considering the letter E and assuming that the identity and settings of the intervening wheels were such as to carry the current to position 15 on BSl. For a. different arrangement 

of the intervening wheels some other plain-text letter would ho.ve led to position 15 and the 

same cipher digraph would have resulted. Consequently, the identity of the plain-text repetition is not an essential element. For CWld at A, any plain-text repetition which leads to 

position 15 on BSl will correspond to the cipher digraph FU. 

Had we o.ssumed a position on BSl other than 15, a different cipher digraph would have 

resulted, e.g.: TABLE v 

Position Dlpaph Position Digraph PmltloD Digraph 

1 AV 10 RI 19 llP 

2 Ell 11 LF 20 KB 

3 PG 12 sz 21 CR 

4 ZQ 13 DX . 22 JT 

6 VI 14 XN 23 HL 

6 TH 16 FU 24 OA 

7 BE 16 NJ 26 WC 

8 QK 17 GS 26 YO 

9 IY 18 UD 

I 

For CWld at A, these 26 digraphs represent the only combinations which can correspond 

to plain-text repetitions at interval 1. .A:ny digraph, not contained in the above set, cannot 

correspond to a plain-text repetition. This procedure can be carried out in detn.il for every wheel and every setting, yielding 26 

digraphs for eo.ch case. The results can be set up in a series of tables (one for each wheel) which 

give the correct digraphs for each setting. It must be observed that these results will hold for 
26 

~terval 1 only. It is possible in the same way to construct tables to correspond to any required 

interval. On the other hand, it is poBBible to obtain information about any desired interval 

from tables fo~ interval 1.. ~o ill~trate, we know that ~for CWid at A is a correct poBBibility. 

1:he correct. digraph begmmng with U for CWid at Z IS US. Consequently, FS is a correct 

digraph for mterval 2 for CWid at A. In the same way, since SP is a poBBibility for interval I 

when CWld is set at Y, FP is a correct digraph for interval 3 \\ith CWld at A. The extension 

to any interval follows along the same lines. One must be careful in working with a reverse 

wheel to remember that the wheel settings progress in the normal order and not in the reverse 

order as for direct wheels. These tables are given in Appendix II, basic cipher-text sequences. 

Our chief interest in these tables is to be able to pass from a known digraph to a set of possible wheels and settings. To get this information, the tables just described must be rearranged 

in the following way: Instead of listing the digraphs corresponding to wheels and their settings 

we list separately each digraph and the positions for which it is a possibility. This has~ 

done for interval 1 in Appendix III entitled "first-interval data, cipher-text relationships." 

20. Application of :first-interval data to a knoWD. 1 'V' • me...,e.-Let us now proceed to make 

use of these tables to try to find which cipher wheel is the one involved in the test message 

employed as an illustrative example on page 23. 

Take the first pair of equivalents: 

Hp (locus 3P-3)=V•}case 1 Hp t locus 4P-3) = c. 

FIGUBll 24 

Refer now to .Appendix III, table V, line C; there are found the following cipher wheels and posi- tions indicated for the digraph VC: 

Wheel 8ett1111 Wheal llet&Jng 

ld K,L,Z 6d p 3d v lr R 

4d N 2r F 

Sd A,B,P 3r G 

FIGUlllll 25 

Take another pair in the same lines of the message: 

Sp (locus 3P-14)=A.Jcase 2 Sp (locus 4P-14)=Z. 

FIGURE 26 

Wheal Set&lng 

4r I 

ISr • 6r K 

Again ref erring to Appendix III, table A, line Z, there are found the following cipher wheels 

and positions indicated: 

Wheel 8ett1111 Wheal Sot&Jng Wbael Bet&lng 

ld z 5d C,D, Q 2r F 2d u 6d D,O Sr u 3d c,s lr x 6r N, .J 4d z 

FIGUBll 27 

27 

The only indications common to cases 1 n.nd 2 are CWl~, set n.t Zand CW2r! set at F for 

line 3P. This means tliat if CWld, set o.t Z is c.orrect for hnc 3P, then. for th~ hne IP, CWl 

must have been set at B; if, on the other ho.nd, CW2r, set at F for .lme 3P is correct, then 

for the first line CW2 must have been set at D. Let us seek corroboration for one or the other 

of these two possibilities: 

DP (locus 1P-13)=Nal Case 3 DP (locus 2P-13)=Dcf 

Fmuu: 28 

Refer to Appendix Ill and we find corroboration, for on table N, line D, CW2r at D is indicated 

as a possibility, whereas CWld set at Bis not so indicn~ed.. . . 

For lines 2P and 3P, we should find CW2r set at E md1ce.ted for the following p&ll'S: 

AD (locus 2P-9)=Xe} Case 4 A.p (locus 3P-9)=D. 

EP (locus 2P-12)=Dc} Case 5 Ep (locus 3P-12)=Ye 

A. (locus 2P-26)=Lc} Case 6 AP (locus 3P-26)=K. 

F1GUBll 20 

Referring to .Appendix III it is found that CW2r set at E is indicated for the first two of the 

three cases but for the thi~ case CW2r set at F, not E, is indicated. This is not a contradiction, J , "'b o.k" thli as will be explained later (p. 37), but it indicates that the 26' re m e nes occurs 

either at or before column 26. At any rate, there is now no question but that we have located 

the cipher wheel in position I, together with its initial setting. . 

All the foregoing was, however, predicated upon known facts: First the 1!1ess~ was kno"!° 

to be a "V" message, and secondly, the plain text was available, so that identical letters in 

columns were known. What if these two facts were not known? 

In order to answer the questions proposed, a slight digression must be made. 

21. Stati1tical study of 11V" messagea.-Consider 1 a large amount of plain text to ho ~t 

· hand. It is desired to determine the probability that tw.o lettei:s chosen at random from it 

shall be the same. The probability that one of the letters lB an E IS the normal fre,_u~ncy of E. 

The probability that both are E's is the square of the normal frequency of E. Sunilarly, the 

chance that botH. are A's is given by the square of the normal frequency of A. The sum of 

these two numbers gives the chance that the two letters are either both E or both A. The 

probability that both letters are the same, regardless of what particular plain-text letter they 

may happen to be, is the sum of the probabilities for each pair of identical letters and hence ~e 

sum of the squares of the normal frequencies of all the letters in the alphabet. The calculation 

on page 27 of Part I shows this result to be 0.066. . . . . 

If, instead of plain text, one were given o. monoo.lplie.bet1c. ~ubstitution, the reosonmg 

would still be the same. i'or the particular identity of the repetition w~s of n.o consequence 

in the reasoning. Moreover, two like cipher letters correspond to two like pl~n-text ~ett~rs. 

Hence1 the probability for a repetition of two cipher letters in a monoalpho.betic substitution 

cipher is 0.066. 

& The reader la advised to review the mathematical analysis contained in the discussion in Pa.rt I (pp. 26-31} 
28 

Suppose now that a polyalphabetic message is being studied. If the number of alphabets 

is known, it is poBBible to rewrite the message so as to break it up into its constituent monoalphabets. If now the number of coincidences is tabulated in each monoalphabet, the situation 

is still the same. The total number of coincidences for all the alphabets should still correspond 

to a probability of 0.066. 

What happens if the number of alphabets is not known and the message is incorrectly 

written out? What kind of result will be obtained from a tabulation of the total number of 

coincidences in such a case? To answer this question completely, it will be assumed that the 

message under consideration is homogeneous, i.e., that each cipher letter has practically the 

same probability of appearance as every other one. Such an assumption is not a very great 

restriction since any fairly good cipher satisfies it. Even a polyalpbabetic message with as 

few as six alphabets has a very flat frequency table. In such a case then, two like cipher letters 

in a column may represent any plain-text letters whatever. Select a particular cipher letter 

in a colwnn, say fl.. The chances that any other letter in that column is fl. are the same for 

every cipher letter, i.e., 1/26=0.038. This number is so much less than 0.066 that it should 

therefore be a simple matter statistically to determine the proper number of alpha.bets in a 

polyalphabetic message; for an incorrect assumption will yield only three-fifths as many 

coincidences as a correct one. The difference between the numbers 0.038 and 0.066 is significant 

enough to show up very plainly, 1 

22. BISsumlS.--Summarizing what has been said up to this point in connection with "V" 

motions, it appears that every "V" cipher message can be determined provided only that it 

be at least 125 or 150 letters long.1 In determining a message to be "V", the identity and position 

of the first wheel are obtained as incidental items of information. Moreover, if the meBB&IJ8 is 

of sufficient length, the "650" break may be determined by the same analytical test, for that 

break defines the beginning of a new set of alphabets. The letters above the break will not yield 

the proper percentage of coincidences with the lettem below it and if the message is long enough 

this property permits the break to be definitely located. This additional information gives 

the initial settJ,ng of the second control wheel and the initial setting of the second wheel. However, it does not determine the identity of the second wheel except in very special cases. (For 

instance, it might happen that the first wheel in a particular message has been determined to be 

CW2d set at I. If the second wheel is found to begin at any letter between A and H, it must 

be CWl, because in the numerical key that letter would have to correspond to 1. Such eases 

are however very unusual.) 

The actual application of the test for "V" messages can now be explained by using a message 

whose motion and plain text are unknown. 

23. Application of statistical method to an unknown message (Serial Bo. 189).-To begin 

with, the message was written out in lines of 26 letters; only 12 lines ware actually used in the 

test, inasmuch as it was felt that this amount of text was quite sufficient. Twelve lines of text 

afford 11 X26=286 pair of letters (at interval 1) that may be employed to find the cipher wheelif a "V" motion is involved. According to theory, we should find 286X0.066=18.88, or approximately 19, coincidences; hence, we should find one wheel in one position (all indications being 

1 The advantage of such a method of determining the number of alphabets involved in a polyalphabetic 

message over the commonly wied one baaed upon repetitions is that a much BIDal.ler amount of text is necessary 

to obtain unquestionable results. It is possible in this way to determine the number of alphabets with only 

5 or 6 letters in each alphabet, provided the number of alphabets is fairly large. An illustration of this and 

other applications will be found in S. Kullback, 8lali1ticaZ Metl&orlB in Cryptanalyri1, Technical Publication, 

Signal Intelligence Section, 1934. 1 The total number of possible coincidences will be about 26X1Ca=260; large enough to give fairly reliable 

results. 

29 

reduced to yield tho i11iti11.l setting) iudico.toJ o.hout 19 tines. Incorrect wheels should yield 

286X0.038=10.8, or approximately 11 imli~utious. 

Serial No. 169 

INDICATOI!~_QOO_~ __ EHHBE_DM_S_C_H __ _ I ' ' ' • ' ' ' ' ' " n:~ " " ~ m ., " " ,. M " "' I 

I 1!Fl4EIWIGCVCWGFQCDVGGLNXVSVP I 2lswoTCMKFJCESPOCHPFOLVMOJVA 

I 

3IUYRPPSYIHIEQONWIMVPBGNJGZW 

4 ANCIEKLCBVGVTGDBRKFYBYQXKZ 

\ 

5 CXZVBOPMLUBLDQXIDWTEHZMFDU 

6 NGSGJLNCZRMLMXQISUIXMATRKD 

7 1 DCWLZOTHRGZPEYKYRXRSJPZHHQ 

s!ZWGEILAYVVEOZVQPUFEEUSSEAR 

9 ZWLGBXNSGBEYLEARUCMYJPXVRV 

10 H T X N T Q S X H T Z H M T H V Y V A E Z V Z Q S G 

11 UMAHBABWWOMQUDUNIYBSFXDWFP 

12 B V E D Y Y M 0 L Z Z J S Y N U G T K R K X W S C C 

l~IGURE 30 

A digraphic to.hie was constructed or the pai~ in _n.djo.ccnt lines; thus, Cor the first and 

second lines, FB, MW, EO, etc., for the second and third Imes, BU, WY, OR, etc. . . . 

Referring then to Appendix III, the indicutions Cor FB, MW, EO, etc., were dlStnbuted m 

the following nmnncr: TABLE VI.-Talile fur tl1e interval between l:ne1 1 and B 

-· 

Setting 

\ I I I I . I ; I 

CWld 

CWlr 

CW2d 1 I 3 ! 1 !_!_!~.-P-~H-~ I i 2 I 1 _1 1-- _!.__1 ~-l!-~ CW2r ~I ' \ ' l • I • 1_._, ~~[ _ _!_I_ ~ 1 

• • !... • I ..__!._ 

CW3d 2 ,-1 -1 3=! 1 I 1 1_1 ~ 2 :-1 1-1 i_I__ ·_1 ~ 1 I-~ • 2 • ~ CW3r 2 rr1t21i 1 I 2 \ I_~ L-1 1 1

_1 1_1_1 \_1 1 1 1 ....:__, 1 _ _!__ 

CW4d ! 1 r---cl11 I ~!__l~_l_l ~j_l i_l~_l_!__lb=l_1 t_l ~-l _ 3 

CW4r ~~~_ --Lk-~!-p~-1 1_1 ~-~-· ~- • , __ 1 

CW5d _ _1_1a _1_ ~__1_ _1_\_!._I_ 1 _ _!._~l_...:_ __ 1 !_1_ ~---,~--1_1_1 

CW5r 2 I 1 11 fli_1 i 1

_1 ___ 1 __ ,_1 __ 1 1

1 I I •I• LI I ~ 1-1 _!._\-·-

CW6d t-! I 1-j1··1-1-2 Lrt 1_1 1_1 ~I 2 \ _ _l_l 1 1 1 2 1 1 "f 1 3 -rt+ 

CW6r 1 i-1 is-11 1 ' 21 i 11 121 i 3 i 1 1 1 1 ' 1 1 I 

71836--:Jl"--3 

,. 
30 

Tho indications for BU, WY, OR, etc., were then distributed in the same to.hie, but the 

positions indic1tted wero reduced to initial settings. 

This process was continued for all the other po.irs in the digraphic table, with this final result: 

'l'ABJ.l!l VII 

.------- - --· 

Setting 

A B c n B F G :e: I I J Ix L KN o P Q B s T 

~I~ w x y z ------------· I ____ .-·-----

CWld 13 12 13 15 16 24 5 7 13 IO 8 10 11 9 9 16 10 8 7 IO 7 6 IO 11 11 IO - - --- - - --- - - --- ---- - - - - - - CWlr 9 16 11 9 7 18 5 12 9 8 IO 12 11 10 9 10 7 7 11 10 8 12 14 12 15 rn ----- ------ --- - - - - - CW2d 11 15 7 IO 16 9 7 14 10 14 10 9 9 10 11 8 6 8 18 9 9 8 13 6 17 8 

-- - - - - - - - - - - - - CW2r 10 13 9 14 15 19 7 15 !) 7 16 12 13 15 15 16 10 IO 8 4 12 5 11 6 7 16 

-- - - - - - - - - - - --- - ------- - .. -·- - ··- - .... - CWad 18 13 11 9 17 5 10 9 12 !) 12 9 11 !) 4 11 14 6 14 14 6 11 7 13 11 13 - - - - - - --·-- --·- ----· ---·------ - - - - - r--- - - CW3r 6 13 8 12 1:1 9 9 IO 5 8 14 8 11 11 11 12 8 13 9 16 IO 17 8 10 17 10 ---·------·----·---· --- .. - - - ---- - - - - - -- - - --- - - - CW4d 7 13 11 16 12 ~__!_~~11r 15 ~ IO 14 8 7 8 8 10 12 8 13 13 12 r--

CW4r 9 9 9 13 12 15 9 10 8 8 11 11 10 12 lG 14 Iii 9 14 10 6 9 10 13 10 13 

---------i----

CW5d 16 17 10 16 11 15 10 11 IO 13 12 12 11 6 12 10 14 6 rn 7 15 20 IO 11 7 9 r-- -1-----··-·------ ....._ 

CW5r 12 19 14 13 17 12 7 9 13 11 ~ • 7 13 15 9 13 4 12 14 8 13 12 8 15 16 

CW6d 13 12 12 11 11 --·--------

13 I 11 18 6 12 12 __!_~ 12 --IO 10 11 9 -12 8 11 15 -

7 11 -17 8 

CW6r 8 9 9 6 10 91 7 10 14 12 11 14 9 13 14114 -12 11 9 12 7 12 12 13 7 15 

Note now the number of indications for CWld o.t F; it is 24 o.s ago.inst o.n average of 11.0 

for ell other alphabets and positions. This means that not only are we dee.ling with a "V" 

message, but also the theoretico.l expectancy, 19, was really lower tho.n the actual, 24, and 

that there are more repetitions in columns than v;o.s anticipated. 

As a check on this result the same process was carried out for interval 2, that is, tho letters 

of line 1 taken to form po.irs with the letters in the so.me columns of line 3; those of line 2 with 

those of line 4, etc. The total number of tabulations is 200, tho expected number of coincidences, 17. The actual n1m1ber found for the setting F, CWld was 20. The percenta.go of 

coincidences for 286+260=546 digraphs for the setting F, CWld is therefore 8.1 percent instead 

of the theoretico.l 6.6 percent. 

This result is really better than was anticipated. There can hardly be any doubt but 

that the right wheel and setting have been found. In less-fortunate co.ses, it may be neceSRary 

to tabulate and sum the do.to. for severo.l intervals before a conclusive result can be obtained. 

It should be observed here that the occurrence of tho "650" breo.k in o. message may 

co.use some difficulty in the actual test. AD.y two lines which have the breo.k between them 

will not furnish correct information. However, for small intervals the degree of error introduced 

is practically negligible. For example, in using intervo.l 1 only ono pu.ir of lines at most will 

be incorrect, viz, those with the break between them; for interval 2 only two pairs, etc. In a 

message of at least six lines, the correct result will still be obtainable. 

Having found the correct setting for the cipher wheel in position 1, it follows that the 

lotter D in message indicator DMSCH must equal Fp; also F indicates that a wheel is in the 

direct position. 

l 

31 

When message Serial No. 169 was conYerted so o.s to remove the first cipher wheel from 

consideration, tl1e following polyalpho.betic messnge resulted: 

}"muRE 31.-Serial No. 169 converted 

1 DZTUCUROQOCRDPOGQRRYVHQE 

2 QAWGRCTOBLETINJRTYJLRDVORE 

3 VSUGIXXHGWNWRDMQVWBYXCTQST 

4 EVLCHAORBHIMPMQPKIDRTEIEVF 

5 RULZIAJDBSVXJVQMZGQUFYHISE 

6 QXYZCZAOYENKJOJPITCWTPJFSK 

7 D R W M K U C H A S E V C J B T I T E R E0 Z Y J C S 

8 SNGSIURZBLKKUOGKDYPAUUPQQU 

9 BTWPRGHYLDGHFERFVAJCIEUQYS 

10 A S B R E K R Y S E B R P B N R B A W A C V P A P Y 

11 S X A R I U L I L D D F R E A V A H Q Z L 0 S B V D 

12 S W P W K L A A T E M R R B F A N I Q Z S 0 S C Y F 

13 X X B I C K C D W V R Z X R B G E Z V H I 0 F L B L 

14 V T E R M C K V L B P I G X H Q A L Q C I E P V Y F 

15 V X G W M H W C V N S Z F T Y A V Y Q S M 0 K G W R 

16 M 0 A S S G J E Y T G Z W T V Z J J S C E C L A Q Q 

17 B G M U Q G S Q N D X N C U N Z J S V C I E N Q V X 

18 S P H I V N L A E J M A U Y K Q B P D C N Z U U G Z 

19 J U J T T K S M S K S Z E T R A V T Y J K V C T N Y 

20 V U Q I N K V G 

A study of the repetitions in the message o.nd of the monoalplmhets down ea.ch column 

seemed to indicate tho.t the "650" break occun·ed between lines 6 and 9. On using the o.nalyticol test based on coincidences, it turned out that the break was either on line 7 or 8 and 

consequently the second letter of the messngo indicator must be either P or Q. The number 

of coinciden<'es obtained when lines 7 1tnd 8 were tested with the preceding lines were so nearly 

alike as to yield no definite information. Hence, in the message indicator DMSCH, Ma=P or Q. 

Enough hits been shown, it is thought, to indicate the procedure tl10.t was followed with 

unknown cipher messages to determine whether or not they were "V" messages; when encountered, the value of the first letter of the message indicator, o.nd whet.her its plain-text equivalent meant "direct" or "reversed" constituted important collatero.l information. 

After testing out tl1e method on several unknown cipher messages o.nd finding it to be 

efficacious, there seemed to be no point in spending further time with similar cipher messages 

with unknown plain text. After o.11, the cipher messages with known plain text would yield 

identical results in much shorter time, since identities of plain-text letters were indicated in 

the messages themselves when transcribed in lines of 20 letters. Consequently, all the plaintext messages were studied in connection with their cipher versions in order to shorten the 

time required for o. complete solution. The possession of the 55 "known" cryptograms 

admittedly fo.cilitatcd solution of the 110 "unknown." Nevcrt.heless, the solution was not 

made possible by, o.nd would not in practice require possession of, plain-text messages with their 
32 

cryptographic cquiv1tlents. After several dnys' work along these lines mn.ny values and determinations were obtained from the procedure. ' 

24. Consideration of "W" messages.-The foregoing rnuthods arc 1tppli<·Hble to "V" 

motions. How 1tbout "VI" motions? In 1t "W" motion the first wheel is either stationary 

or moves continuously; the se<'.oncl wheel move~ every 2li. The proper aF.1sumption<1 r<'l!'.Rrriing 

the setting of the first wheel and its motion toget11er with 1t cori·ert ussurnption ns to the second 

wheel mukes the prnblNn ec1uivalent to t.he one just discussed. This pro<'edure ii:; n. bit morr. 

complicated since it involves trio.ls on two wheels o.nd the numb<.'r of necessary triuls is t.hereforc greatly increased but otlwrwise the two problems nre identir.nl. There is no reason whv 

such me:lsuges c1mnot be picked out by tl1<' nhove procedure. In the present test such n sitm;-

tion did not arise been.use it wo.s found possible to get sufficient information from "V" motions 

o.nd "Z" motions (to be discussed) to obtain a complete 11olution of tlie problem. 

A po.rticulnr idea in this connection should be emphasized. Suppose that in o. given series 

of messages all of the "V" messages are found before a search is begun for "W" messages. 

In such a case, the number of tri1tls mentioned nbove is considerably reduced, since in many 

o~ the "W" messages. the first letter will be known. Any wheel assumed in the first position 

will then be entered m only one possible setting and the detl•m1inntion of "W" mess11ges will 

not be of much greater difficulty than the determinntion of "V" messages. 

Sin1ilarly, o.fte~ o.ll the "W" messages ho.n been found, a search can be made for "X" 

messages by o.ssunung the first throe wlleels, two of which will in some co.ses be known. 

A generul solution can be arrived at by such a J>rocedure. 

25. First interval data, plain-text relationships .. -It has already been remarked that the 

mess~es most ame~o.blc to study are those whose motions nre eithr.r "V" or "Z", but u.s yt•t 

notlnng has been soul about the latter. Jn 11uch IL motion, iC the message is written out in lines 

of ~6, and letters down a column are conside.red, the fifth wheel is the only one which ho.s mo,·ed. 

Tins property may be put to use in a manner similar to that employed for "V" messages. 

Suppose that the wheel in position 5 i::1 CW5d set at A, and that the plnin-text letter beinO' 

enciphered is E. The cmTent passes from E on the ItFS to Y on MAL5 thence to Y on N AL5~ 

l RFS ______ y L V R Z X C P F 0 I Q A M J B N S E K D G H T U W 

~1AL5 ____ J 0 R X Q E G I S C F N A U Z M H V ~ L K D B T W P • 1, _________ ~~ 

NAL5 _____ A B C D E F G H I J K L M N 0 P Q R S T U V W X t Z 

l 

FIGURE 32 

From this point on, it g?es through the remaining four wheels, finally emerging at some cipher 

letter 8,. After the enc1pherment of 26 letters, CWli hns moved to setting z. 

J. 

RFS ----- Y L V R Z X C P F 0 I Q A M J B N S E K D G H T U W 

I 

MAL5 ---- P J 0 R X Q E G I S C F N A U Z M H V Y L K D B T W 

1--------------------~----------------I 

N AL5 • . . . Z A B C D E F G H I J K L M N 0 P Q R S T U V W X Y .... 

FIGURE 33 

If now the phiin-text letter be Z, the cunent po.sses from Z on R:F'S to X on MAL5 thence to X on 

NAL5. The cunent is now at the so.rue point on BS4 as the ('Urrent for the preceding E. Since 

the other four wheels are in identically the some position as before the po.th traversed through 

L 

33 

them by the current is the same in both r.11.ses n.nd the snme cipher letter will result. It thus 

follows tlmt for CW5d set nt A, the. sequenr.e. EZ of plo.in-text letters at a distanr.e of 26 will 

yield a cipher repetition. Similarly the sequence AB \\ill yield a cipher repetition. Continuing 

in this way, it becomes possible to set up 26 digrnphs which represent u.11 the possibilities of 

pln.in-text pnirs which shall yield like ciphl'r letters when CW5d is in the fifth position nt A. 

These digraphs are: 

AB 

BD 

CQ 

DL 

EZ 

FR 

GI 

T.•.BJ.E VIII 

HM 

IC 

JK 

KG 

LA 

MU 

~p-~ 

OT VX 

PS WV 

QN XH 

RW YF 

SJ ZY 

TO 

It is to be observed thnt it makes no difference just w-hn.t t.he cipher letter is. That \\ill depend 

on the fi.1'3t four wheels. The essential element is the fact that the cipher letter repeats. Any 

digraph not r.ontained in the above 26 c1mnot yield a cipher repetition for CW5d set at A. 

Let this procedure be carried out for every whel'l in e\·ery setting. A series of tables will 

then be obtained which will give the 26 digraph~ ('orresponding to cipher repetitions for any 

po.rticulatr wheel in nny given setting. It is, of course, understood that this infonna.tion will 

apply only to interrnl 1, i.o., to letters which are 26 apn.rt in the plll.in text. 

For intervals ot.her t.lmn 1, a similar procedure enn be followed whiclt will give the so.me type 

of informn.t.ion. Thus, one can const.ruct tables which will give the correct digraphs for intervnl 2 

or interval 3. It is, however, possible t-0 derive o.ll of these further tables from th<i tables for 

interval 1. For if P1P2 is n. possibility for CWJ d n.t Y and P2P3 is a possibility for CWld at X, 

both beinv; consiclerecl for interval 1, then P1P3 is a possibility for CWld at Y for interval 2. 

Similarly if P,P11 is a. possibility for CWlr at A and P5P8 for CWlr at B, both for interVlll J, then 

P4P11 is a possibility for intervo.l 2 on CWlr G.t A. 

It is possible int.his wo.y to combine <ligmphs for different intervals and get desired information about any interval whatc,·er. All of this informu.tion co.n be conveniently combined into 

one set of tables (one for euch wheel) which hav<~ bPen designated 11 Busic Plain-Text Sequences" 

(Appendix IV). To ex11ln.in just how these tnbles nre used, I'flference is ma.de to the squo.ro for 

CWld. The lettP.rs down the outside of the box rl~pr<•sent the settings of the wlwel. If, for 

CWld, digraphs are desired fol' intt"l'vo.11 at setting A, the first letter is reud Crom line A, o..nd the 

second is fo-.md by rending diagonally to the right, thus YT, HX, ZY, et<'. ]for interval 2 nt 

setting A, the first letter is ago.in found on line A, the seco1!d is one removed along the diu.gonal, 

e.g., YC, HL, etc. In every cuse, the first letter is found on the line eorresponding to the desired 

setting n.nd the second letter is obtained by reading diagonally downward nnd to the right. The 

distance between the first nnd S<'c<mcl letters of the digraph is th~ interval under consideration. 

Suppose the tables for intervnl 1 are inverted, i.e., suppose thn.t the dn.ta o.bove obtained is 

n.rro.nged with respect t-0 the digrnphs 11nd not with respect to the wheels nnd their settings . 

This \\ill be found in Appc·ndix V, "~'irst-lnterval Do.ta, Pin.in-Text Relationships". Then the 
34 

tables will give information of a. different character. Thus, under the letter B, it is found that 

the digraph BJ will yield o. cipher repetition for en.ch of the following settings: 

d r 

lY 1D 

2M 2T 

3F 3Z 

40 5T 

4R 5V 

4Y 

FmuaE 34 

The dio.gro.ph BN will yield a cipher repetition only for CW4r at O; there is no other possibility. 

Similarly, any particular digraph is associated with o. definite set of possibilities for the wheels 

and their settings. It is interesting to note tho.t the wheels a.re so constructed that no plaintext doublet can ever yield a cipher doublet for interval 1. 

26. Application of plain-text relationships to messages with known plain text.-The 

application of the above information to the discovery of "Z" messages when the plain text is 

known is very simple. Consider Serial No. 155. 

1 2 a ' 1 a 1 s o ro n u u H u ro u ~ w m n ~ ~ M ~ • 

l {J A P A N E S E A N D C H I N E S E S T I L L H 0 L 

KCMTZVUFELYTDQRRTNUXCSOFNE 

2 {D I N G L I N E S E X T E N D I N G F R 0 M A B 0 U 

SWHXDVWIWGPHZOBRAHXCBYFKEH 

3 {T E I G H T K I L 0 M E T E R S W E S T 0 F N A Z I 

DCBEWRBWOTEWWTQUUHCSTEPUWS 

4 {A N G N 0 R T H T 0 L I U H 0 P E R I 0 D N 0 S E R 

BGEIRTINXAPWVRYVPREFNBFSNM 

5 {I 0 U S F I G H T I N G B U T S K I R M I S H E S B 

COVJKFCLWEOLOQEGSVIRJCJMUT 

6 {E T W E E N 0 U T P 0 S T S H A V E T A K E N P L A 

YAYFWNJDYLKTYVESTQWORSAZQN 

7 {C E I N L A S T T W E N T Y F 0 U R H 0 U R S P E R 

GVTAJJCbFSFCLLETTMZUJFNFPY 

8 {I 0 D C E L E B R A T I 0 N 0 F R E P 0 R T E D V I 

DGBFEGKKOLGXLHVFSPTQFXHTIX 

9 {C T 0 R Y B Y C H I N E S E T R 0 0 P S T 0 0 K P L 

JSNQUCBHHSNXZOGZDRUIAOWOAB 

lO {A C E I N S E T T L E M E N T 0 N E V E N I N G 0 F 

UXCSKWBMVWJXOUTLIFZJBJTYGY 

35 

i 1 a ' 1 a 1 s o ro n ~ u H ~ ~ n ~ w m n n ~ ~ z • 

{

FOURTHCOMMABUTLARGECROWDSW 

ll V N S G K Q P G 0 R P K A U M C Y J J R V M B B S W 

{

EREDISPERSEDBYPOLICEANDNOS 12 Z S A K G D F H W S W L E J G Q D D U D Z R N N C E 

{

ERIOUSDISTURBANCETOOKPLACE 13 D A E J G 0 P K M Q L S G I W Q Q W 0 E K F R L C N 

{

PERIODSHANGHAIISSHOWINGSOM 14 V R L F M I R D W H U W S Z I L V H U A E A J G A U 

{

ESIGNSOFGRADUALLYRESUMINGN 15 N N U W D M A B E L B R N G N T L U I K Q C C F C S 

{

O R M A L C 0 N D I T I 0 N S P E R I 0 D A D M I R 16 Q D N Q F T H R A L E L C V J C X D X M B I T G B Z 

{

ALKELLYINFORMSMETHATHEHASB 17 N T D 0 Q K M A Z Q R D I M U B P X B Y B 0 T E P N 

{

EENASKEDBYHISGOVERNMENTWHY 

lS K Z T A G I F I V Q W D H X U B E J G A A U D J J L 

{

HISRELATIONSWITHMEWERENOTC 19 D L E Z Z C P E A J U R M U D W R U J A M D J M D P 

{

LOSERPERIODOURRELATIONSHAV 20 B L M B U D Z G K H E F X A B V K N H Y Q T F E L R 

{

EBEENCLOSEANDCORDIALANDHEH 21 B T Q U W C P V C E W K L L M J 0 K L R W S E B A F 

{

ASKEPTUSFULLYINFORMEDOFALL 22 D Z L M K V K Z V T R X V L M Z F H P U P U Z G C X 

{

STEPSHEHASTAKEN 23 E H Z L C P L Z R X L 0 W Q P G 0 P 

FmuaE 35 

On lines 1 and 2, the plain-text digraph EI corresponds to the cipher repetition VV in column 

6 and to the repetition RR in column 16. If the message is a "Z" message, then the only possibilities for the last wheel a.re 

d r 

2G 1I 

2I 3B 

2W 6E 

3B 

3Y 

4! 

6B 

FIGURE 36 
36 

Now consider the digrnph GE which in rolumn 18, lint's 2 :md 3 corresponds to the cipher 

repetition HH. The possibilities which it yil'lds for the firth wheel 11.re 

d j_r ____ j 

lW I 2M 

tF 3M I 

2H I 4H I 

2L 4R 

3H 4Z 

5W 6B 

6J 

6T 

6X 

J!'IGURE 37 

But it must be remembered that in passing from line 1 to line 2, the setting of wheel 5 hn.s 

changed in the reversed direction for n. direct wheel and in the normo.l direction for tt re\·ersed 

wheel. To compare the second set of possibilities \vith the first, it is therefore necessary to 

compensate for this shift. Tho second set of possibilities will then become 

[.=~ci" r 

IX 2L 

lG 3L 

21 4G 

2M 4Q 

31 4Y 

5X 6A 

61 

6S 

6W 

FIGUKi: 38 

It is now found that only one entry is common to both sets, viz: CW2d n.t l. If the message 

is a "Z" messu.ge nnd the fifth wheel is 2d set at l, it should he possible to check this fact by 

using other cipher repetitions, for example, WW in column 12, lines 3-4. The plnin-tl~xt digrnph 

to which it corresponds is EI and one would expect 2G to be listed o.s n possibility under this 

digraph. This is found to be the cnse. Similarly, t.hc l!igmph TH in column 15, lines 5-6 is 

found to check. 'fhe necessary conclusion must then he thnt Wl' nre dea.ling with n. "Z" messu.ge whose fifth wheel is CW2d initially set o.t l. 

If a procedure such o.s ho.s been outlined o.bove does not result in one setting common to 

all the possibilities, the message ctmnot be o. "Z" message.1 

It is thus seen that if the plain text is known, the dis<"overy of "Z" messages is a matter 

of relative simplicity and that ench time such a. messuge is found the identity and position of 

the fifth wheel are determined. But this is not all the infomu1tion whiC'l1 is obtn.imtble. The 

same test that has already been applied will give information u.bout the first two wheels. 

1 If only one or two of several yield appa:-ellt contradictions, they may be the result of factors which are 

explained in what follow&. 

.. 

L.. 

37 

To see how this comes about we procel'd es foilows: Considl'r th<> riph\>r repetition BB on 

lines 20-21 in column 1. The rorresponding plain-text digraph is LE. :-3ince the fifth wheel 

is originally set a.t l 1mcl progresses in o. reverse direc.tion, it should ha..-e o.i·1·h·cd 11.t R for line 20. 

In other words, one of the possibilities which should appenr under LE in tho tables of intcrml 

1 is 2Rd. But, on refcronl'e to the tables, thiA ent.ry iM not found opposite Li:!:, nit.hough 2Qcl is 

found. 'fhe explanation for this nppenrance is not difficult. When a messogl' is written out 

in lines of 26, the first column should be that one which corresponds to H on the first control 

wheel. This was not to.ken into account when the cipher message w1is set down, nnd it would 

consequently be e..'=pccted t.l111t some of the columns would be out of place. 'fhnt is r.xnctly 

what happens in this co.sc. Column 1 really belongs on the right of column 26 nnd the digraph 

BB should ltJlJlPll.f on lines 19-20 ruthPr thnn on lines 20-21. For these !ines, it would be expected 

that LE would correspond to 2Qd, ns it actually does. (One must bP <'nreful not to oye.rfook 

this fact in searching for "Z" messages.) 

The question now e.rises: "Do«.>s column 2 belong on the left or right?" In order to answer 

it, one must first find a cipher repetition in co1umn 2 and chec·k the <'Orresponding plain-text 

digraph against the tables. When this is done with LL on lines 19-20, it is found thut column 

2 really belongs to the right of column 1. 

The continuation of this rcnsoning introduces the use of othc•r interrnls tho.n 1 since neither 

column 3 nor column 4 contains o. cipher repetition o.t tho.t intern1l. Hut this is not an essential 

difficulty. The use of interval 1 up to this point has bc~en purely a mnttcr of convenience; any 

other single interval or even any combination of intervals would lui.ve 1tiven the san1e results. 

It is found by this procedure that columns 3 o.nd 4 r..lso belong on the right leaving column 5 

as the H column of the finnl set-up. 

. J AP A These results ho.Ye two importa.nt consequences. In the hrst place, the Ictte1'8 K C M 1 

at the beginning of the message must st11n<l nlone nt the rigl1t «.>nd of line 1. Tluw eorrespond 

. . l ' d" d b h 1 tt b . . N E S E . . ' B t "t to o. different settmg from t iat m icate y t e e crs egmmng z V U F . . • • u 1 

was these latter letters which corresponded to the setting 21~. Consequently the message 

ren.lly begins with the firth wheel 2d at J and not I. 

Secondly, since the fifth column corresponds to Hon the left eontrol wheel, it follows that 

the initial setting of the control wheel is L. ~loreowr, that initfol setting gin•s the 11etti!1g of 

the first cipher wheel. This means thnt the indicator EQPRZ of Serio.I No. 155 is deciphered 

as L ... J. 

This is not yet all the information which might be obt.itined from this message. Suppose 

it were long enough to contain the "650" break. Could not that break he loc:i.ted by the 

same procedure? To this end ltit us theoretically consider the line on '' hirh the break tukl~s 

plo.ce. This brenk is due to tt motion of two of the fir1:1t four whePh~ which lutd been stn.tim111.ry 

throughout. 'l'he rc.>lo.tive set.ting of all four ns n. unit is thP.refore chnn:;ed nncl it fa no longer 

correct to say that the first four wheels remain unchn.ngecl down n. column. Rut thnt wns tho 

very property which permitted us to make use of the tables of plil.in-tex:t relo.tiouships, and 

since it no longer holds, the line on which the bren.k take!> pl.tee will not check \\ith those above it. 

It will check only with thoso below it. 

The application of this notion is quite simple. It is merely a nuitter of finding the first 

line whid1 does not check with those o.bo,·c it. Serini No. 11;), indicator RSPVQ, furni,.,he~ n 

good example of this procedure. 
38 

SERIAL No. 115 

{

1 2 a ' 5 e 1 B e ro u ~ ~ u ~ ~ 11 18 w 20 n ~ ~ M 25 m 

l ESTIMATESITUATIONTWELVEHUN 

GQCBFHANWJIPDNACUMIIKLPLAV 

2 {D R E D T W E N T Y 0 N E F E B R U A R y J A p A N 

BEGCLLLVCOFQGOZABXORBOUEMF 

3 {E S E F 0 R C E S A S H 0 R E I N C L U D I N G N A 

DUPWDEKTDVUUDMOBTWUJPDOMFX 

4 {V Y T W E N T Y T W 0 T H 0 U S A N D T H R E E H U 

DXHCPWXPMKRMUKSYRPJTFLHGLK 

5 {NDREDOFTHESETWENTYFIVEHUND 

UVKKYPLVEFMFSSDJANNLWPCLPY 

6 {R E D I N W 0 0 S U N G A R E A 0 P P 0 S I N G C H 

JRCEGXWGMIBAVTIGPCCVZYPLBC 

7 {I N E S E F 0 R C E S A B 0 U T F I F T Y F I V E T 

OSDKOBARZAPHONMGMKMXTJJRTD 

8 {H 0 U S A N D J A P A N E S E F 0 R C E S M O V I N 

GIJHBYKEVLIGFZVXYAJCOLGJEZ 

g {G A B 0 U T S H A N G H A I A R E A F I F T y S E V 

PKDHNDFRZLZLWJWRGUCYKNDHMN 

io{ENVESSELSINJAPANESEADVANCE 

HBZDTLADJITFFZVCTCKCYAKOIK 

ll {O N K I A N G W A N Y E S T E R D A Y V E R y L I T 

NKZANQKJLZKMIOALFOXFZPTOTT 

12 {T L E P R 0 G R E S S M A D E A N D A T T W E L V E 

YFMMXYAYLLANZGXAZPQOFLERSI 

13 {H U N D R E D C H I N E S E S T I L L H O L D I N G 

JFHNPGGWYKLMUHABJLORJPDAHH 

14 {W E S T E R N E N D 0 F T 0 W N C H I N E S E E N T 

PQWIZRSTFYJYXZIYSTPAQGHTUG 

15 {R E N C H E D W E S T 0 F R A I L W A y A N D y E s 

MDJLPZKOBOCHIDSHHQBCNCLPCS 

16 {T E R D A Y H A D 0 N L Y A F E W O U T p O S T s I 

KNRRYNCXOHJDGEKIEEINEXWGVA 

l7 {N K I A N G W A N B A T T L E A R E A I T I S E V I 

LVEUEOSTMMEPLGZRLOIFGWSAAG 

18 {D E N T I N T E N T I 0 N 0 F J A p A N E S E I S T 

WUVFSSHGUMYEFYHEDUKNPCTXFX 

19 {O E X E C U T E A N E N V E L 0 P I N G M O V E M E 

UAWJKSAWQQWCZCPFHZXKKBUPPB 

20 {N T S 0 U T H W E S T T 0 C U T O F F C H I N E S E 

KWMHVYYBMGFLTYVLENKVMMAEEZ 

l 

39 

1 2 3 4 fi 6 7 8 9 10 11 12 13 14 Ui 16 17 18 19 20 21 ~ 23 M 25 211 

21 {I N C H A P E I N 0 R T H S T A T I 0 N A R E A 0 F 

AVUPQASGDLVMJLODDITHOYUSPU 

~{CHAPEISHELLEDALLYESTERDAYA 

GNEOQVAZPXFXLQILDFRWOMWQQG 

23 {N D L A S T N I G H T B U T N 0 A D V A N C E 0 F J 

UNIEPBRNZWQMUKYDCSMAAYFSER 

Etc. 

FIGURE 39 

The message is found to be o. u Z" message with the first wheel originally set o.t I and C\V6r 

at V in the Inst place. If it is written out ns in figure 39, it will be found thn.t. line 14 checks 

'\\·it.h those below it but not with those above it. Consequently line 14 represents I on the second control wheel. On counting back to line 1, it is found that the second control wheel was 

originally at V. This gives the setting V for the second eipher wheel and shows that the indicator RSPVQ is deciphered as IV .. V . 

Returning to Serial No. 155, it is found that every line of the message checks with every 

other, and the break does not appear anywhere in the message. As u. result it would seem thu.t 

the initial position of the second control wheel is unobtainable, nnd in general, this would be 

true. It happens though that the particular message under consideration proves to be an exception because of its length. Since the Inst line checks with all the others nbove it, it must correspond to a setting of the control wheel other than I. Suppose this setting were any other letter 

than J or K. Then it is found by counting buck that some line in the message would represent 

I and would ho.veto contain the brenk. Consequently, the la.st line must he either J or K o.nd 

the initial setting of the second control wheel must be either H or G. This reduction to two 

possibilities is as fnr n.s one may go with the met.hod given above. 

It may be useful to summarize what hos been so.id up to this point nhout "Z" messages 

dth known plain text. In the first place, it can be determined by the use of the tables of plaintext relationships whether or not the message is in a "Z" motion. This procedure results in a 

knowledge of the identity o.nd original posit.ion of the fifth wheel. Secondly, the original position of the first control wheel can be det.ermined nnd if the message is long enough, thnt of the 

second control wheel cnn also be found. Tbe information about the control wheels givt's the 

original settings of the corresponding cipher wheels. 

27. Application of plain-text relationships to messages with unknown plain text.-The 

next element to consider is the study of mess1tges for which no plain text is available. For 

them, some statistico.l method must be devisecl which will indicate the correct result by a study 

of frequencies. Suppose that the machine is set for a "Z" motion with wheel 4 direct at S in 

the last position. If the plain-text letter E is hit 26 times in succession a series of cipher letters 

will result. If the next 26 plain-te.xt letters o.re all C, the second <'ipher line will be idcntico.l 

with the first because, acco1·ding to the tu.hie, an E and a C at a distance of 26 will yield the 

same cipher letter. 

Suppose now that the first line had been nil E's but the second line ordinary plain text. 

Then in any column where the cipher letters are identicul the second letter must represent C. 

If the cipher letters in the column a.re not the so.me, the second letter cannot be C. Hence, 

the number of coincidences is the same as the relative frequency of C in the second line. 

If the first 26 letters h11d been plu.in text the number of E's on the top line 'vould have 

corresponded to the normal frequency of E. The chances of finding on these two lines a. 

cipher coincidence which represents EC are given by the product of the normal frequencies of 

E and C. The chances of fmding o. cipher coincidence whose first plain-text equivo.lent shall 
40 

he A arc representr.d by the prodllct of the normal frequenl'ies or A and N sincl', n.ccording to 

the t.able, AN is one of the digmphs to be sought for at intt~rvnl 1. 

It now follows tlrnt the clumc.e for the o.ppe11r1mce or any t•iphcr repetition regardless of 

what plain-text digm11h it mny rcprl.'sl'nt, is obtnined by summing the results for 11.U 26 correct 

digraphs. The calcullltions nre given below: 

AN= 0.072 X 0.076= 0.0055 

BZ= .012X .001= .0000 

CS= .034X .058= .0020 

DK= .040X .00-'= .0002 

EC= .126X .034= .0043 

FY= .030X .021= .0006 

GF= .018X .030= .0005 

HP= .033X .027= .0009 

IH= .076X .033= .0025 

JM=0.002X0.025=0.0001 

KU= .004X .030= .0001 

LJ= .036X .002= .0001 

MW= .025X .014= .0004 

NQ= .076X .003= .0002 

OV= .074X .013= .0010 

PR= .027X .083= .0022 

QI= .003X .076= .0002 

RX= .083X .005= .0004 

FIGURE 40 

SB=0.058X0.012=0.0007 

TL= .OUOX .036= .0032 

UE= .030X .126= .0038 

VA= .013X .072= .0009 

WT= .014X .090= .0013 

XO= .005X .074= .0004 

YG= .021 X .018= .0004 

ZD= .001 X .040= .0000 

The expected theoretical number of cipher coincidences at intervn.I 1 is 0.032 of the total number 

of tn.buln.tions. The n.vern.ge incorrect rl'.sult is %1, since it ma.y be assumed thnt all ci1>her 

digraphs hnve an equnl probability of apper.re.nce. Hence, the a\·eragc incorrect result is 0.038 

against a correct result of 0.032. 

Jn considering cipher repetitions on the first o.nd third lines, it is necessary to use interval 2. 

Similarly, in compa1fo.g line 1 with other line~ or tlrn messn.ge, new inte.rvnls must be introduced. 

The corr<.>ct rl'strlt.s for CW4d at S (as cnlculntl'd above) are given ht>re for a few inten·nls with 

the correEiponding incorrect result in ea.ch cnsc. 

7 

8 

9 

TABLI!: IX 

0. 048 0. 038 12 

. o-t3 . 038 I 13 

. 037 . 038 I 14 

2 

3 

4 

5 

6 

0. 043 

• 03-i 

. 038 

. 031 

. 038 

0.038 

. 038 

. 038 

. 03S 

. 038 : g:: I : ~:: II ~: _I ---· ._L __ ·----~-~-------'-1· _ __,_ __ ---'-------' 

0.038 

. 038 

. 038 

. 038 

. 038 

10 

11 

0.034 

.034 

. 043 

. 033 

• 013 

Should one ";sh to study repetitions between line 2 and the lines below it, it would be m~cessury 

to consider wheel 4 as being set nt R. The results obtained for the first 15 intervals or this 

setting nre: 

T.o\DLE x 

I lntcrv.11 

I 

r I I 1! I , 

C"nrre~t 

I 

1!1mrl'1'ct I Jntun·,ll I CnrrL·t•I lncorl'N't l:1n1emil C'orrect I Incorrect I result resuit i I resu!t I regult ., result result 

r 

1-- -·-··--:·--1 

I 

I 1 0. 042 0.038 ,, 6 0.036 0. 038 11 o. 041 0.038 I 

I 2 . 033 . 038 7 . 032 . 038 12 . 030 . 038 

3 . 031 . 038 Ii 8 . 045 . 038 

~ 13 . 033 .038 

4 . 042 

I 

. 038 

II 

9 

I 

. 032 . 038 14 • 036 . 038 

5 • O·i3 . 038 10 • 040 .038 15 . 030 .038 

l 

l 

41 

These results seem to indicate that the incorrect rt>.sult is often laJ1.?er tlmn the correct 

one o.nd that c\·on in those cases where the cor1·ect one is greater, the difference is not very 

o.pprecio.ble. In other words, o. mere count of cipher repetitions cannot give o.ny information 

o.s to whether or not n. message is in o. "Z" motion. 

However, it is to be expected that the clistrihut.ion of the repetitions will vn.ry with the 

probnbility. li'or exnmple, iC the correct result for two lines is O.O·Hi, it is naturn,l to expect 

more cipher repetitions between the1n than bctweN1 two Jim's whmie probnbility is 0.030. It 

st~ems rmisonu.bll' then to multiply the number of repetitions between two lines by the corresponding probability o.nd to sum the results for nll possible pnirs of linl's. Such a procedure 

was followed in several tests and tho following results wPre obtohwd. (In most cuses the 

ncorrect settings were picked ut rnndom. The correct one is the first one listed.) 

Serin.l No. 139 ( 10 li11cs) 

lCd 

17771 

lDd 

17596 

4Sd 

17903 

Serial No. 131 (10 lines beginning as in cipber mesAage) 

4Sd 

14519 

lBd 

14597 

lEd 

14735 

Serial No. 131 (10 lines beginning at proper po1dt.ion) 

[This test assumes a knowledge of first control wheel] 

4Sd 

14108 

lAd 

13098 

lBd 

13941 

lCd 

13488 

lEd 

13929 

Serial No. 131 (17 lines beginning at proper position) 

[This test n.ssumcd tha.t there was 110 bl"e"k in the firi;1. 17 Ii nett] 

4Sd 

58491 

lEd 

58192 

FIGUBE 41 

The results obtained above do not seem very satisfuctory. In several cases, an incorrect 

setting gti.vc tt larger totnl than the correct st>tting. Even in tl1ose cn11es \\here the correct setting 

gave a la.rger result than the Iew incorrect positions used, the percentage difference was very 

small. Consider the final test., where 17 lines were used. The diffl\rcncc between the correct 

d · · · 299 

nn mcorrect settmgs is hi l · h If f. I h d 

58491 w c 118 one- a o 1 percent. t appears t o.t one cannot etermine "Z" motions by comparing the cipher repetitions between pairs of lines only. One must 

use more than just two lines. 

It is not difficult to see how this can be done. It has already been shown that for 11 given 

wheel in n. given position o. cipher repetition between two lines, at any interval whatever, can 

represent only 1 of 26 poAsible digro.phic combinations. To put it differently, if the pin.in-text 

equivnlent of the first of the two cipher letters is o.rbitm1ily assigned, the equivalent of the second 

is completely determined. In exactly the same \vn.y thl'n, if three or more like cipher letters 

appear down any one column, and a plain-text equivalent is assigned to any one of them, the 

equivalents of the others will be fixed. Naturally, tl1ese equiYalcnts \\ill vary witl1 the different 

wheels and their different settings. 
42 

To illustrate this notion, consider Serini No. 155. If this messnge is written out in lines of 

26, the cipher letter Dis found to ttppen.r five times in column 1, the first nppenmnce corresponding 

to the setting H on the correct wheel, 2 direct. The posit.ions ol the other letters D correspond 

to the settings, C, X, R, 0. Th<.'se letters H, C, X, R, 0 give the intervals between the repeated 

cipher letters, viz, 5, 5, 6, 3. If we RRsumP. thr first D to be r<"prPsPntl'd by A, then the second must 

be B, because the tables give AB ns a correct digraph for intervnl 5 when "·heel 2d is set at H. 

If the second D is suppm;ed to be B, then the third must be W because BW is n. corrl'ct digro.ph for 

interval 5 ttnd for wheel 2d set nt C. The fourth and filth lettrrs in this same wn.y become G 

and J, so that finally if the first of the set is A, the entire set is ABWGJ. This same procedure can 

be carried out by assigning enC'b of the 26 letters in turn to the first of the cipher letters D and 

as a result, the following sets of 5 lett.ers are obtained: 

I<IYMNHBTLOZQXVWGSFJDERACPU 

LDVCJONIPZYHMKWTFSQARUBXEG 

JGBAOXLEUZVMHNSFRDITYCWPQK 

PUZIFKVHTJOYNRCAXMSWDLGEBQ 

MQHXWYSARKCOBFNDVTZUGEJILP 

93 167 79 211 1116 136 194 !!J' 286 81 142 156 ISO 205 UIG 2.'iO 11!9 :M:I 1-10 246 288 308 117 2G7 203 81 

FIGURE 42 

The number n.t tho foot of each column represents the sum of the relative frequencies of 

the letters in it. The highest of these sun1s, 397, which comes from the set TIEHA is round on 

comparison ''ith the known plain text of the message to be the correct set or letters. 

Given any set of repeated cipher letters in a column, it is 11osRible in this wny to rehtte to it 

26 sets of plain-text letters, provided, of course, that the entire set of cipher letters is contained 

within ono block of 650. 

This notion cam be extended still further. Suppose a fnirly long message is being studied 

and that the original positions of the control wlu~els are kno\m. (Such 1m assumption is not 

unreasonable, since this information is obtainable from a study of "V" messages.) In sud1 a 

message one can relitte cipher letters in one blol'k of 650 to letters in other blocks by using the 

properties of the "iO:l" cycle, in which ns has already been shown a shift of one letter arises in 

both of the fixed sequences. 

To illustrate the procedure, consider Seriul No. 115, on which the proper breaks luive been 

indicated. 

I H 

1 2 a 4 s e 7 s u ro 11 u ~ H ~ w u ~ w m ~ n m 24 z ~ 

VV GQCBFHANWJIPDNACUMIIKLPLAV UW 

WU BEGCLLLVCOFQGOZABXORBOUEMF TX 

XT DUPWDEKTDVUUDMOBTWUJPDOMFX SY 

YS DXHCPWXPMKRMUKSYRPJTFLHGLK RZ 

ZR UVKKYPLVEFMFSSDJANNLWPCLPY QA 

AQ JRCEGXWGMIBAVTIGPCCVZYPLBC PB 

BP OSDKOBARZAPHONMGMKMXTJJRTD OC 

CO GIJHBYKEVLIGFZVXYAJCOLGJEZ ND 

DN PKDHNDFRZLZLWJWRGUCYKNDHMN ME 

EM HBZDTLADJITFFZVCTCKCYAKOIK LF 

FL NKZANQKJLZKMIOALFOXFZPTOTT KG 

GK 

HJ 

I H 

JG 

K F 

LE 

MD 

NC 

0 B 

p A 

Q z 

RY 

s x 

T W 

UV 

vu 

WT 

x s 

YR 

z Q 

A p 

B 0 

C N 

D M 

EL 

F K 

GJ 

HH 

I G 

J F 

KE 

LD 

MC 

NB 

0 A 

p z 

Q y 

RX 

s w 

TV 

I 

i 

l 

43 

I H 

1 2 3 4 S 6 7 S D 10 11 12 13 14 1~ 18 17 IS 19 20 21 22 23 24 25 2fi 

YFMMXYAYLLANZGXAZPQOFLERSI J H 

J FHNPGGWYKLMUHABJLORJPDAHH H I 

p QWIZRSTFYJYXZIYSTPAQGHTUG G J 

M D J L P Z K 0 B 0 C H I D S H H Q B C N C L P C S F K 

K NRRYNCXOHJDGEKIEEINEXWGVA EL 

L VEUEOSTMMEPLGZRLOIFGWSAAG D M 

w UVFSSHGUMYEFYHEDUKNPCTXFX C N 

u AWJKSAWQQWCZCPFHZXKKBUPPB B 0 

K WMHVYYBMGFLTYVLENKVMMAEEZ A p 

A VUPQASGDLVMJLODDITHOYUSPU z Q 

G NEOQVAZPXFXLQILDFRWOMWQQG YR 

u MIEPBRNZWQMUKYDCSMAAYFSER x s 

Q TKLTOWMMLRWKZDXRPBVKFGHKZ WT 

v LBEVSWUQKWKWYLVPQNDHJLLIU vu 

u JXJILYATAMQKCTSFWFOOMYHKP u v 

s FJSZKZQGJOWZIJEFECAHYFMHJ T W 

L QMYNXYZLDMVDJBSYAENHXGFJW s x 

H MAAGYKVZTLUTMUOYCIDXPZMZC RY 

K PVIFDQNXGVTBLGSQKNBGOKBBL Q z 

BYGADODXXSNFTJXYRLUUEPJQPS p A 

ODUWJKIYATKOLSBIQYHREUWIOF 0 B 

ZLQRQIXAOZLYKKXQHBGLAFNSHG NC 

V X J D G W J S W G S Q I F W C M M W I X J 0 P E 0 MD 

J G R p 'fl C Y Q Z V F D J X A K X S T K B T H B C I LE 

JEOZMANEIAOLIKABMRXVTUIWAO K F 

NDHEKPENUICTAPNTAPZMJNLYHG JG 

A TjM M K N F 0 S K F W G F T N U 0 L 0 Z D J U K R HH 

FFP D GO FI MAX 0 A QC JC EX U Z GS NF P G I 

z CEAQCXIBDNXFZUUGOWHKNFOIG F J 

T YLSOWDDF9PSIOWHSKWGNIQYSE EK 

0 CLEZNNFYCTCOHSWDPSLZZVVBO D L 

x SUCXRRAOQUBTLQRVNNYUSFEKH CM 

v LBXAIBFGBYBUZOYKGWNMJACFZ B N 

s OIRAVOYOPERADODMQAOAHIXDR A 0 

s CTRIYKZVKAKXDKPADUSAEYQRN z p 

I D C N p L J S I Z Z A B G J I R N I D Y E Z F V B y Q 

OXRHNRXKGPPLFSZMTZEDSUJFCB XR 

s VKHQUSPRJWGWHZRKMXLSIGPEL w s 

F I C F J C T N J Z T S X 0 Y A Y A P X Q P C N Q P VT 

WTQWNVOYHOJMKLBKCTNAECIUCS u u 
uu 

VT 

w s 

XR 

y Q 

z p 

A 0 

44 

I H 

1 2 3 ·1 5 6 i K II 10 II 1J 13 H In 10 17 18 1!1 20 21 22 23 21 23 26 

BEVDMYUTFSOZZDQPOCWQGYAKUJ TV 

ZVHSPPLWYUXVVWJBUYTJXBKLBG SW 

QYGYUYINFUJPLSOWGDZFMVQBPS RX 

J A V J T I Y U G L K T Q A K G P S V J 0 P S H Y F Q Y 

A L K I 0 C V P C G I P Z V X Y A R 0 A N U U L B L P Z 

FLDBXSDUGPYWVQUVJPKKMYLRLR OA 

YSUZYTQGUSMJJ NB 

FIOURE 43 

Iu column 1 of block 1, the letter G is found repeated at interval 7. ]for wheel G re\·erscd, 

sPt tLt V, this pair ran represent one of 26 possible digr:iphs, obto.ino.ble from the to.hies for tho.t 

wheel. Tlu.•sc digraphs are 

KJ PD MB FE 

BI RL DV GF 

QX us IN OM 

LA XG JP YT 

cu so vz TC 

NR HQ ZY 

WK AW EH 

FIGURE 44 

Let us rcrnll just how thrst' digraphs \Vere obtained. Suppose th~t the first of the cipher 

letters G ho.cl represented the p!n.in-te:x:t letter E. Then '\ith wheel 6 reversed, set o.t V, the 

current would have traversed the following pa.th: 

RFS + ______ Y L V R Z X C P F 0 I Q A M J B N S E K D G H T U W 

I N.AL6 _____ V U T S R Q P 0 N M L K J I H G F E D C B A Z Y X W 

I ... ! 

~IALGr ____ N D R T H L B I J Z E Q X S 0 W F P U K G C Y V M A 

+ 

[4 intervening wheels] 

I 

LFS_ -- - - - - T E G D N S X U P Q Y V H A M B K R F J L Z I W 0 C ~ . 

FIGURE 45 

Just what po.th is trnversed through the first four wheels is of no concern since those wheels 

remain fixed down the column. 

L 

45 

To see who.t plain-te.""tt letter the second G represents, it is first necessary to shift the last 

wheel to the setting C, 7 places removed from V. Then in this position the strips appear as 

follows: 

+ RFS_ - - - - - Y L V R Z X C P F 0 I Q A M J B N S E K D G H T U W 

I NAL6 _____ C B A Z Y X W V U T S R Q P 0 N M L K J I H G F E D 

I I 

MAL6r ____ K G C Y V M A N D R T H L B I J Z E Q X S 0 W F P U 

+ 

(4 intervening wheels] 

LFS _______ T E b D N S X U P Q Y V H A M B K R F J L Z I W 0 C 

+ 

FIGUBlll 46 

The last four wbeels are in identically the so.me position as before. Consequently, if the current 

emerged at G, it must have followed the so.me po.th as before o.nd must have come from G on 

CW6r. G on NAL6 is opposite H on RFS. It is thus seen that the second of the cipher letters 

represents H. This result cl1ecks with the results o.s shown in the table. 

Suppose now that the letters in the second block o.re being considered. Since 703 leaves a 

remainder of 1 on being divided by 26, it is necessary to relate the letters of column 1 in the first 

block to those of column 2 in the second block. Moreover, as a result of the shift in the fu::ed 

sequences, the letter G of block 1 must be related to D in block 2. The second oolumn of block 2 

is found to contain tho letter D three times. The second of the letters G having been supposed 

to be on line C, the first D will be on line K. For this line, the setting of the strips becomes 

+ RFS ______ Y L V R Z X C P F 0 I Q A M J B N S E K D G H T U W 

I NAL6 _____ K J I H G F E D C B A Z Y X W V U T S R Q P 0 N M L 

I I 

MAL6r ____ Q X S 0 W F P U K G C Y V M A N D R T H L B I J Z E 

+ 

[4 lntervenlng wheels] 

- . . I - . 

LFS ___ -·-- T E G D N S X U P Q Y V H A M B K R F J L Z I W 0 C 

-~ 

FIGUBll '7 

In this setting the first four wheels ii.re in the same position as before, but ho.ve been shifted 

one place as a unit relative to the LFS. The path of the current to D on the LFS from MAL6r 

will be the path previously followed to G on LFS from MAL6r but will be shifted down one place 

along its entire length. This means that the current to D on LFS must have come from S on 

MAL6r and therefore from Eon RFS. D0 on line C must therefore represent EP. 

The equivalents of the remaining D.'s in column 2 block 2 can now be obtained without 

difficulty. 

'11838-315--4 
46 

If the cipher letter N appeared in column 3 of block 3, a similar procedure to the one described above would determine the corresponding plain-text letters. Here again a shift of the 

fixed sequences must be introduced in the so.me way as before. Tb.is method of relating letters 

in each of two or three blocks of 650 makes it possible to study larger sets of letters thn.11 would 

otherwise be obtained. For example, in Serio.I No. 115, more than 25 sets of such letters were 

found where each set contained at leo.st 5 letters. In a message of but one block, tho occurrence of even four or five such sets is rare. 

For eo.ch assumption as to the identity o.nd origino.l setting of the fifth wheel, 26 combinations of plain-text letters can be assigned to each set. For, by the above procedure, after any 

one of the cipher letters in such o. set ho.s been arbitrarily assigned a plain-text value, the equivo.lents of all the others can be determined. To illustrate, consider the cipher letters G, D, and 

Nin columns 16, 17, and 18 of blocks 1, 2, and 3, respectively. The total number of occurrences 

of these letters is 7 and the sets of plain-text letters obtained on the assumption that the fifth 

wheel is CW6r at V are given below: 

B 

c 

N 

Q 

R 

M 

Q 

GSPAHXMOZQTVEKYNDFIUJLBCRW 

EFMTCJIXAURKDLSGOQWBV~PZYH 

JZXAVCDHIOMLEBQPRKUFSWGNTO 

BXOTWMRNZGEJICHLQDVUKYASPF 

CIUYJZSXHKBQPTVAGRWDLMEFON 

HFMRZQLXKGOWAYSJICVETPNUDB 

FBXOTWMRNZGEJICHLQDVUKYASP 

liOI HI 4%1 '811 

Fiaun11 48.-Columns 16, 17, 18-GDH 

Of these sets, the combination ATATYRO represents the greatest total frequency, viz, 502. On 

reference to the known plain text, this set is found to be the correct set. 

It now appears that for a correct assumption of the fifth wheel, the proper letters will be 

found from a set of 26 possibilities by a summation of frequencies. That the co~ct letters 

c1Jrrespond to tho greatest sum is substantiated by the fact that only one exception was found 

in more than ten tests of this nature. Hence, it may be assumed that in each group of 26 sets 

the column giving the greatest sum is the only one to be considered. Suppose such a procedure 

were carried out for every set containing at least 5 letters, not only for the correct setting but 

also for all incorrect settings. How would the grand .total of the frequencies of all the sets in 

the correct case compare with a.Ii incorrect case? If the former should be the greatest of all 

or among the greatest, one would then have a method of testing unknown messages for "Z" 

motions. Moreover, there is no question about the fact that such will be the case for messqes which are sufficiently long. Unfortunately, this is not true for a message of the size of 

• 

47 

Serial No. 115. A series of tests carried out on the latter message gave negative results as 

follows: 

TABLm XI 

Cipher Jetten Cohmml Carnot llllllll'feet 

•tUn1 •t&IDK 

GDH 16 502 560 

ZD 17 417 471 

HAii 19 383 415 

FJL 26 468 436 

EGD 25 455 883 

KRF 7 210 414 

JLZ 19 308 505 

2,743 3,184 

Unless one can obtain longer messages, the methods herein discussed will not permit the discovery of "Z" messages whose plain text is unknown. Some other plan of attack will have 

to be devised for use in such cases. 
REF ID:A70315 

APPENDIX I 

INSTRUCTIONS 

TEST OF HCM 

' 

APRIL 1, 1932. 

1. There are four sets of variables in the HCM which must be adjusted before a message 

can be enciphered or deciphered, namely: 

(a) Code-wheel arrangement 

(b) Code-wheel lineup 

(c) Control-wheel setting 

(d) Ratchet action 

The code-wheel wirings and end wirings are semipermanent, but remain unchanged for 

long periods of time. They will remain :fixed for this test. 

2. The method by which the above listed variable adjustments are set is as follows: 

(a) Each message contains an extemal. indicator which shows, by reference to a printed 

cipher or list for the date in question, _the initial key and hence the set-up of the HCM. It 

al.so shows which one of the six cipher wheels is to be omitted from consideration for that day. 

Ordinarily, the initial key would change daily, but for this test it will remain the same throughout. 

(b) In each message, a message indicator follows the external indicator. With the HCM 

set up as determined by the external indicator, the message indicator (5 letters) is enciphered 

on the HCM. This encipherment produces the message key. By the use of a simple code, 

the message key determines an entire new set-up for the HCM. The set-up thus obtained is me.de 

and the encipherment or decipherment of the message proper now begins. 

The message indicator, and therefore the message key, changes ltith every message. 

(c) The actual set-up of the four variables is derived from the key as follows: 

(1) Oods-'IDheel arrangemmt.-If the key were YSRIP, for example, the order of the wheels 

would be 5, 4, 3, 1, 2. A table in the cipher shows whether each wheel is to be used in the 

direct or reverse position. If the table were 

Direct ______ A B C D E F G H I J K L M 

Reversed ____ N 0 P Q R S T U V W X Y Z 

the code-wheel arrangement would be 5R, 4R, 3R, ID, 2R, sinr.e Y, S, R, and Pin the table show 

that the wheels are to be used in the reversed position, and I in table shows that its wheel is to 

be used in the direct position. The wheflls are then placed in the HCM in that order and 

position, from left to right. 

(2) Oode-whee/, line-up.-The key itself is used as the line-up setting of the code wheels. 

Thus, wheel 5R, which is now installed as the left-hfllld wheel, is set with the Y (on the whefll 

periphery) against the bench mark; wheel 4R is set with Sage.inst the bench mark, etc. 

(3) Oomrol-wheel setting.-The first two letters of the key a.re used e.s the control-wheel 

setting. Thus, the left-hand control wheel is set e.t Y; t.he right-hand wheel at S. 

(49) 
(4) Balchd aclioo.-The arrangement of the code wheels has alree.dy been derived as SR 

4R, 3R, 1D, 2R. The first two digits, 5 and 4, are applied to a table in the cipher to find th~ ratchet-action setting. Such a table would be 

Second digit 

1 2 3 4 5 6 

I l I 

21-Jt.---l·-i---

1 

! s 1--- 1---~~~.~~!·~--~ 

s 

6 

The setting of the ratchet action from the table is ACY. 

APPENDIX II 

BASIC CIPHER-TEXT SEQUENCES 

Setting 

Z VMGQIHEKYWFZXNUJSDPBRTLACO 

Y CHBDYWAGRVOJIUSPLXNQKFEZMT 

X ETAKNVOMDFHCLWPXQZUSYRJGIB 

W KGEMRSHCBNJATZOQUYIPXVFLDW 

V ORDGBFXATKSLMEICYPVWQUHJZN 

U SCFNDKJUMERXZBGWTVQHOYPALI 

T WXTJSNRLPBGFUIKDOEHYACVQMZ 

B IOUELXSFZQKDJPWRNCGAVMTHYB 

B KWCPGZUXJIYRNLQOFSTDMHBEAV 

Q HROTQDIPULWVFSZYCJXENBAKGM 

P BAFCEYNWQPZOHJXIVTLUGSKMRD 

0 NKMJTGVSOYQICALUWHEZPDXRBF 

N JSRBLEDHXCVYWTMZPOAGIQNUFK 

K RLXFKZGNAUTHVOEBIQCMDWYSPJ 

L LFZUJRIDSMPEAHCGKWYTBNOVXQ 

K YZJIPLFWNXBQGMATDROVEKSCHU 

1 PVILWQZJOSUKYDBMENFCHGRXTA 

I MQHWZOYILCXPRVNKBGSJTADFUE 

B GBYAOICVWZTUQFHSRKDXLEMNJP 

G Q.DKVMCWTHOIEPYJAXFRNUZGBSL 

P ZYNRHBTO.EACW.GQJLMUJ,SPIDKX 

B UIVSFAKECGMTODYHZBPLJXQWNR 

D ·FPWHXJMRGTDBECNVAIKQZLUYOS 

0 XJQOAULBFDENKGTSHMWRYIZPVC 

B TULYCMPZKJNGSRDEXABOFVWIQH 

A AEPZVTBQIRLSDXFNGUMKCJHOWY 

BABIC ClPBllB-Hrl' Bl!IQUJINClll l'OB CWl DIBllCT 

(11) 
52 53 

Setting Setting 

z VFIXNHWQDOKECMALGYTBPJSUZR z UFIZRMYJNOQEHBVAXSDCGTWKPL 

y FHJWUSAOYNCRGTBMZDVEKQLXPI y ZPJWIFBVLSCYGAKHMUXNTDEORQ 

:x WJALOPXMCVSTFDEKBINHGRYZUQ :x YIQLOWJKHZXTVDMRABPUSENGCF 

w YOLMZCQUBTHXEJNGRKWSADFVIP w JVWYZCOLRAIUEHNBFMKQPXGSDT 

v QVCZBITYPKEAUGLSDFROXMNJHW v ELHOVITCZFMWPGASKJBRYQUDXN 

u OYHTIKWEVQRGMPDZXNJFCUBSLA u SGZACHWETIJBOQDMXRLKFVYPNU 

T MCVAEWROGHYFDBQNIUSLJTPKXZ T PXDIMTAOGEWLKCYNBUFZRJHVQS 

s IBTHMGOFCDAVJNKYSWPXZLEQRU B XQUNWBEMCDGOZRTVSKPJIFLAHY 

R PWKEABDCJTNMHLSRVXOQUIZGYF B. VUYPSOKGBTNDCIFEHXRQLWJZMA 

Q JQORGMKNTLESBAZXFHUCYPWIDV Q MHPVQXCRDKESNTWJGAUFYZOLIB 

p HLYCFDBRSEZGXKMIUJAPTVQOWN p KBAQHYUTFNRGXSEOLDMPJVICZW 

0 SAZVTJNKFXGIDURBWPLMQEHYCO 0 ORKMYAVPEJSFDUXGCZNBQLHWTI 

N CXMIHELSRJUDWNPFKOQZBYGAVT 11 WCFRBVMHQGLXJNPUDTISKYZAOE 

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B PEUYWANCKRVLSDQBXGOZFHJMIT B MBSUZCRJKTFPENOXGDQIHYLVAW 

l!' GPVOMSTRFHZXNYKUDCIJALBWEQ l!' KXPITFLREJQGSCUDNYWAVZHMOB 

G QHCBXEFJAIUSVRPNTWLMZKOGYD G U Q I E J Z F G LY D X T P N S V 0 II H I A B C KR. 

H ATKUGJLMWPXHFQSEOZBIRCDVNY H YOGLIJDZVNUEQSXHCBAWMKTRFP 

I ERPDLZBOQUAJYXGCIKWFTNHSVM I CDZWLNIHSPGYXUATKllOBREFJQV 

l FQNZIKCYPMLVUDTWROJESAXHBG l NIOZSWAXQDVUPllERBCKFGJLYHT 

K YSIWRTVQBZHPNEOFCLGXMUAKDJ K WCIXOMUYNHPQBGFKTRJDLZVAES 

L XWOFEHYKIAQSGCJTZDUBPllRNLV L TWUCBPVSAQYKDJREFLNZIHMGXO 

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• TLDMHFOBVUNEZGWSQRYKJXIAPC • QERYAUBVHFSZJDLIXWOllKNPTGC 

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p SKMLTRAQXDWNCUVJHFZPOBYEGI p JHBQRAMLUWZSIOPCTKFXYGNEVD 

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8 WDLKHQXTUGYMIBZOVEFANSCPJR s HLKRWYTOPCEVGDJZQASUNMXIBF 

T NZRAYUEPDVBWKICHGJMSXTQLFO T ZRFOVECQTGHDNLIYMXPSBUWKJA 

u IFMVPGQNHKORWTADLBXUEYZJCS u FJCHGTYEDANSZWVBUQXKPORLllI 

v JBHQDYSARCFO~llNZKUPGVILTXW v LTADEVGNMSXIOHKPYURQCFZBWJ 

w KAYNVXMFTJCGBSIRPQDHWZEUOL w EMNGHDSBXUWCARQVPFYTJIKOLZ 

x MVSHUBJELTDKXWFQYNAOIGPCZR x BSDANXKUPOTMFYHQJVELWRCZIG 

y HXAPKLGZENRUOJYVSllCWDQTIFB y XNMSURPQCEBJVAYLHGZOFTIWDK 

z UllQRZDIGSFPCLVHXBTONYEWJKA z SBXPFQYTGKLHllVZADICJEWONRU 

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60 61 

Settl111 lldUlll 

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B YENRBQHKSXLWZFVIPTOUGM~JDA B SFXIRZVLEUPHKTGWCJNMYDOQAB 

c GSFKYARXUZOIJHWQECPDBTLNMV a JUWFIHZGPQAREDOTLSBVNCYMKX 

D XJRVMFUPICWLAOYGTQNKEZSBHD D POJIAIDQYMFGNCEZXKHSTVBRUL 

B LFHBJPQITOZMCVDEYSRGIXKANU B CLOMWNYVBJDSTGIURAXEHKFPZQ 

l!' JAKLQYOECIBTHNGVXFDWURMSPZ .. ZCBOSVHKLNXEDWPFMUGARJQIYT 

G MRZYVCGTWKEASDHUJNOPFBXQIL G TKCXHARZSUGNOQJBPDMFLYWVEI 

B FIVHTDEORGMXNAPLSCQJKUYWZ·s· B RTUAMFIXPDSCYLKQNBJZVOHGWE 

I WHAENGCFDBUSMQZXTYLRPVOIKJ" I EPMBJWUQNXTVZRYSKLIHCADOGF 

l AMGSDTJNKPXBYIUEVZFQHCWRLO l QBKLOPYSUEHIFVXRZWATMNCDJG 

K BDXNELSRQUKVWPGHIJYATOFZCM K KRZCQVXPGAWJHUFIOMEBSTNLDY 

L NUSGZXFYPRHOQDAWLVMECJITBK L FITYHUQDMOLAPJWCBGKXESZNVR 

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0 SOQZAVLBEHXKTWMRNGICDFJUYP 0 ABYHXREIKVITGFSJQNPOUMLZCD 

p CYIMHZKGAUREOBFSDWTNJLPVQX .p KVAUFGORHIEDJXLYSQCPBZITNM 

Q VWBAIRDMPFGCKJXNOESLZQHYUT Q HMPJDCFAOGNLUZVXYTQKIWESBR 

B OKMWFNBQJDTRLUSCGXZIYAVPEH B BQLNTJMCDSZPIHUVEYRWOGXKFA 

s RBOJSKYLNEFZPXTDUIWVMHQGAC 8 YZSELBTNXIQWAPHGVFOCDURJMK 

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u TZUFHIXDLWYPGSQOCAKMVNBEJR 'U UDIRGXPOVCBYMNALTESQJZKFHW 

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BABIC ml'DB-TBXT s11qu11xc11s l'OB CW6 UVllBBllD 

APPENDIX III 

FIRST-INTERVAL DATA-CIPHER-TEXT RELATIONSmPs 

TABLll A 

A 

B 10 2T :5Z 5V 5T lY 211 :5F 40 4R 4Y 

v~~a~~~~~~~~u~~~e~fil 

Y 2I :5I 4V 4N 4D 6X 6F 6P 6T lA U 2L 2P :5L 5A 

QIDft~~~~~lP~ll~~~~~~ 

P 5K 2A 2Z mi 4P 4Z 5P 6R 

U 1 V lB 2G 2E 40 4P lB 2S :SS 4W 5E 60 

X 2Y 2W 20 4C 5A :5R :5S 4G .§L 

B lM :5F 6I 2C ,21 g§ ~ :5X 4E 6X 

•~~~~9m&~~~~fil~~~~ 

D lS ~ 2J 2F ~ :5V :SQ :5E 4E lE lH il §Q §[ 

G 1RlLlF2V2R:5G406Z6Q6G~4I5W6I 

111 lX lJ lI :5T 4L 5Z 5Y 5N 6N lT 2H g_ ~ ~ 611 

T 10 2H 5R 5I 6R ![ ~ ~ §f 

0 lN lC 2B 2A ll 10 2X 4A 4D .§g 5V §& 6G 

ou~a4Ree~~~~~~4L~~g.~9 

W 4J6J2G~m!6H 

I 2C :50 :5N 5G 6B lN lR !Y 2D 2R :5T 

Z lZ 20 :5S :5C 4Z 5Q 50 5C 60 60 1:1 g.[ 50 6J 6N 

L lW lG 2X 2P :5K 4Q 5W 5H 2I 20 gg :50 5N 6Y 

1 lE 2K 50 611 6C §g 

P~:5X9~~~4GOOIDW~~94C~~~~~ 

B :5J :5A 4S 4Z l,K 2K ~ 4F 4N 40 §I §1l 

K~~~~~~~~~~:5G~~~3~ 

B 1K2Z:5R3H4W5X6V!L.§~~~5H§§ 

)I[ 411 

Underlined type denotea wheela in reversed poaltlons. 

(63) 
64 

TABLll H 

A 4N 

B 

V 1E2U3A5W5Ull~3E4N~4X 

Y lU lI 18 3P 3C 4I 5T 5M 5K 5F 6M ll g§ 2V :5X ~ 4S 6S 

Q 2J 3J 4W 40 4E 6Y 6G 6Q 6U lZ lI 2K 20 3K §Z 

P~~~~~~~~~llDg~~&a 

U 5L 2Z 2Y 3M 40 g 50 §g 

X lW lC 2H 2F 4V 4Q lA 2I ~ 4V §Q .§12 

S 2Z2X2P4058~3R~6K 

1' 1N3G6J2820gs3T3W~§! 

D~~~~6X~e~~3U~~~~~~ 

G lT 20 2K 2G 3Z 3W 3R 3F 4F lQ lG 4X "68 §I 

B lS lM lG 21 2S 3H 4P 6A 6R 6H 31 4H .§! 6H 

T 1 Y lK lJ 3U 4M 5A 5Z 50 60 .!§ 2G 3H ~ 5I 6L 

0 lP 2I 5S 5J 6S lE ~ 4R 60 

0 10 10 2C 2B lH lN 2W ~ ~ §f 5U 6F 6Z 

Wll~~4S4G~~llW~~~~~~~6N~ 

t~~~e~oo · 

Z 20 :SV 30 ~ 6C lM !Q lT 2C g.Q 3S 

L lA 2V 3T 30 4A 5R 5E 50 6P 6E 11' 2E 5T 6I 6M 

l lX lH 2Y 2Q 3L 4R 5X 5I 2H 2N 2P :5N §II -~ 

J!' lF 2L 5V 6N 6D 6P 

K2E~:5X3M~~~~WIBll~~~$3~3~ 

K 3K 38 4T 4A lJ 2J 3P 4E ~ 4T 60 6T 

Ba~a211~3N~~~~~~3~sg 

M: lL 2A 3S 3I 4X 5Y 6W lK 2A ~ 30 4I 5G 6A 

Underlined type denotes wheels in reveraed positions. 

65 

TABLll v 

A lM 28 3T 3J 4Y 5Z 6X l.!l 2Z 38 3N ~ 5F 6Z 

B 40 

v 

Y lF 2V 38 5X 5V lW 2K 30 4M 4P 4W 

Q 1 V lJ lC 3Q 3D ~ 5U 5N 5L ~ 6N lX 2R 2U 31 4R ~ 6R 

P 2K m< 4X 4P 4F 6Z 6H 6R ~ lY lH 2J 2N 3J 5Y 

UH~4M~~6Mll~~W~84F~3S 

X 5112YgJ;_m.4N~§H§f 

S lX 10 2I 2G 4W 4R lZ 2H 3H ~ §Q §I 

JI 2A 2Y 2Q 4E 5C .m! ~ ~ ~ 

D 10 3H ~ 2A 2C g.Q 3S 3V ~ ~ 

G~9~~~6J~~B~~~9~~g 

B lU 2P 2L 2H ~ 3X ~ 3G 4G lC lF ~ §A §12 

T lT lN lH 2X 2T :SI 4Q e 6S 6I 3I ~ 5U 6G 

0 1ZlLlK:SV4N585A5P6Pl82F~j!§H§K 

0 lQ 2J 5T 5K 6T lQ • ~ 6N 

W lP lE 20 2C lG lM 2V 4Y ~ .§Q 5T ~ §I 

1uro~ft~4D6U~ll~~~~ft~96M6U 

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L 2E 31 3P 5I 6D ~ lP lS 28 2P 3R 

l 18 2W 3U 3E 4B 5S 5F 5E 6Q 6F lV m §.§ .§li ma 

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K lG 211 5W 60 6E 60 

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·. · B · :SL :SC 4U 4B lI 2I 30 ~ ~ 4S 6C 6S 

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Underlined type denotes wheela In reversed poaJtiona. 
66 

TABLll y 

All~~ro~~4B~~~~3J~~~~ 

H lN 2C 3U 3K 4Z 5A SY lI 2Y 3A :5M 4G ~ §.! 

V 4P 

y 

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8 5N2X2W~~~.§l§Q 

lf lY lE 2J 2H 4X 4S lY 2G 3G ~ §ll §A 

D 28 2Z 2R 4F 50 30 ~ 40 SI 

G lP 3I SL 2Z 28 2P 3R 3U 48 6U 

B~~file~~002R~~3W~S9~6W 

T lV 2Q 2M 2I 38 3Y 3T 3H 4H ll ll 4V SZ SC 

0 lU 10 lI 2Y 2U 3J 4R SC ST 6J 3H 4F 5T SF 

0 lA lM lL 3W 40 5C 58 5Q SQ 1Q ~ ~ 4H 5G 6J 

W lR 2K 5U 5L 6U lC 4J 4P 611 

I lQ lF 2E 20 lF 1L 2U ~ ~ 5N 55 6X SO 

Z~~4A~~~~ID~3Y~~~~5H~~~ 

L 4MSM204N5A6E 

l 2F 3X 3Q ~ 6E lK 10 lR 2A 20 ~ 

Jr lC 2X 3V 3F 4C 5T 5G 5F 6R 6G lU 2C 5R SG ~ 

B. lZ lJ 2A 25 3N 4T 5Z 5K 2F 2L 2N 3L 5K SV 

K 1H2N5XSPSF§!! 

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M: 3M ~ 4V 4C lH 2H 3N 4C 4K 4R e SR 

Underlined type denotes wheels in reversed positions. 

67 

TABLll Q 

. A 3N 3E 4W 4D J& 2G :5M 4B ~ ~ §A .§Q 

HWll~~~~~~fil9~~~~~6G 

V 10 20 3V 3L 4A 58 SZ .!ti gx ~ 3L 4F 50 6X 

y 4Q 

Q 

P lH 2X 30 5Z 5X lU 2I 38 4K 4N 4U 

UllR~~~~9~~fil~!!~~3U4X~~ 

X 2M 311 4Z 4R 4H 68 6J 6T" 6X. lW lF 2H 2L 3H 5W 

8ll4X~~~001I~}L~2J~4D5Hfil~ 

lf 50 2W 2V 3J ~ ~ §I. 6N 

D lZ lF 2K 2I 4Y 4T lX 2F 3F 4S 5A SZ 

G 2C 2A 25 4G 5E .mi 30 4C SH 

B lQ 3J 6M 2Y 2A 20 ~ 3T ~ 6T 

T~~~~6A~6E~3Y3R3V~~~6R~ 

0 lW 2R 2N 2J 3C 3Z 3U 3I 4I lA 10 4U SY S8 .. ----- 0 lV lP lJ 2Z.2V :5IC 4S 00 6U ~-3G C 55 6E 

W 18 lN 111 3X 4P 50 5C 5R 6R lP 20 3E 4G 5F §! 

I 15 2L 5V. 5M 6V 18 4I 40 . SL 

Z lR lG 2F 2E lE !K ~ 4W 4Z 511.5R 6W 6C 

L lC 2Q 48 4V 4J 4F SW lC lR 3X ~ ~ 4H 4R 5G 5U SK S5 

l.. 4N ~ 2C ~ sz· §12 

Jr 2G 3Y 3R 5K SF lJ lN !Q 2Z 2N ~p 

B. 10 2Y 3W 3G 4D 5U 5H 5<,; S5 ~ lT § S 6F 6J 

K IA lK 28 2T'30 4U 5A 5L § 2K 211 3K 5J SU 

B lI 20 5Y SQ 6G 611 

M:2H~~~3H4M4K~~u102R~~~~~~oo 

Underlined type denotes wheels in revened positions. 
68 

TABLll p 

A~~~~~4N~~llllll~~4X~a~~~ 

B 303F4X4E!f2F3L4A4I~~~ 

v~w~~~~~M6J~9~9fil3~ 

Y lP 2E 3W 3M 4B SC 6A !Q 2W ~ 3K 4E 5C 6W 

Q 4R 

p 

U' lI 2Y 3E 5A 5Y lT §I 3A 4J 411 4T 

Xll~~3T3G411~~~fil~WOO~~G~§Q 

s 2N 3N 4A 4S 4I SC 6K au SY lV lE gg 2K ~ 5V 

•u~e9~~IBalln~n~~mm 

D 5P2V2Ug,~4U5K611 

G lA lG 2L 2J 4Z 4U lW 2E 3E 4R 5Z §I 

B 2D 28 2T ~ 5F 3M 3N 4B 6G 

T 1R3K6Ngx2Z~~3S~6S 

02X~~6D6B6116F~~~~~~~~~ 

0 lX 2S 20 2K 3D 3A 3V ~ 4J JZi 10 ~ §I §A 

w lW lQ lK 2A 2W 3L 4T 6E av 6L ~ ~ 5R §12 

I lC 10 lN 3Y 4Q 5E 5D 5S 6S 10 .2.Q ~ 4F 5E 6H 

z lT 211 5W 5N 6W M 41 4N §K 

L lS lH 2G 2F lD .U 2§ 4V 4Y 5L §Q §! §I 

lW~~@~~~IB~D~~~~~~~g 

P 4060~4L5Y6C 

B 2H 3Z 3S 5L 6G ll 111 lP 2Y 211 30 

K lE 2Z 3X ~ 4E 5V 5I 5H ST SI lS g& 5P 6E §1 

B lB lL 2C 2U 3P 4V 58 5M 2D 2J 2L ~ 5I 6T 

K 1J2P5Z~6H§L 

Underlined type denotes wheela in reveraed position&. 

69 

T.t.BU u 

A lK 2Q 5A 6S 6I §K 

B2J~~~~40~6Allll~~~il3~3~611 

V 3P 3G 4Y 4F ll ii ~ ~ ~ !Q .§! §Q 

y~~~~3V~C~~~~~~5I~g 

Q lQ 2F 3X 3N 4C 5D 6B .u: ii B ~ ~ 58 §!l 

p 4S 

U' 

X lJ2Z3F585ZlS2G3Z~~~ 

su~ro~~4N~~~~~ll~~~~~~ 

R 20 30 4B 4T 4J 6D 6L 6V 6Z lll.112 m: ~ ~ .§Jl 

n~~~-~-~~~~w~m§•~~a 

G 5Q§lgi:ml~~al.§k 

B 181H2112K4A4V1,!2D3D~m:§I. 

T 2E2C2U4I5G3L3~§l 

0 1S3L60212Y21130~il§B 

Oll5V~6E~~~m3~~~3~~ll 

W lY 2T 2P 2L 3E 3B 31'1 3K 4K lY ll ~ §I §Z 

I lX lR lL 2B 2X 311 4U 6F 6W 611 ~ ~ S §Q 

Z lD lP 10 3Z 4R 15F 5E 5T 6T lH &I ,& ~ §D mi 

L lU 2N 5J 50 6X lZ ~ 411 §l. 

1 lT lI 2ff 2G ~ ll 2R 4U ~ ~ §f fill §A 

P~2S~4X&~~MR~~~~~3~~~ 

B 4P6P&l.§l§ll 

)[ 2I 3A 3T 511 6H lH .lL 10 2X 2L 3N 

B lF 2A 3Y 3I 4F 51' 5J 5I 6U 6J lR ii. 50 m! §H 

JI lC lM 2ll 2V 3Q 41' 5C 5N ~ ll ii ~ §Ii ~ 

Underlined type denot. wbeela in ravened poaitiona. 
70 

TA.BL• x 

A 10 lN 2E 2W 3R 4X 50 50 28 2H 2J ml ~ §B 

B lL 2R 58 6T 6J 6J 

V2K2S~3D3Ke~6Bll~~~~~~~~s~ 

Y 3Q 3H 4Z 4G 10 20 3J ~ ~ ~ 6X 6N 

Qllll2X2S9~esv~~~~~5H~ro 

P lR 2G 3Y 30 4D 5E 6C lE 2U 9 g_ 4C 5A fill 

U 4T 

x 

S ·1K·2A 3G 5C 5A !B g[ 3Y 4H 4K ~ 

JI lA 10.11:13V 3I 40 5Z 5S"5Q 5L 6S. lS 2M if m·4u 4M.6M 

D 2P 3P 4C 4U 4K 6E 6M 6W 6A ll lC 2E 2I ~ §I 

G~~4RMM~~~ll~~~~~~~ 

B 5R 2T 2S 3G 4I 4S· 5I §K 

T lC lI 2N 2L 4B 4W lU ~ 3C 4P 5X·6W 

0 2F202V4J5H~3L~§I 

0 lT 311 6P 2V _gx 2L 3N· ~ 41· .§;. 

w~99~rooo~~3V~~~9ssooss 

I lZ 2U 2Q. 2M. 3F 3C 3X 3L 4L ll li. ~ §! 6Y. 

Z 1 Y lS lM 2C 2Y 3N 4V 6G 6X 6N 3D ~ §f .§D 

L lE lQ lP 3A 4S 5G 5F 5U 6U .l! 2A 3B ~ §Q 6F 

1 lV 20 5Y 5P 6Y !I 4F ~ 6I 

P ·. lU lJ 2I 2H ll lH gg 4T 4W 5J 50 6T 6Z 

•~~~~4M~~ll~~ga4E~~~~~ 

K 4Q 6Q &i 4J 51' 6A 

B 2J 38 3U 5N 6I 1J! 1.1 ll &!( ,2K 311 

K lG 2B 3Z 3J 4G 5X 5K 5J 6V 6K !Q 2Y §Ii .§1' 6G 

Underlined type denotes wheels in ravened positions. 

71 

TABLB 8 

A lH 2C 3A 3K 4H 5Y 5L 5K 6W ~ lP 2X §II .§D §f 

B lE 10 ~ 2X 3S 4Y 5E SP 2A 2G ll 3G ~ §Q · 

V 1M2S5C6U6K6I 

Y~ft~~3L4Q~~~lli1.12N~4U~5X~~§K 

Q 3R3I~4H!Q2Cg,~~4116W611 

Pllllft~~~4G9611~g~M~5JOO 

u lS 2H 3Z 3P 4E 5F ro m· 2T 3V 3H ~ §Z n 

x 4U 

s 

JI 1L2B3H5058!Q2Eg4G4J~ 

D~~ll93Je~M.99~lla~~ft4L~ 

G 2Q 3Q 4D 4V 4L 6F 6N 6X 6B lS 18 2D 2H 30· §§ 

BW4B4S~~6S~ll~~g[&g4Z~~~ 

T 5S2S2R~4H4R§H§!Z 

0 lD lJ 20 211 4C 4X lT ~ 3B ~ 3 6V 

0 ~ 2E 21f 4K 5I ~ _ms; 4Y ro 

W lU 3N 6Q 2U 21 2K 311 ~ 4W §f 

I2A5X~6G~~~211~3N~-~~~~~ 

Z lA2V2R2N3G3D3Y3114MlJ!lZ~6U6X 

L lZ 1 T lN 2D 2Z 30 41' 6H 6Y 60 3C i& §Q 6A 

1 lF lR lQ 3B 4T 5H ~ 5V 6V ~ 2Z 3A 4C 58 ~ 

P lW 2P 5Z 5Q 6Z ,II ~ 4K 6H 

B 1 V lK 2J 2I lA lG 2P 4S 4V 5I §I 6S 6Y 

xromo4Z~4J6All~~9~~~~S6GOO 

B 4R~2Yjl5V6Z 

K 2K3C3V506J!f:~lM2V2J3L 

Underlined t,ype denote& wheels in reversed positions. 
72 

Tau N 

A 2L 3D 31 5P 6K lE lI lL 2U 2I 3K 

B lI 2D :5B 3L 4I 5Z 5M l5L 6X 611 10 a! ,m.· §A 6IE 

V lF lP 2G 2Y 3T 4Z 5F 5Q 2Z 2F 2H ~ 5E 6P 

'!' lN 2T 5D 6V 6L 6H 

Q2M2U~~~~•mw~wg~ft~9~~~ 

P 3S3J4B4I!la1:5H~~~6V6L 

UUll~3U~~~~~~3X~ss~·~g 

X lT 2I 3A 3Q 4F 5G 6E lQ .&§ 3U 3G 4A 5Y 6S 

8 4V 

11 

J) 1 .. 20 :SX 5E 5C lf 2D 3W 4P' ~ ~ 

G lC lQ lJ 3X 3K 4Q 58 5U 5S 5N 6U !Q 2K 2N 3P ~ ~ §K 

B 2R3R4E4W4116G606Y6C1Jii!2CgQ3C.2 

TID~ft~~~rornro~a~g~®~ 

0 5T.2BiQ~4G~mi§l 

0 lE lK 2P 2N 4D 4Y lS 2A ~ 4N §! fill 

W 2H 2F 2X 4L 5J 3I 3J 4X 6C 

I lV 30 6R tt 2V 2J. 31. 30 4V 60 

Z 28 5Y 50 6H 6F 6Q 6J m.. 3T· _a ~ 5Z 5IC ,S 611. §Q 

L lB 21 2S 20 31i ~ 3i 3N 4N· lV lY 4P 8T 6W 

l lA 10 10 2E 2A 3P 4X ~I 6Z 6P :5B 4Z 5N 6Z 

.. lG lS lR 3C 4U 5I 5H 51 61 !K gx 3Z ~ a m 

B 1X2Q5A5R6Al!~~§g 

I: 11 lL 2K 2.J .lZ D: 2Q • ~ ml ml 6R 6X 

Blli~~4A40~~~~~~g~-a~-~ 

JI 4S6S,21~§.Y§1: 

Underlined t;ype denotes wheels In ravened poaitiona. 

73. 

A· 4T f1r .D ~ . .§% §1 

B 2M3E3X5Q6LlD1HlK2T2H3J 

V lJ 2E 3C 311 4J 5A 5H 511 6Y 6N lN g! 5K 6Z. 6D 

Y lG lQ 2H ~ 30.41 5G 5R 2Y 2E gg 3&: 5D 60 

Q 10 20 5E 6W 611 §i 

P2N:5H~~3N4S~~lllllI~~4S~~g.9fil 

u .3'1' 3K.4C 4J u 26 ~ ~ ~ 4K' 6U §K 

Xllll2A~3Z~~~~~·3~~~~6A 

8 10 2J 3B 3R 4G. 5H 6F 11 2R 3T. 3F 4Z. §I 6R 

11 41 

D 

G 1N2D3J5F5D!Q2C~4E4H40 

BIDll~~3L~~~~·~6VR~a~~4J~ 

T .2S 3S ·4":41 o4iN 6H 6P 6Z 6D !Q lZ 2B ~ 3B ,S 

0 lE 4D 4U 51 5L 6U' !C. ,Ml JI: lll 2D. 20 4X 5B §g 5I 

0 50 gQ gf m2 .:.~§I: §H 

W 1FlL2Q2041!:4ZlR&ZB•ml£ 

I 2I2G2Y4115K~_n~§! 

Z lW 3P 6S 2§ 20 2I ~ .mi jg §li 

L~~~fil6G6R6Ka3~~g~~~~ 

l lC 2X'2T 2P 3I 3F 3A 30 40 1111:1 40 6S 6V 

I' lB lV lP 2F 2B 3Q 41' ~ 6A 6Q B 4Y'5M 6Y. 

B lH lT lS 3D 4V 5J 5X ~ 6X lJ. 2X 3Y 4A §I ~ 

K lY 2R 5B 5S 6B ll ~ ~ 61' 

B 1Xlll2L2Kll,U!2N~£§(i§Lfill6W 

Kll~~Ge4L6C~~m~D~4L~~~~ 

Underlined t:ype denotes wheels In ravened posltlona. 
74 

TABLll G 

AU~~~~G~llll~n~~g~a~~ 

B 4U6U2V~5S§! 

V 2N 3F 3Y 5R 611 lC ,lg l!l, 28 ,gQ n 

Y 1K2F3D3N4K5B505N6Z60.llm:l§l6Y§g 

Q 1HlR2I2A3V4B5H5S2Xmgf.mlml§!! 

P lP 2V 5F 6X 6N §f: 

U~8M~~ft~~~ll~B~~5R~~a~ 

:X: 3U3L4D4K,li,2Z~4U~4J6T§l 

SIBll~3W~~~~~~~~~~~~ 

1' lV 2K 3C 3S 4H 5I 6G lA IQ 3S ~ ~ 3 §Q 

D 4X 

G 

B 10 2E 3K 5G 5E lN 2B ml 4D 4G ~ 

T~~n~~~~9~~~~n~~~gm 

0 2T 3'f 4G 4Y 40 6I 6Q 6A 6E !f ll 2A 2E ,M §f 

O~G~~~~~llll~~§~~~~ 

W 5V2P20~~~.§i~ 

I lG lM 2R 2P 4F 4A !Q 2Y 3Y ~ .§! §§ 

Z 2J 2H 2Z 4N 5L ~ ,mi 4V .§6 '. 

L lX 3Q 6T .21 2T 2H ~ ~ 4T· §11 

1~~~~~~~~~~~~~~6K~ 

P lD 2Y 2U 2Q 3J 3G 3B 3P 4P ll ll 4N 6R §ll 

B. lC lW lQ 2G 2C 3R 4Z 6K 6B 6R ~ ~ §L 6X 

K lI lU lT 3E 4W 5K 5J 5Y 6Y !I 2! 3X 4Z §! §I 

B lZ 2S 5C 5T 6C !Y ~ 4H 6E 

K lY lN 211 2L lX lD gM 4P ~ §f ~ .§f .§! 

Underlined type denotes wheels in reversed poaitioDll. 

75 

TABLll E 

A lZ 10 2N 2M lW !Q. 2L ~ ~ 5E 5J §Q 6U 

Bll~4J@~~~Wl!l,~~~~4J§!9§g~ 

V 4V. -~ 2U 4E §8 §! 

Y 20 3G 3Z 5S 6N 18 lF lI ~ g[ 3H 

Q lL 2G 3E 30 4L 5C 5P 50 6A 6P 11. ~ 5I 6X 6B 

p lI lS 2J.2B 3W 4C 5I 5T D 2C ~ 3C 58 611 

U lQ 21 5G 6Y 60 .§I 

X~~3J~~~4S6G!QllW2J~~~.§1~~6G 

S 3V~4E4Lll§:~,il~4I§§.§l 

1' lC 18 2C 3X 38 3Y 4K 5A 6Q 30 ml 3A ~ 5C 5F §I 

D 11 2l. 3D 3T 4I.5J ~ lZ 2P 3R ,ml~§! 6P 

G 4Y 

B 

T lP 2F 3L 5H 5F !I~ 3T 4C ~-4M 

O~ll~~~~~~~-~6X~~~~~4H~ 

O 2U. 3U_ 4H 4Z 4P. 6J 6R 6B 6F ~ lX 2Z 20 3Z §Q. 

wwe~~~~~aw~2B~~~~~ 

I 51 IQ 2N 38 ~.4N 50 6F 

Z 1HlN2S2Q4G4B!f,213X4K5S§B 

L 2K 2I 2A 40 511 3F.3G ~ 6Z 

1 lY 3R 6U gQ. 2S 2G n 3L 4S §L 

P2E~9~fil6T611~~3J~35H~-~6N 

B. lE 2Z 2V 2R 3K 3H 3C 3Q 4Q ~ ll ~ §Q 6'1' 

K 10 lX lR 2H 20 38 4A 6L 6C 6S 3Y ~ §K. §! 

B lJ 1 V lU 3F. 4X 5L 5K 5Z 6Z lH &! 3W 4Y 5X §A 

K 1A2T505U6Dll~~60 

Undsllned type denotes wheels in revened positions. 
76 

TABL9T 

A 182U5E5V6E~~~§Q 

B lA lP 20 2N !! ll &K ~ ~ §12 §I 6N §t 

v a~~4E4S~~lllI~~~gg~~g~ 

y 4W 6W 2T ~ .§.Q 6U 

Q 2P 3H 3A 5T 60 lAll lH gQ~~ 

p 111 2ff 3F 3P 411 5D 5Q 5P 6B 6Q !I § §H §I §6 

u lJ lT 2K 2C 3X 4D 5J 5U 2V 28 2D _a §A §b 

x lR 2X·5ff 6Z 6P §Q 

s ~H~~~~ft~~~lln~~~~~~§E 

• 3N 3W 4r 4M ll H ~§~~§B§H 

D lD lC 2D 3Y 3C 3Z 4f:. 5B 6R mi ,m: ~fill §I .§1 §1. 

G lX 211 3E 3U 4J 5K 6I !! 20 ~ :SC g 5U §Q 

B 4Z 

T 

0 lQ 2G. 3M 5I 5G 1.L gz ~ • ~ jL 

0 ww~~~~~~9M~~m~~~~-~ 

w 2V 3Y 4I 4A 4Q 6X 6S 6C 6G l!i ll: &I .G .U: .§8 

I lH 4G 4X 5Z 50 6X ll !12 lC li gj 2L ~ .§! .§1 §[ 

z 5X2N2113A4C~~§I 

L lI 10 2T 2R 4H 4C 10 21' .3 ~ §8 §Q 

l 2L 2J 2B 4P 5N 3E 3F g §I 

l!' 1Z3S6V~,U2F~~g§K 

B. 2F 5C 5S 61. 6J 6U 6N ~ ~ n·~ §! §Q §11.§1 §I 

K lF 2A 21' 2S 3L 3I ~D 3R 4R ,U! lY ~ if §§ 

B lE lY lS 2I 2E 3T 4B 611 60 6T Bil §i §! 

Jrl lK lW lV 3G 4Y 511 5L 5A 6A Ji gy 3V ~ §I §Z 

Underlined type denotea wheela In revened poait.loaa. 

i 

...... 

i.L 

A 

B 

v 

y 

Q 

p 

u 

x 

s 

• D 

G 

B 

T 

a 

0 

w 

I 

z 

L 

l 

l!' 

B. 

K 

B 

M: 

77 

TABLll c 

lL lX lW 3H 4Z··5N 511 58 68 lF 2T 3U ~ 5V §! 

lC 2V 5F 5W 6F lR il 4E 68 

18 lQ 2P 20 lU lA 2J 4M 4P 5C .§ti 611 6S 

~2A~e~4P6G~IB~~~~~9~~fil 

4X6X2S~§f6T 

2Q 3I 38 5U 6P lZ lD lG 2P 2D ~ 

lN 2I 3G :SQ 4N 5E 5R 5Q 6C 6R lJ 2R 5G 6V 6Z 

lK lU 2L 2D 3Y·4E 5K 5V 2U 2A ,G 3 3 §K 

lS 2Y 5I 6A 6Q §Q 

2R~~~3Ra~fill01PIB2ff~~~~5S5J~ 

3X 30 4G 4N 11' 2W ~ ~ 4Z 4G §g 6G 

lE lD 2E 3Z 3D 3A 4111 5C 6S 311 3S 3Y 5N 5A 5D 6W 

lY 2N 3F 3V ~ 5L 6J ll 2N 3P 38 4V 5T 6N 

4A 

lR 2ff 3N 5J 5H lK 2Y 3R 4A 40 4K 

lH 1 V 10 3C 3P 4V 5G 5Z 5X 5S 6Z lL 2F 2I ~ 4N ~ §E 

2W 3W 4J 4B 4R 6L 6T 60 6H 111 lV 2X 28 ~ .§1!1 

lI 4H 4Y 5A 5P 6Y !! !Q ll lI 2Z 2K 4T 5X 5Y 5E 

5Y 211 2L 3Z 48 ~ 58 6D 

lJ lP 2U 2S 4I 4D lN ~ ~ 4I .§.Q 6P 

211 2K 2C 4Q 50 3D 3E 4S 6X 

lA3T6W20gQ2E~~~6J 

2G 5D 5T 6M 6K 6V 60 2G 30 3H 3L 5U 5F 5L §H §b 

lG 28 2X 2T 311 3J 3E 3S 4S !Q 1 T ~ 60 .§8 

lF lZ lT 2J 2F 3U 4C 6N 6E 6U 3W 4U 5I 6U 

Underlined type denotes wheels in re\·ersed position1:1. 
78 

TABLll 0 

A lG lA lU 2K 2G 3V 4D 60 6F 6V 3V 4T 5H 6T 

B lM 1 Y lX 3I 4A 50 5N 5C 6C ll 2S ~ 4V 5U 6X 

V 10 2W 5G 5X 6G !Q 4X 40 6A 

Y lC lR 2Q 2P 1 T lZ 2I 4L 40 58 5G §L 6R 

Qrn~~4G~~~llW~~~34G~~~~ 

P 4Y 6Y 2R 4B 50 6S 

U 2R :5J 3C 5V 6Q lY lC lF 20 2C 3E 

X 10 2J 3H 3R 40 5F 5S 5R 6S 60 lI gQ 5F 6U 6Y 

S lL lV 2M 2E 3Z 4F 5L 5W ~ 2Z 2B 3Z 5Y ~ 

N lT 2Z 5J 68 6R 68 

D~li93L~4X~~rnlOID~3H~~~~5Im 

G 3Y 3P 4H 40 1 V gI 3B ~ 4Y 4F §f §[ 

E~IB~~~~4N~~~~3X511~~6V 

T lZ 20 3G 3W 4L 5M 6K lW 2M 30 3A £l 5S 6M 

0 4B 

0 

W lS 2I 30 5K 5I lJ 2X ~ 4Z ~ 4J 

I lI lW lP 30 3Q 4W 5H 5A 5Y 5T 6A 1.K 2E 2H 3J 411 4E 6E 

Z 2X 3X 4K 4C 4S 6M 6U 6E 6I lL lU 2W 2A 3W ~ 

LW~4Z9~~ll~llIB~~4S~5X~ 

1 5Z~2K3Y4A4K5A§Q 

F lK lQ 2V 2T 4J 4E lM 2U 3U 4H 5P §Q. 

R 2N 2L 20 4R 5P 3C 30 6W ~ 

K lB 3U 6X 2N gf 20 3F 3I 4P 6I 

B2H~~~~6W~~~~~~9~6G~ 

M: lH 2C 2Y 2U 3N 3K 3F 3T 4T !f lS ~ mf §Q 

Underlined type denotes wheels in reversed positions. 

L .. ~ 

79 

TABLll w 

A lI 20 2Z 2V 30 3L 3G 3U 4U 10 lR 4I 611 6P 

B lH lB lV 2L 2H 3W 4E 6P 6G 6W 3U 4S 5G 6S 

V lN lZ 1 Y :5J 4B 5P 50 50 60 lD 2R 3S 4U 5T 6W ------ y lE 2X 5H 5Y ~ lP 4W 4C 6Z 

Q 10 lS 2R 2Q lS 1 Y §I 4K 4N §A .§[ 6K §Q 

P 10 2C 4N 4H 4V 4R 6I !Q lF 3L 30 3R 4V 4F 5U 5I 6Y 6G 

U4Z~gg4A5Nm ----------

X 2S 3K 30 5W 6R lX 18 lE 2N ~ 3D 

S lP 2K 3I 3S 4P 5G 5T 5S 6T 6E lH 2P 5E 6T 6JC ----- N 111 lW 2N 2F 3A 4G 511 5X 25 2Y li 3Y 5X 6I ------ D lU li 5K 6C 6S 6A 

G~~3N~~a@6K~~w~~-511~~~~ 

E 3Z 3Q 4I 4P lU 2U 3A 4P 4X 4E 60 6E -------- T W~~~~~~9W~~9~~9W 

0 lA 2P 3H 3X 411 5N ~ lV 2L 3N 3Z 4T 5R ~ ------- 0 4C 

w 

I lT 2J 3P 5L 5J lI 2W 3P 4Y 4B 4I ------ Z W ll~~3R4Xfil9~~~wm~~4L4Dm 

L~3Y4L4Dft~6V~~ll~~2Z~~--- ------ 1ll4J~.~96A~ll~W2X~4R~~~ 

1!' 5A 2K 2J 3X 4Z 4J ----------~ §g 

B. lL lR 2W 2U 4K 4F lL 2T 3T 4G 50 6N ------ 1[ 202112E4S5Q3C3B~6V 

B lC 3V 6Y 2M 20 2C 3E 3H 40 ~ 

-~~~006M6X~2E~~:5J~~~~~ 

Underlined type denotes wheels in reversed positions. ---------
80 

TABLB I 

Aru~~~~6Y~~~~~9~~~m 

B lJ 2E 2A 2W 3P :5M 3H 3V 4V lN !Q ~ 6L §Q 

V lI lC lW 211 2I 3X·4F 6Q 6H 6X 3T 4R 5F §R 

Y 10 lA lZ 3K 4C 5Q 5P 5E 6E lC gg _m 4T 5S 6V 

Q lF 2Y 51 5Z 61 10 · 4V 4B 6Y 

P · lE 1 T 2S 2R !B ll 2G 4J 4M ~ 5E 6J 6P 

uu~~~~4S6J~ll~~~~~~msx~ 

X 4A 6A 2P 4Z §I .§g 

S 2T 3L 3E 5X 6S lW lA lD 2M 2A 3C 

N lQ 2L 3J 3T 4Q 5H 5U 5T 6U 6F lG 20 5D 6S 6W 

D lN lX 20 2G 3B 4H 5N 5Y 2R 2X 2Z ~ 3 6H 

G lV 2B_5L 6D 6T 6Z 

B~~~~~4Z4X~a~IB~~~~~~~~ 

T 3A 3R 4J 4Q lT 2T 3Z 40 4W ~ ~ 6D 

c~w~~~:5D·e~sv3J~~~~~~ 

0 lB 2Q 31 3Y 4N 50 6M !!! gx ~ 3Y 4S .§Q 6K 

w 4D 

I 

Z lU. 2K 3Q 511 5K lH 2V 30 4X ~ 4H 

L~ll~~3S~5J~~~001I~~3H«~OO 

l 2Z 3Z ~ 4E 4U 60 6W 6G 6K lJ lS fill 2Y 3U 5J 

Pa«4B~~~~llllll§~~~~~ 

B 5B ru 21 3W 4Y ~ §! §A 

K 1MlS2X2V4L4GlK2S3S~§fi§M 

B 2P 2N 2F 4T 5R :SA :SB ~ 6U 

M: lD 3W 6Z ~ &Ii .§ :5D ~ 4N §g 

Underlined type denotes wheels in reveraed positiona. 

! 

L . 

.. 

81 

TABLB Z 

A 1E3X6A2K2M2A~3F4M§[ 

B~~~~00~6S~~~3H~~~~6H 

V lK 2F 2B 2X 3Q 3N 31 3W 4W lM lP 4G 6K 6N ----- y lJ lD lX 2N ru 3Y 4G 6~ 6I 6Y 3S ~ -~ .§g 

Q lP lB lA 3L 40 5R 5Q 5F 6F lB gf ~ ~ 5R 6U 

P lG 2Z 5J 5A 6J lN 4U 4A 6X 

U lF lU 2T 25 !Q lW ~ 4I 4L 5Y ~ 6I §Q 

X lQ 2E 4P 4J 4X 4T 6K 10 10 3J 3M 3P 4T 4D 5S 5G 6W 6E 

8 4B ~ 20 4Y 5L 6P ----------- N 2U 3M 3F 5Y 6T lV lZ lC 2L 2Z 3B ------ D lR 2M 3K 3U 4R 51 5V 5U 6V 6G .![ 2N §Q 6R 6V 

G 10 lY 2P ~ 3C 41 50 5Z gg 2W gx 3W 5V 6G 

B lW 2C 5M ~ 6U 6Y 

T~~~~3V4A~~~ay~~«~~~~~ 

C 3B 3S « 4R lS 2S :SY 4N 4V 4C 6M 6C -------- 0 lI lH 21 30 3H 3E 4Q 5G 6W :SI 30 3U 5J 5W 5Z 6S ------- w lC 2R 3J 3Z 40 5P ~ 1 T 2J 3L 3X 4R 5P 6J . ------- I 4E 

z 

L lV 2L 3R 5N 5L lG 2U 3N 4W 4Z 4G ------ l lL lZ lS 3G 3T 4Z 5K 5D 5B 5W 60"1H 28 2E 3G 4J 48 6B . ·- ------- p 2A 3A 4N. 4F 4V 6P 6X 6H ~ lI. lR 2T 2X 3T 5I ------ B lM 4L 4C 5E 5T 6C lU lY lX lE. 2V 2G 4P.5T 5U 5A" 

K 5C 2I ~ 3V 4X 4H ---------- 5x: 6Z -----·-- . B lN lT 2Y 2W 4M 4H lJ 2R 3R 4E 5M 61:. ------ M: 2Q 20 2G 4U 5S 3Z 3A.40 .6T 

Underlined type denotes wheels in reversed positions. · 
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A 2R 2P 2H 4V 5T 3Y 3Z 4N 6S 

H lF 3Y 68 2J §. _u 38 3E 4L 6E 

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Q lK lE lY 20 ~ 3Z 4H 6S 6J 6Z 3R 4P 50 6P 

P lQ lC 18 311 4E 5S 5R 5G 6G lA gQ ~ 4R ~ 6T 

U lH 2A 5K 58 6K 111 4T ~ §1 

X lG lV 2U 2T lP lV 2E 4H 4K 5X 5C 6H 6N 

8 ll~~4K~~6L~~~~~4S4C.§B~~6D --------- B 4C6C2N4X§K60 

D 2V 3N 3G 5Z ~ lU lY ll &K 2Y 3A 

G 1S2N3L3V4S~5W5V6W6Hll.21.§B~6U 

B lP lZ 2Q 2I 30 4J 5P 5A 2P 2V 2X 3V §ll §[ 

T 1X2D5N6F~6X 

0~2E~~94B4Z6NWll~~~~.§l~~~~ 

0 3C3T4L4S!R2R3X4114U~§L6B 

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I 10 2S 3K 3A 4P 5Q 60 lS 2I 3K 3 !Q 50 §! 

z 4F 

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P~llH3H3U4A~~~~6EW2A2D~~~~ 

B 2838404G4W6Q~6I6111H!Q2S2W~5H 

K~4M4D~~6DllllllWm~~~~~ 

B 502H2G3U~4G3§I 

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Underlined type denotes wheels in revened poaltlou. 

83 

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A lP 1 V 2A 2Y 40 4J !H gf 3P 4C 5K ~ 

H 2S 2Q 2I 4W 5U :5X 3Y ~ §8 

V lG 3Z 6C 2I &K 2Y ~ 30 ~ 6D 

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Q lM 2H 20 2Z 3S 3P 3K 3Y 4Y lK lN 4E §! §1:! 

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U lR 10 lC 3N 4F 5T 5S 5H 6H lZ 2N ~ !Q §f 6S 

X lI 28 5L 5C 6L lL 4S 4Y §! 

8 lH lW 2V 2U 10 lU 20 4G 4J 5W 58 6G 6M --------- - ~~4R4L~~6M~ll~~3N~~~~~oo 

D 4D 6D 2M 4W .§l §t! 

G 2W 30 3H 5A 6V lT lX lA Sl ~ 3Z 

B 1 T 20 311 3W 4T 5K 5X 5W 6X 6I 10 2L 5A 6P §A 

T lQ lA 2R 2J 3E 4K 5Q 58 gQ 2U 2W 3U 5T 6E 

0 lY 2E 50 6G 6W §! 

0 2X.3R 3Q 2F :5X 4C 4A 60 lI lJ lY 28 3C 4I 5I 5L 5M 50 6Y 

w 30 3U 4M 4T lQ gQ 3W 4L ----------- 4T 4A 6K 6A 

IllW~~~~4Sfil~~~~~~~~ 

Z lE 2T 3L 38 4Q 5R 6P lR 2H ~ 3V 4P fill §H 

L 4G 

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B lN 18 lU 3I 3V 4B 5M 5F 50 5Y ~ lF 2Z 2C 3E 4H,4Z 6Z 

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B 10 4N 4E 5G 5V 6E !§ lW 1 V lC 2T. 2E 4N .§B ~ §! 

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Underlined type denoM!I wheela in reveraed poaitiona •. 
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B lQ lW 28 2Z 4P 4K lG 20 30 48 5J 6I 

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X lS lE lD 30 4G 5U 5T 5I 6I lY 2M 3N 4P 50 6R 

S lJ 2C 5M 5D 6M lK 4R 4X fill 

N lI lX 2W 2V lN 1 T 2C 4F 4I 5V 5A 6F 6L 

Dll~4S4114A~6N~ll~3J311~4A~~~e 

G 4E 6E gL, 4V 5I GM 

B 2X 3P 3I 58 6W lS lW lZ &! 2W 3Y 

T lU 2P 3N 3X 4U 5L 5Y 5X 6Y 6J lC 2K 5Z 60 .§§ 

0 lR 18 2S 2K 3F 4L 5R 5C ,g}! ,2I 2V 3T 5S 6D 

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B 2D 3D 4Q 4I 4Y 6S 6A 6K 60 l[ 10 gg 2U ~ 5F. 

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Underlined lype denotes wheels in reversed poaitiona. 

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S lT lF lE 3P 4H 5V 5U 5J 6J lX 2L 311 40 5N §Q. 

N lK 2D 5W 5E 6N lJ ~ 4W 6T 

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B 4F· 6F ~ ~ 5H 6L 

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Underlined type denotes wheels In ravened poeitlom.. . 
86 

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Underlined type denotes wheels ID reveraed poaiticma. .. 

I 

1 

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TABL:m B 

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S lQ 2L 2H 2D :5W 3T 30 3C 4C lG lJ 4A 6E §H 

lf lP lJ lD 2T 2P 3E 411 6lC 60 ~ :5M ~ 2! 6K 

D lV lH lG :5R 4J 5X 5W 5L 6L lV 2J :5K 411 §1:. 60 

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l ~ :5Y 4Q 4X !I 211 :5S 4H 4P 4'1 6G 61 

I' 10 lN 20 2J 3N :5K 4W 511 6C ~ n 30 .§12 §g 5T 611 

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K 4K 

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Underlined tJpe denotes wheela in reveraed poaiticma. 
88 

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Q 5J 2B 2A 30 ~ 4A .§Q ~ 

P lU lA 2F 20 4T 40 lC 2K 3K 4X 5F 6E 

U 2X 2V 2N 4B 5Z 3S ~ ~ 6M_ 

:X lL 3E 6H m2 gf: 2T 3V g: 4F 6Y 

sa~~~~m~~~~~SJ~~~~ 

N lR 2M 2I 2E 3X 3U 3P 30 4D lF lI 4Z §J2 6G 

D lQ lK lE 2U 2Q 3F 4N 6Y 6P 6F 31. ~ 5X ~-

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B 4L 

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Underlined type denotes wheels in revened po11ltio.1111. . . ..... . -

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APPENDIX IV 

BASIC PLAIN-TEXT SEQUENCES . 

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BABIC PLAIN-TEXT SEQUENCES Fon CW5 DIRECT 

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0 YIXONABSZJUDTCVGMLHQFEKWRP a KJQXAUHDIYTBVFRNGPZSEWLOCM 

D LQCISMNEXBWGUPRHJVTAOKDYZF D DBACMWTGQLUNROZSHFXEKYVIPJ 

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Jr RMFAKBEDPSLTYOXUNZWJQGHVCI Jr HSJFBLWTMRYEXQCKUIPDGVZAON 

G ZJOMDNKGFEVULICWSXYBAHTRPQ G TEBONVYUJZLKCAPDWQFGHRXMIS 

B XBIJGSDHOKRWVQPYECLNMTUZFA B UKNISRLWBXVDPMFGYAOHTZCJQE 

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•... 

J.. 

APPENDIX V 

FIRST-INTERVAL DATA-PLAIN-TEXT RELATIONSmPS 

TABLE B 

B 

l 1 Y 2M 3F 40 4R 4Y 10 2T 3Z 5V 5T 

Mlim~~~~~~~ll~~4G9~fil~~ 

A 10 lL 2N 2R 3N 5C 2G ----------- 3G 4T 4L 4B 6V 60 6N fil! 

Q~ll~ll~~~~~~ll~4H~~~ 

I 2E 2D 3R 4'1' 4D 5T 6V 5G 

0 lG 20 30 4B 5J 6I !Q lW 28 gz 4P ~ 

F 3X 3Y 4M 6R 2S gQ 2I 4W 5U 

P 2J2L2Z3B3E4L6E!fg:~ 

o~~~~~~-~~~~~~~~~~ 

X lN lQ 4H 6L 60 lJ 2E 2A 2W 3P 3M 3H 3V 4V 

Z 3U 4S 5G 6S lH 18 1 V 2L 2H 3W 4E 6P 6G 6W 

R lE 2$ 3T 4V 5U 6X lM 1 Y lX 3I 4A 50 5N .§Q §Q 

V lR 4Y 4E 68 ~ 2V 5F 5W 6F 

L lV 18 2K 4N 4Q 50 5I 6N 6T lA lP 20 2N 

YWW~~3V~~~~~~ll~~~4R4N~ 

W 2V4F5S6W4U~ 

U 10 lH lK 2T 2H 3J 211 3E 3X .§Q 6L 

T 10 2W 5L 6A 6E lI 20 3B 3L 4I 5Z 5M 5L ~ §I 

B 2A 2G 2I 3G 5F 6Q lE 10 2F ~ 3$ 4Y 5E 5P 

G 6J lL 2R 58 6T 6J 

Dll~~~~~9~~9~2J~~~3J~4M4S~ 

K 1F2F3L4A4I4P6Z6P30~~~ --------- B9~~~~900Wllm~~~~~~ 

S lI 2Y 3A 3M 4G 5E 6Y lN gQ ~ ~ ~ §A §I 

N 

Underlined type denotes wheela ID reversed positions. 

(101) 
B 

l 

102 

TABLll J 

K lZ 2N 3G 4P 4S 4Z lC § 3Y ml 58 

A~~~~~~6Vllllll311~4FS~~~~ 

Q 101M202830502F~4S~4A6U6C611§Q 

I~Wlllia~4L~~9~4P4GM~6G 

0 2F 2E 38 4U 4E 5U 61 .§£ 

I' lH 2P 3P 4C 5K ~ lP ll 2A 2Y ~ 4J 

P 3Y 3Z 4N 6S a gf 2H 4V 5T 

0 2K 211 2A 3C 3F 411 6F lE 3lC 6A 

xm~~M9~M~M~~9~6N~~ ------- z 10 lR 4I 611 6P lI m 2Z 2V 30 3L 3G 3U 4U 

:a 3V 4T 5H 6T lG --------- lA lU 2K 2G 3V 40 60 6F 6V 

v lF 2T 3U 41 ---------- 5V 6Y lL lX 11 3H 4Z 5N 511 58 68 

L 1S4Z4F6CJA2U5E5V~ --------- Y lW lC 2L 40 4R 5E ~ 60 6U ll !Q g.H ga& 

W~~~~3"4A~~~~~Wll~~~411~ 

U 21 4G 5T 6X 4T 6T 

T lE lI lL 2U 2I 3K 2L 3D 31 5P §K 

B lP ll 511 6B 6F lH 2C 3A 3K 4H 5Y 5L 5K 6W 6L 

G 2B 2H ~ . 3H 5G ----------~ 10 lN 2E 21' 3R 4X 50 50 -------- D 6K1KgQ5A686I 

Kllll~~3R4X~~~~6N~~~~M4N4L4R~ 

B lG 2G 311 4B 4J 4Q 6A 6Q 3N 3E 41 ~ 

83JC3D~M~OO~ll~~ro~~4B9~ 

.. lJ 2Z 38 3N 4H 5F 6Z --------- 111 28 3T ~ 4Y 5Z 6X ------- Underlined type denotes wheela in revened poaitiODB. 

103 

TABLB M 

B lK 2A 3C 30 4I 5G 6A lL 2A ~ 3I 4X 5Y 6W 

l 

• A lA 20 3H 4Q 4T 4A ll 2R 3X: 5T 5R 

QWn2Z~4E~6W~~ll~3Y~~g~~g 

I 1E1N2P2T3P5E2E3E4R4J4Z6T686L6P 

0 lR lV lU 18 28 m --------- 411 5Q 5R 5X: lP 40 4F ~ 51' 6F ------ :r 2G 2F 3T 4V 4F 5V 6X §1 

P lI 2Q 3Q ~ 5L 6K 10 lU 2Z 2X ~ ~ 

0 3Z3A406TgQ&Q2G4U58 

X 2L2N2B3D3G4N6Gl03W~ 

Z2E311~~~~~~~~~~006116X§Q 

R lP lS 4J 6N 6Q lH 2C 2Y 2U ,mi 3K ~ 3T 4T 

V 31' 4U 5I 6U ll lZ ll ~ ~ 3U 4C 6N 6E 6U 

L lG 2U 3V 4X 51' 6Z 1:1 ll ll ~ 4Y 511 5L 5A 6A 

Y lT 4A 4G ~ lA 2T 50 5U 60 

W lX 10 211 4P 4S 5F 5K 6P 6V 1 Y lN 211 gL 

U 11' lL 3R 3U 3lC 4B 4L 5A 50 6E 611 lI 21' 4H 4B 4P 4L 6C ------- T 2X4H5U6Y4S§§ 

B 

G 

D 

lF lJ 111 2V ~ 3L 2K 3C 3V 50 ~ 

lQ 2Y 5N 6C 6G lG 28 3Z ~ 4G ~ 5K ~ 6V 6K 

2C 2I 2K 3I 5H ---------- 68 lC !II m 2V ~ • §Q 5N 

K ~ lJ 2P 5Z §B §ti 

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S lH 2H 3N 4C ~ 4R 68 ~ 311 30 4V ~ 

ll'3Y3E3K~9~M~ll§~D~4AS6G 

Underlined type denotes wheela in revened poeition&. 
104 

T.a.BLll A 

B~~~~~~6JIB~~2M~~4Z~.§[ 

J 1L2B303P4J5H6Bll2Z3R3H~~6V 

K 

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Q lB 2P 3I 4R 4U 48 lA gg 3W 58 §Q 

IID2XU~4F4X~lPIDU~3X~OO~~~~ 

0 lF 10 2Q 2U 3Q 5F 20 30 ~ 4I 4Y §§ 6A 6K §Q 

I' 18 lW lV lC 2T 2E 4N 5R 58 5Y !Q 4N 4E 5G 5V 6E 

P 2H2G3U4W4G5W6Y50 

C lJ 2R 3R 4E 5111 6L lN lT 2Y 2W ~ 4H 

X 3A 3B 4P 6U 2P gH 2F 4T .§R 

Z 2111 20 2C 3E 3H 40 6H lC 3V 6Y 

K~~3G3K~~~00~~~~6N~6W~ 

V lQ 1 T 4K 60 6R lG 2B 2X 2T 3M 3J 3E 3S 4S 

L 3X 4V 5J 6V lE lY 18 2I 2E 3T 4B 6M §12 6T 

Y lH 2V 3W 4Y 5X 6A lJ 1 V lU ~ 4X 5L 5K 5Z ~ 

W lU 4B 4H 6E lZ 28 5C 5T 6C 

U lY lE 2N 4Q 4T 5G 5L 6Q 6W lX 1111 2L ~ 

Tll~~~~~4M~~~6NIB~~~~4Km 

B 2Y4I5V6Z4R6R 

G lG lK lN 2W 2K 3111 2J 38 3U 5N 6I 

D lR 2Z 50 60 ~ !E 2A 3Y 3I 4F 5W 5J 5I 6U ~ 

K 20 2J 2L 3J 5I 6T 18 lL 2C 2U 3P 4V 5B 5M 

B 6M lI 20 5Y §i §Q 

8 lA lZ lP 28 3T 4Z 5Z 5C 50 5U 6P &g 3A 3Z 30 3G. 4L 4J ~ .§X 

N lI 2I 30 40 4L 4S 6C 68 3L 3C 4U 4C 

Underlined type denotes wheels in reversed positions. 

106 

TABLE Q 

B lJ 2J 3P 4E 4M 4T 6D 6T 3K 3B 4T 48 

1~3G3111~00~~~1Pg.Q2L~~~~~ 

M: lM 2C 3E 3Q 4K 5I 6C !!l 2Y ~ 3G 4V 5W 6U 

A 

Q 

I lC 2Q 3J 4S 4V 4C ll 2P 3V 5R 5P 

OIB~~3D~~~WW~3J3W~~~~~OO 

I' lG lP 2R 2V 3R 5G.2C 3C ~ 4H 4X 6R 6Z 6J 6N 

PllllUm~~~~~~~-4M®~~6D 

C 2I2H~4X4H5X6Z5C 

X lK 28 38 4F 5N 6M lM 18 2X ~ 4L 4G 

Z 3B 3C 4Q 6V 20 2M 2E 4S §g 

K 2N 2P 20 3F 3I 4P 6I .Ill 3U ~ 

v~~3H~~~~~~gg®~6M~~oo 

L lR lU 4L 6P 6S !I 2A. 2W 28 ~ 3I 30 3R 4R . 

Y ~4W5K6WlDlX!H§i"~38~.§L6C68 

W lI 21 3X 4Z 5Y 68 lI .!Y lT 3E 4W 5K . .§!l. .§I 6Y 

U lV 4C 4I ~ lY 2R §D 58 68 

Tll~~4R~~96R~ung~ .. 

Bll~3T3W~®~oo·~oooow~4F4Z~~& 

G 2Z.4J· 5W.& ~ §Q 

D lH lL 10 2X 2L 3N gI, ~ 3T 5M 6H 

K 18 U 5P 6E 6I lE 2Z 3X ~ 4E §! 5I 5H 6T 6I 

B 2E 2K 211 3K 5J 6U 1A !K 2B 2T 30 4U 5A 5L 

S 6NlHgH~6P.§[ 

NIBll~~3U~~®~~~~~~~~4Kil~~ 

Underlined type denotes wheels in reversed positions. 
106 

TABLll I 

B W~llm~4B~~~96R83YB~~4J~4NH 

l lK 2K 3Q 4F 4N 4U 6E 6U ~ 3A ~ ~ 

][ 38 3H 3N 5C 5P 5S 6L !f 10 2P 2K ~ ~ 4X §Ii §12 

A lN 20 3F 3R 4L 5J 60ll 2Xm!~~§! 6T 

Q 

I 

0 10 2R 3K 4T 41 4D lY 20 .ml §Q 50 

I' ~2Z~3E4H4Z6Zllll~M~-5M~m~6F 

p lH lQ 2S 2W 3S 5H 28 ~ 40 4G 41 §Q 6Y 6I 6M 

c lU lY lX lE 2V 2G 4P 5T 5U 5A 111 jL ~ 3 5T .§g 

x 2J 2I 3W 4Y 4I 5Y & §1 

z lL 2T 3T 4G 50 6N lL lR 21 2U 4K 0 ------ B. 3C304R6WglfgLm~§f 

v 202Q83G3J4Q6JlA~6W 

L 2H 3P 3I 3M 5V 5G 5M 6I 611 §: 5C H §L 6J §Y §ff 

y lS lV 4M ~ 6T ~ 2Z i! 2R 3K ,mi 3C ~ ~ 

w 3Z 4lC 5L 6X 1& 11 lQ 2G 2C 3R ~ 6K §I §8 

'U lJ 2X 3Y " 5Z 6C lH lT lS 30 4V 5J 5I ~ 6X 

T 11 40 4J 6G 11 gg --------- §A .§R §A 

B lA lG 2P 4S 4V 5I 5N 6S 6Y ll 1:K 2J 2I 

G llW3U~:5A4E~~5R6H~~2T4Ea411~6Z ------- D U4K5X684P6P 

K lI lM lP 2Y 2M 30 .21i ~ ~ ~ §g 

B 1 T 28 5Q 6F 6J !D 2Y :5W 3G 40 .§.\[ .§Ii ~ 6S §H 

s 2F 2L 2N 3L 5K 6V lZ lJ U 2S 3N 4T 5Z 5K -------- 1' 60 J.g 211 §I 60 §g 

Underlined type denotee wheels in reversed positions. 

B 

l 

][ 

A 

Q 

I 

0 

I' 

p 

0 

x 

z 

B 

v 

L 

y 

w 

'U 

T 

B 

G 

D 

K 

B 

8 

1' 

107 

TA.BLB 0 

6P ![ 2L §! 6N 6D 

IDWIB~9~00~5G~6Sm~:5W3Lm~4G~6U 

lL 2L 3R 4G ~ 4V 6F 6V ~ 3Z 4R 4Z 

3C 3I 30 50 5Q 5T 6M 10 lN 20 2J 3N ~ 41 511 6C 

10 8 3G 3S 411 5K 6E 18 21 30 3E ~ .§ll 6S 

lE 2S 3L 4U 4X 4E lX ,mi ~ 5P 5N 

~um~~"&llllill~~"~3~~~ 

lI lR 2T 2X 3T 5I U :5A ~ ~ j! 6P 6X §H 6L 

lV lZ lY lF 2W 2H 4Q 5U 5V 58 !L 4K • 50 ~ 68 

2K 2J 3X 4Z 4J 5Z 68 5A 

lM 2U 3U 4H 5P 60 1:K lQ 2V ll ~ 4E 

303E4S6Xg,U;2C~50 

2P 2R 2F 3H 3K 4R 6K li 3S §! 

2I 3Q 3J 3N 5W 5H 5N 6J 6N ~ 58 .§R 6K 6I 6T 6JI 

lT lW 4N 6R 6U !D ll ill &Q 3J :sG ~ m! ~ 

3A 4Y 5M 6Y 18 !! lP §: gj ~ 4Y 6J 6A §Q 

lK 2Y 3Z 48 5A 6D J.g lS !R 3C 4U §1 §Ii 5W 6W 

lX 4E 4K 6H 11 2P 5Z §Q. §Z 

18 lH 2Q 4T 4W 5J 50 6T 6Z lU l:!l, ll 2H 

li~~3Y~Oe~~~~~2S4D~~~~ 

284L5Y6C~§Q 

lJ lN lQ 2Z 2N 3P 2G 3Y ,mi 5K 6F 

lU 2C 5R 6G 6K 1& 2X ~ 3F 4C §1 5G 5F 6R 6G 

2G 211 20 3M 5L 6W ll ll gz m a 4S 5Y Ji!l 

UnderliDed type denotee wheela ID reveraed poeitlona. 
108 

TABLll F 

B 2H 2N 2P 3N 5M 6X !I .Ill 2Y g.Q ~ 4R 5X 5I 

l~IB~~611~ . 

KIBIDll~~4D~~~~~~31~-3K~~~4L~ 

A lM 2M 3S 4H 4P 41 6G-6W 3H g: ~ 4Y 

Q~3J~~~~~m~~~3113J~~~ 

I lP 2F 3H 3T 4N 5L 6F lG 2V ~ ~ 4S · 5T 6R · 

0 

I' 

P lF 2T 311 4V 4Y 4F !JI 2M 3S 50 511 

OIB~~~4J@~~ll~~~4Z~~~9~ 

X lJ lS 2U 2Y 3U 5J. 2Z ~ 4M 4E 4U 60 6W 6G §K 

ZllllllWll~~~~00~~4AOO~~ 

B. 2L 2K 3Y 4A 4K 5A 6C 5Z 

V lN 2V 3V 4I 5Q 6P lJ lP 2U 2S ~ 40· 

L 3E 3F 4T 6Y 2L 2J 2B ~ 5N 

Y 2Q2S2G3I3L4S6L.!!~6U 

w~~3K~~~~~~-~~~6J~~~ .. 

'U lU lX 40 6S 6V lC ll ll 2P 3I ~·3A 30 40 

T 3B 4Z 5N 6Z lA lU 10 2E 2A 3P ~ .§I §Z, §f 

B lL 2Z 3A 4C 5B 6E ![ JB !Q -3B 4T 5H 5G 5V 6V 

G lY 4F 4L 6I 1 V 20 5Y 5P 6Y . 

D lC lI 2R 4U 4X 5K 5P 6U 6A lT lI 2H 2G 

K 18 lQ 31 3Z 3C 4G. 4Q 5F 5T 6J 6R 10 2R .. 4C ~ ~ 4G 6X 

B 2C 4M 5Z 60 4N fill 

s lK 10 lR 2A 20 3Q 2F 3X ~ 5J §I . I 

Ii lV 20 5S·6H 6L 18 2W 3U ~ 48 5S 5F 5E §g 6F 

Underlined type denotes wheela in reveraed poaitiO!lll. 

109 

T.&BLB p 

B lW 2E 5T 6I 6111 lA 2! ~ 30 4A .§Ii §I 50 6P 6E 

l 2I 20 2Q 30 5N 6Y !! lG ,U 2P 3K ~ §I §ti 

K 6R 10 2!l §I 6L ~ 

A~IBWll~~~~~~6U~~3U3J3B~~4K6S 

Q 1N~3T4I4Q4X6H6X3G~~4X 

I3E3K~~~~~~~a~3L~4U~6A 

0 lQ 2G 3I 3U 40 5M 6G ![ fill 311 ~ 4R 5S §g 

I' 

p 

0 lG 2U 3N 4W 4Z ~ 1 V ~ 3R 5N 5L 

X lI 2C 2F 3H 4K 4C 6C lK ll .!B ~ 3S 4Y §!l. §Q ~ §! 6C 

Z lK lT 2V 2Z 3V 5K 2Y g: 4L 4D 4T fill 6V 6F 6J 

B.ll~llIB~~4S9~~w~g~~~ 

V 2M2L3Z4B4L5B~g 

L 10 2W 3W 4J 5R 6Q lI 10 ll 2R 4H ~ 

Y 3F 3G 4U 6Z 2K 2I &A 40 §I 

W 2R 2T 2H 3J 311 4T 6M lX ~ 6T 

'U~~3L~~5J~6L~~~~.§I~~§K 

T lV lY 4P 6T 6W 18 2W ,g§ 20 ~ 3E ~ 3N 4N 

B 3C 4A 50 6A ll ll lN ~ 2Z ~ 4W 6H §I §Q 

G 111 2A 38 4D 5C 6F ll !Q 1f 3A ~ 5G .§[ 5U .fill 

D lZ 4G 411 6J !Y 2N 5X 50 §! 

K 10 lJ 2S 4V 4Y 5L 5Q 6V ~ lS !H 2G ~ 

BWll~~~4H~~~~6SWg.Q~~~~6W 

S 2D4N5A6E~611 

Ii lL lP lS ~ 2P ~ 2E ~ ~ 5I ~ 

Underlined type denotes wheela in reveraed poaitiona. 

'118811--81---8 
110 

TABLll C 

B lM lQ 1 T 2C 2Q 3S 2D ~ ~ 5H §.Q 

l 1X2F5U6J6NJ,12U3S~4Z.§Q§Q5C606D 

JI[ 2J 2P 2R 3P 50 6Z lV 1J: gJ! gQ ~ ~ 5V 5G 

A 6S lC &! 55 6K .§A 

Q~DH~~~~M~~~U~~~~~4D~~ 

I 10 20 3U 4J 4R 4Y 6I 6Y 3F 3W ~ --------- 4W 

o~~~~M9~all~~~~~~~ 

P 1R~~3V4P5N6Hll2T3L~S§B6P 

p 

0 

X lH2V304X4A4HlJ1~~5M§K 

zw~~~4L4D6DWll!Q~~4XM§~~~ 

B lL lU 2W 2A 3W 5L 2X ~ 4K 4C 4S §1 ~ 6E §! 

V lY lC lB lI 2Z 2K 4T 5X 5Y 5E lI 4H 4Y 5A 5P 6Y ------ L 2N 2M 3A 4C 411 5C ~ 5% 

Y lP 2X 3X 4K 55 ~ ~ lN g§ gg 4G ~ 

W 3G 3H 4V 6A 2J .mi 2Z 4N 5L 

'U 25 2U 2I 3K 3N 4U 6N lW ~ §§. 

Ta~311~~~~~~28~~6H~~~ 

H lW lZ 4Q 6U 6X !A 2V 2R 2N 3G 3D 3Y 311 411 -------- G 3D 48 5P 68 lY !§ 11 2C 2Y 3N 4V 6G ~ 6N 

D lN 28 3C C 5D 6G lD lP 10 3Z 4R 5F 5E 5T 6T 

K lA 4H 4N 6K lT 21( --------- §I §ti 6W 

B lE lK 2T 4W 4Z 511 5R 6W 6C !B ~ ~ ~ 

SID~3Y~~~~~~~~IB~4A~~C6V ------- • 2E 40 58 6F ~ fil:! 

Underllned type denotes wheels in revened poaitloll8. 

111 

T.&BLll X 

B 2F 4P 5C 6G ~ §K 

l lN lR lU 2D 2R 3T 2C ml 3N 5G 6B 

K lY 2G 5V 6K 60 ll 2T 3R ~ 4Y 5P 5C 58 6N .§Q 

A 2K2Q2S3Q5P6A!Yll2V2Ng~§Y5F 

Q 6T 18 2H 5R §l ~ 

I~~U~M~~~~~6W~ll~~~C~~~ 

0 lP 2P 3V 4K 4S 4Z 6J 6Z ~ :5V 4N 4V 

P~311~~~~~~W2K~~~4S~~ 

P lS 2I 3K 3W 4Q 50 6I lD &§ ~ ~ ~ fill 60 

0 

x 

Z lI 2W 3P 4Y 48 4I ll el 3P 5L 5J 

Bll~~~411~~llU~3D~~~~~~& 

V 111 lV 2X 28 :5X 511 2W 3W 4J ~ ~ ~ 6T 6D 6H 

L~mwwua~~~~~~4X~~~ 

Y 202N3B4D4N5D6F5W 

W lQ 2Y 3Y 4L 5T 6S ~ 111 gs 2P 4F ~ 

'U :5H 3I 4W 68 2I 2G 2Y 411 §K 

T 2T 2V 2J 3L 30 4V 60 ll 30 6R 

H~~3N3R~~~6N~~~~6G~~g 

G 1XlA4R6V6Yll.§ZgQ2113F~~3L4L 

D 3E 4C 5Q 6C lX !B !L § 2X 311 4U .§!: §I §II 

K 10 2C 3D 4F 5E 6H lC 10 lN 3Y S §I 5D 5S 6S 

B 18 4I 40 6L lS 2L §! §.II 6V 

S lF lL 2U 4X 4A 5N 5S 6X 6D !Q .ll: 2E 2D 

5~ll~~~4J~M9~00llgQ4Z~4H4D~ 

Underllned type denot.ea wheels In ravened poaitiom. 
112 

T.ABLll Z 

BDWM:5D~~~~~~~ll~~4S~~~ 

l 2G4Q5D6H4JGJ 

M: 10 lS lV 2E 2S 3U 2B 3T :511 5F GA 

A lZ 2H 5W GL GP lX 2S ~ ~ 4X 50 5B 5A Gii §I 

Q 2L 2R 2T 3R 5Q GB lT lD 2U 2M 3H 4N 5T 5E 

I GU lA 2G §Q GI GY 

0 lI lH lX 2A 3B 4H 5H 5K 5L 5C GX 2Y :5S 3R 3G g 4D 4B 4H GP 

l!' lQ 2Q 3W 4L 4T 4A GK 6A :5D 3U 411 4U 

P~~~~~~~WlI~~g~~~~ 

0 lT 2J 3L 3X ~ 5P 6J lC 2R :5J 3Z 40 5P GN 

x 

z 

B lJ 2X 3Q 4Z 4C 4J lS 2I ~ §K 5I 

vn~~3K4Ne~rn~ro~~~M~~~~ 

L lN lW 2Y 2C 3Y 5N &! ~ 4I 4A ~ §K GS GC GG 

YllllIDll~211~~~Mwe•~~g 

W 2P 20 3C 4E 40 5;E GG .§! 

U lR 2Z 3Z 4M 5U GT lF lL gQ 20 4E 4Z 

T 3I 3J 4X GC 2H g[ 2X 4L 5J 

H 2U 2W 2K 311 3P 4W GP lU 3N §g 

G~3V~:5S99~~~~93~~~~ 

D lY lB 4S GW GZ lY 2T 2P 2L 3E 3B 3W ~ 4K 

K 3F 4D 5R GD lW lQ lK 2A 21' 3L ~ §1 §! .§1' 

B lP 2D 3E ~ 5F GI lB lN 111 :5X 4P 5D 5C 5R 6R 

8 lC 4J 4P Gii lR 2K 5U 5L GU 

l{ lG 111 2V 4Y 4B 50 5T GY GE lP lE 2D 2C 

Underlined type denot.ea wheels in reversed pos.itiom. 

113 

T.&BLll R 

B lH lN 21' 4Z 4C 5P 5U GZ GF .!Q lD 2C ~ 

1W~~~~4L~~~~~ll2114X~O~~ 

:M: 2H ~ 5E GI ~ §I 

A lP lT lW 2F 2T 3V 2A ~ 3L 5E GZ 

Q lA 2I 5X 611 GQ ll 2R 3P 3Z 4W 5N 5A 5Z .§1' GA 

I 211 2S 2U 3S 5R GC lS ]& 2T 2L 3G ~ 5S 5D 

0 ~ lZ 2F 5P 6H 6X 

l!'W1Ill~~~~~9~~2X~~~:5X~Q~~ 

P lR 2R 3X 411 4U 4B 6L GB 3C 3T 4L 4T 

0~~3U~9~~1IIB~~~~~M~ 

X lU 2K 311 3Y 4S 5Q GK lB gg 3I 3Y 4N 50 §I 

z 

B 

V lK 2Y 3R 4A 4D ~ lR 2H 3N 5J §Ii 

L~~2J~40~00WW~~~~~~95R~ 

Y 10 lX 2Z 2D 3Z 50 2U ~ 4H 4Z ~ 6J 6R 6B ~-

W ~ D~n~~·~~~D4E~~9~ 

U 2Q2P3D4F4P5F6H5U 

T lS 2A 3A 4N 5V 6U lE lK ~ 2N 4D ~ 

H :5J 3K 4Y GD 2G ~ 2W 4K 5I 

G 2V 2X 2L 3N 3Q 4X GQ lT 3M GP 

D~9~~~~M~~~.§!~~~~OO 

K lZ lC 4T 6X 6A lX 2S 20 2K :5D 3A 3V 3J 4J 

B 3G 4E 5S GE lV lP lJ 2Z 2V 3K § GD 6U 6K 

8 lQ 2E 3F 4H 5G 6J lA 111 lL 3W 40 5C ~ §Q §g 

l{ lD ~ 4Q GN lQ 2J 5T §K GT 

Underlined type denotes wheels in reversed positions. 
114: 

T.uw V 

B lE 4L 4R 60 lP ,U, §§ 5J 68 

l lI 10 2X 4A 4D SQ SV 6A 6G lN lC 28 2A 

MIBU~~M4Mft~~~~ll~ff~4E4A6R 

A 2I 4S 5F 6J 4H 6H 

Q lQ lU lX 2G 2U 3W 2Z m ~ SO 6Y 

I 182J5Y6N6R!!gQ303Yil5MSZ5Y6K§Z 

0 2N 2T 2V 3T SS 60 lR 18 28 2K 3F 4L SR 5C -------- ]!' 6W lY .21 50 6G 6W 

PllLlll~~4J~99~~~~~3E3W4B4Ze~ 

0 lS 2S 3Y 4N 4V 4C 611 6C ~ ~ 4K 4S X3J~3V~~~mIBW~~~~e~~ 

z 1 V 2L 3N 3Z 4T SR 6L --------- lA gf ,mi 3X 4M 5N 6L 

:a 

v 

L lL 2Z 3S 48 4E 4L ,W 2G 3M SI SG 

Y~~~3Me4H6Hll~~~~~~sx~~~ 

W lP lY 2A 2E 3A 5P 2% 3T 4G 4Y 40 6I fill §A 6E 

urow~~~~a~~~ll4D4U9~~ 

T 2R 2Q 3E 4G 4Q 5G 6I §I 

B lT 2B 38 40 SW 6V m !i 20 g 4C a 

G 3K3L4Z6E2F.2Q2!4JSH 

D 2W2Y2M303R4Y6Rll3L§Q 

K~~~~~~5U~~2X5U~m~6116F ------- B 1Al04U6Y6BlJ.Di2NgJ_~~~3I~ 

B 3H 4P ST 6F lJl 10 lI 2Y 2U 31 ~ .§Q. ~ ~ 

1' lR 2F 3G 4I SH 6K lZ lL lK 3V 4N 58 SA SP 6P 

Underlined type denot.ee wheels in :revened --------- poaltlona. 

115 

TABU L 

B lS 2G 3H 4J SI 6L !I ll l~ ~ ~ §A 5Z 50 §Q 

l lF 411 4S 6P 10 2H §S SI §B 

M lJ lP 2Y 48 4E 5R SW 68 6H lM ll 2A 2Z 

Allll~~:5J4Na~~~6Yu~~e4D~fill 

Q 2J 4T SG 6K ~ §g 

I lR lV lY ~ 2V 3X 2Y ~ :5J 5C ~ 

0 lC 2K SZ 60 6S lU 2P ~ 3X 4U §L 5Y 5X 6J §! 

l!' 202U2W~ST6E,W.!AgsgJ_3E~~58 

P 6X l:I 20 5N §I! §! 

Callll~3E4K~9~~6A~~~~3V4A~4E~ 

X lT 2T 3Z 40 4W 4D 6N 60 3A 3R ~ 4R 

Z3K~3W~~~~W~~2B~~40~~ 

B lW 2M 30 3A 4U S8 6M ll 20 ~ 3 ~ §II 6K 

v 

L 

Y 1M2A3T4C4P4Mif2F3L5H5F 

ww~a~~~&ll~~~3M4S~3~~~ 

U lQ lZ 28 2F 38 SQ 28 3S ~ ~ 4N §H ~ 6Z §12 

TWIBW~~~a~~~~4C~~~m 

B 2S2R3F4H4R5H6J58 

G lU 2C 3C 4P 5X 6W lC ll 2N 2L 48 g 

D 3L 3M 4A 6F 2E gQ ill 4I 5G 

K 2X 2Z 2N 3P 3S 4Z 6S 1:B 3K 6N 

B~3Y3R~~~~6R~DM~006A6L~ 

S 18 lE 4V ~ 6C ll !Q g 2I 38 g: 3T 3H ~ 

lf 3I 4G 5U 6G ll 1Ji lH 2X 2T 3I ~ § §§ 6I 

Underlined type denot.ee wheela In ravened poaitiona. 
116 

B :sJ 4H 5V 6H lS J.11 lG 2W g§ .mi 4P §A 6R §Ii 

1 lT 2H 3! 4K 5J 6M l.X: l!l. lI 3T 4L §Z 5Y .§N 6N 

M: lG 4N 4T 6Q lN 2G §Q 5H §Q 

A lK lQ 2Z 4C 4F 5S 5.X: 6C 6I lL lA 2Z 2Y 

QWll~3H~~~~~6RSUru~~~~~ ------- I 2K4U5H6L~6F 

0 lS lW lZ 2I 2W 3Y &I ~ 3! 58 6W 

l!' lD 2L 5A 6P 6T lT 20 ~ ,3 il 5K .§1 5W 6I 6X 

P 2P 2V 2X 3V 5U 6F lP lZ gg 2I 3D ~ 5P 5A 

0 6Y lW 2C 5M 6E 6U 

x~n~~~~~~~~6B~~~~3U~G4D~ 

z lU 2U 3A 4P 4X 4E 60 6E 3Z ~ 4I ---------~ 

B$~~9~~~~ll~U~~4N®~ 

v lX 2N 3P 38 4V 5T 6N --------- ll 2N ~ ~ ~ §L 6J 

L 

y 

W lN 28 3U 4D 4G 4N 10 2E 3K 5G 5E 

u~ru~~~~6J~~~3Y~~~~~~~ 

T 1R1A2C2G3C5R2R~4E4W4116G606Y6C 

B lE lI lH 10 2F 2Q --------- 4Z 5D 5E 5K lC ~ § §ll ~ §§ 

G 2T2S3G4I4S5I6K§B . 

D 1 V 2D 3D 4Q 5Y 6X 18 lH 211 2K 4A 4V ------ K 3M3N4B6G2D282T~§f 

B 2Y 2A 20 3Q 3T 4A 6T !Q 3J 611 

S~~~3W~~9~~~~fil6BS~~ ------- 1' lC lF 4W 6A 6D lU 2P 2L 2H 3A ;sx ~ ~ 4G 

Underlined type denotes wheels in reversed positions. 

117 

TABLll w 

B 10 lG 4X 68 6E 1 T 2Q _gg 2G :5Z 3W 3R ~ 4F 

1 3K 4I 5W 6I lR 1,lt lF 2V gs 3G 40 6Z §Q. 6G 

M: lU 2I :sJ ~ 5K ·SN lW !1 lH 3S ~ 5Y §I 511 611 

A 1H404U6R1Mgf§f5G6P 

Q lL lR 2A 4D 4G 5T 5Y 60 6J lK lZ 2Y _gx 

Illll~~~~~~~~~W~ft4N~~~ 

0 2L 4V 5I 611 4E 6E 

P lT lX lA ru 2X 3Z 2W 30 3H §A 6V 

P lE ~ 58 6Q 6U lS 2N ~ 3V 4S 5J 5W §! 6H 6W 

0 2Q 2W 2Y 3W 5V 6G 10 lY 2P glj 3C 4I 50 5Z 

X 6Z!!~§L~6T 

Z lN 111 lC 2F 3G 4M 511 5P 5Q. 5H 6C 2T ~ 3M 3B ~ 4Y 4W ~ 6K 

B 1 V 2V 38 4Q 4Y 4F 6P 6F 3Y 3P 4H 4P 

V3M~3Y~~®g~~~~~~~~§§ 

L 1 Y 20 3Q 3C 4W 5U 60 lX 211 3E 3U ~ 5K 6I 

y 

w 

U 10 2C 3V 4E 4H 40 lN 20 3J §[ 50 

T~~~~4S4K~~!QW~~~~~~~ro 

B lS 18 2D-2H 3D 5S gg ~ 4D ~ 4L 6F 6N 6X 6B 

G lF lJ 11 lP 2G 2R·4A 5E 5F 5L 18 4A ~ 5T §I 6R 

D 2U 2T 3H ~ 4'r 5J 6L §Q 

K lW 2E 3E ~ 5Z 6Y lA ~ 2L ru ~ 4U 

B 3N 30 4C 6H 2C g& .. 2S 4G 5! 

S 2Z 28 2P 3R 3U 48 6U lf 3I 6L 

-~~~~$~~~6X~~~&6Y~~ 

Underlined type denot.ea wheela In revened positions. 
118 

TAaaU 

B~~~~~~~m~~SM~~~~ 

l lE lH 4Y 6C 6F lS gt! g,z 2F ~ 3V ~ :5E 4E 

K 3L 4J SX 6J !Q !K lE 2U gQ 3F 4N ~ 6P 6F 

A lV 2J :5K 4M SL 60 ll !H lG ~ ~ §I 5W SL §L 

Q lI 4P 4V 6S lL 2E SO §l §Q 

I 111 lS 2B 4E 4H 5U SZ 6E 6K lJ lY 2X 21' 

oau~3J94Q4A~~m~ll~4S4114A3~ 

.. 2M4W5J6N~§Q 

P lU lY 18 2K 2Y 3A 2V :5N 3G SZ m 

C lF 2N SC 6R 6V lB ~ ~ ,ml 4R .§1 ~ SU 6G 6V 

X 2R 2X 2Z 3X SW 6H !Ii lX 20 2G 38 4H SN §I 

. z 6A,lY2A§K~§§ 

B 10 lN lD 2G :5H 4N SN SQ SR SI 6D .§ :511 3L 3A ~ 4X 4V ~ 6J 

v lW 21 3C 4R 4Z 4G 6Q 6G B 30 4G jQ 

L~~~oo9~~wrom2Y~~~9~ 

Y lZ 2P :5R :5D 4X SV 6P ll 2L m 3T ~ 5J 6H 

w 

'U 

T lP m :51 4F 4I 4P 111 2C 3I ~ SC 

Blla~~ft~~llRll3~~9~aam 

G lT lC 2E 2I :5E ST 2P 3P 4C 4U 4K 6E 611 61 6A 

DWllU~2H~G~M511li~~~~~ 

K 2V 2U 3I 4K 4U SK 611 §f 

B 1X2F3F4SSA6Z,lZlf:gJS;ll£~ 

S 30 3P 4D 6I 28 2Z 2R 4F §12 

1' 2A 2C 2Q :5S :5V 4C 6V !Q ,mi §K 

UD.derllDed tne denotes wheela In nvened poeltlona. 

I 

119 

T.a.aaT 

B 2B 20 2R :5T :51 4D 6W lN 3G 6J 

1~~:5V~~~~6V~~~~~616H6A 

K lF lI 4Z 6D 6G lR 2M ll 2E :5X ,ml 3P :5D ~ 

A :511 4K SY 6K R lJ lD 2T 2P :5E 411 §I 60 6E 

Q 11 2K 3L 4N 511 6P lU lG if: ~ ~ SI SV §K 6K 

I lJ 4Q 4W 6T !K m a SE fill 

0 lN lT 2C 4F 4I SV SA 6F ~ lI 11 2W .§ 

-.~~:5H:5K:5N4RG~~m~~~4R~4Z~611 

P 2H4XSK60~6C 

C lV lZ lC a 2Z 38 ,2Y :511 ~ §I 6T 

X 1G20SD6S6W!Q2L~3T~5H§Y~§l:§Y 

Z 2S 2Y 2A ~ SX 6I 111 ll 2N g[ 3A 4G §I SX 

B ~ lT 2Z 5J 68 6R 

vuw~~M~oo~~5J6E2Rn~~~-~~~ 

L lX 2X 3D 4S 4A 4H 6R 6H :5W :5N 4F ~ 

y~~3A~~~~ro~~2X$~4K9~ 

W lA 2Q :5S 3E 4Y SW 6Q 1 V 2K 3C 3S ~ SI 6G 

'U 

T 

B lQ 2E 3X 4G 4J 4Q !L 28 :5H SD SB 

G~2M~:5R~4M611ll!QIB~M~~~S~6S 

D lU lD 2F 2J 3F SU 20 30 G 4T ~ 6D 6L §! 6Z 

KIBallll~~4CM~~~g~3M~ 

B 21 2V 3J ~ 4V SL ~ SO 

S lY 2G ~ 4T S8 6A lY lE 2J 2H ~ 4S 

1' 3P3Q4E6J2A2Y,gQ,4ESC 

Undmtined fi1pe daDofieB wheels In nvened poeltiom. 
120 

TaLJ11 B 

B :5Q 3R 4F 6K 2Z 2X 2P 4D 58 

1 20 2E 2S ~ :5X 4E 6X 111 ~ 6I 

-~3D~~~~~6W&2R~~6X~6G6Z 

A lG lJ 4A 6E 6H !Q 2L 2H &12 9 ~ 30 30 4C 

Q 3N 4L 5Z 6L 10 lI 10 2S 20 3D 4L 6W ~.6D 

I lX 2L 3M 40 ---------- 5N 6Q 1 T lF lE 3P 4H 5V 5U ~ 6J 

0 lK 4R 4X 6U lJ .&Q . 

--------- 511 5D 6.11 

I' 10 lU 2D 4G 4J 51 58 6G 611 lH 11 2V 2U 

P~WM3L~4S4C9~6V6Dll2F~4K~~~ 

0 20 4Y 5L 6P 48 ~ 

lC 11 lA lD 211 2A 3C ,21 ~ 3E 5X 6S 

Z lH 2P 5E 6T 6X lP ~ :5I 3S 4P 5G 5T 5$. 6E 6T 

B 2T 2Z 28 3Z 5Y ---------- 6J lL lV 2M 2E 3Z 4F 5L 51' -------- v 60 lS ,ll §1 6A §.Q 

L lQ lP lF 2I 3J 4P 5P 5S 5T 5K 6F _gg 3K 3J g ~ 4V 4T S §H 

Y lY 2Y 3E 4T 48 4I 6S 6I 3V 3M ~ 411 

W~3V~~~~6Z~ll2B8~:5X4J~~ ---------- u 18 2R :5T :5F 4Z 5X ~ lU 2J 38 3R 4G 5H 6F ------- T 

B 

G lR 2F 3Y 4H 4K 4R lK 2A 3G.50 5A ----- D ~~~~~4N~ll~ro~~4NM9~.~~ 

K~~00~~~~~4A4S~~6K6U~---

B lI lM lL lS 2J 2U --------- 4D 5H 5I 50 lY 4X 40 §Q §[ §Q 

8 2X 2W 3K 4M 4W 511 60 5N 

JI lZ 2H ~ 4U 50 68 lX lQ 2I 2G 4W 4R 

Underlined type denote. wheels In revened positionL 

I 

121 

T.&Br.11 G 

B lA 2I 3I 4V 5D 60 !! 10 gfl g[ 4V ~ 

1 3R 3S 4G 6L 2Y &I 20 4C 5A 

M: 2D2F2T3V3Y4F6Y!L3§H 

A8~:5X~~~~6X~~~~~6U~~ 

Q lH lK 48 ~ 6I lP 2K gQ .&Q 3V 3S 3N 38 48 

I 30 4M 5A 611 lH lH 18 2R 2N 30 ~ .§!: §I 60 

0 lY 211 3N 4P 50 ~ !§ ii lQ ~ 4G 5U 5T 5I 6I 

I' lL 4S 4Y 6V ll. 28 5L 50 6L 

P lP 1 V 2E 4H 4K 5X 5C 6H ~ lG ll 2U 2T 

0 10 lD 3J 3M 3P 4T 4D 5S 5G 6W 6E !Q 2E 4P. ~ 4X ~ 6K 

lC 2P4Z~6Q4A§! 

Z lX 18 lE 2N 28 3D 2S 3K 3D 51 §B 

B lI 2Q 5F 6U 6Y !Q &l ~ 3R 40 5F 5S 5R 6D §§ 

V 2U 2A 20 3A 5Z 6K lK lU §. &12 ~ 4E 5K .§! 

L 6DlR2X5H6Z§f 

Yll~ro2J3K~~~~~6G~3JM~~~4Sg~ 

W 1Z2Z:5F4U4C4J6T6J~3L~4L 

U~9~9~~&ll~~~~9~~~ 

T 10 2S :5U :5G 4A ~y 6S lT ll :5A ~ ~ §Q §I 

B 

G 

D lS 2G :5Z 4I 4L 4S lJ 2Z 3F §1 ~ 

KID~2R~~40~ll~~-~~4113~~~~ 

B lW lF 2H 2L :5H 5W .211 311 ~ ~ 4H 68 6J 6T 6X 

BW~~~~~4EM~~~--~~~~ 

lf 2Y 2X :5L 4N 4X 5N 6P §II 

Underlined type denotes wheels in revened poaitionL 
TABLll D 

B 2Z 2Y 311 40 4Y 50 6Q 5L 

l 182J3J4W5E6Dllll2G2E~~ 

K 3S 3T 4H 611 2X 2V 2N 4B §I 

A 2E2G2U3W3Z4G6Z1K~6G 

Q2X~~~~g~~oo~a~av~~sx 

I lI lL 4C 6G 6J 10 U 2F 2B 3U 3R ~ 3A ~ 

0 3P 4N 58 6N !II lG !A gQ 211 3B ~ 6U 6L §I 

F lZ 2N 30 4Q 5P 6S ll ,!12 lC 3N 4F ~ .§§ §II §8 

P 111 4T 4Z 6W !H 2A .§K 58 6K 

0 lQ lW 2F 4I 4L 5Y 50 6I 60 .ll: lU ~ 2S 

x~~~3N~4U4E~~sx~~m~~~~6J 

Z 2Q4A5N6R~§i 

B. lY lC lF 20 2C 3E 2R 31. 3C §! §g 

V lJ 2R5G6V6ZlJii13G~~5E§B§Q6C§B 

L 2V 2B 20 38 5A 6L lJ ll 2K ,&2 ~ ~ §l ml 

·y 6E!QgJ[5G~60 

W~ll~~3L~5R~~9~~M~3~ft·a~ 

U lA 2A 3G 4V 4D 4K 6U 6K ~ 3K 4C 4K 

T3R:SX~~~fil~llll~m~~4H~g 

H 102T3V3H4B5Z6T1§2H~3P~.§[6D 

G 

D 

K lT 2H 3A 4J 411 4T lI 2Y B §A 5Y 

BW~~3U4Xe~ll~~~~4L323M~ 

S lX lG 2I 211 3I 5X 2L 3L ,il ~ ~ 6A 6I 6S 6W 

NllW~W~~e~~~llg~~m• 

UnderllDed type denot.ea wheels in nvemed positioDL 

I 

123 

TABLll K 

B lL lP 10 lV 211 2X 4G 5K 5L 5R lV 4U ~ 5N ~ 6L 

l 2A2Z3N4P4Z5P6R§K 

K lC ~ 3K 4X 5F 6E lJl lA 2F 20 ~ ~ 

A 3T 3U 4I 6N D 2U 211 4A. §I 

Q 2F 2H 2V :5X 3A 4H 6A lJ 3C 6F 

Ill~~~95X~~6D~~~W6S6D61 

0 1J11140~6K!B2I2E_&\3T~3L,3~ 

F 3Q 40 5C 60 lL .ll: lZ 2P 2L ~ 4I 6T §K 6A 

P lA 20 3P ~ 5Q 6T lQ lC ll ~ 4E ~ mi mi 6G 

0 lN 4U 4A 6X lG 2Z ~ 5A ,ii!l. 

X lR lX 2G 4J 411 5Z 5E 6J 6P ~ lT 2S 28 

z~~3L~3R~O~fil~6G10~4N4H~~n 

B. 2R 4B 50 6S .il §I 

V lZ 10 lG 2P 20 3F gQ 3I ml ml 6P 

L 1K~~616AlJl2H3F~~50§Q268§Q 

Y ~ 2C 2E 3C 58. 611 ll ll U 28 3W ~ 5I 5T 

W 6F lP 2V 5F 6X 6N 

U~~ii~311~~~9~~2N3H~~3N~~G6E 

'l' 18 28 3H 4W 4E 4L 6V 6L 3S 3J ~ 4J 

:e:~~3~~~00llllfi~~3U~3-

G 1Em3W3I4C5A6U!B&Q~~~5E6C 

D 

][ 

B lU 2I 3Q 4K 4N 4U !H 21 30 §I 5X 

Sll~~~~~~ll~,!123R~4K~~9~~ 

N lY lH 2J 2N 3J 5Y ,21 3K 4X ~ 0 §i §8 §R .§! 

UnderllDed type dellot.ea wheels in revened poeitioDL 
124 

T.a.:ar.11 E 

B lZ lI" 2K 20 :5K· 5Z ·2J :5J g ~~§I ml §Q fill . 

l lM lQ lP lW 2N 2Y 4H 5L 5M 5S lU 4T ~ 5M 58 §K 

K 282A:504Q4A5QSSg 

A lD 2L :5L 4Y 5G SF ll ll 2E.2C 4S ~ 

Q :5U :5V 4J SO 2V 2T 2L 4Z 5X 

I 2G 2I 2W :5Y :58 4I SB ll,. 38 SE 

o~~~~~~~&.~~~3~~~~ 

l!' lK lN 4E SI SL 11 fill iJ2 2Z 3$. 3P. :5K g 4Y 

P :5R 4P 5D SP lK ll ll 20 g,K ~ ~ §§ §!l ~ 

0 18 2P 3Q 4S 5R SU if lB lA ~ ~ §J! §Q 5F SF 

X 10 4V 4B 6Y .![ gx .QI 5Z 6I 

Z lS lY 2H 4K 4N 5A 5F SK 6Q !IL~ 2R gQ 

BllW3M~~3~$~~~~~~~~sm 

V 2S 4C 5P ST 4X SX 

L lA lE lH 2Q 2E :5G 2P ,mi ~ ~ §Q 

Y lL 2T 5I 6X 6B ,!L 2G 3E :50 4L 5C 5P 50 SA 6P 

W 2X 2D 2F :5D 5C 6N lH lR ll ~ 3V g 5H 5S 

U 6G 1Q ,2ll ~ SW SM 

Tw~wa~~M9~006Ja~~~~~~~~ 

B lC 2C :5I 4X 4F 411 SW 6M 3R 3I 4A 4I 

G~~~~~~~~ll~~9~4F~~ 

D lF 2V 3X 3J 4D 58 SV !Q 2F 3X 3N 4C 5D S8 

K 

B 

8 1 V 2J :5C 4L 40 4V lG 21' ~ §I 3 

Nll~~9~~~HWW~:5D~~~~M6N 

Underlined type denotes wheels in reversed. poaitioDB. 

121> 

TABLZ s 

Bll2S~3X4A4S~WlIIB~~~M9~~6M 

l lA lJ 2L 2P :5L 5A 2I 3I 4V 4N 4D 6X §[ §f 6T 

Krnll~ll~~~9~M~4S4J~96J 

A 2C 28 3P ~ 4B 5R ST 5I 

Q lE 2M 3M 4Z 5H SG lS 1 Y 2D 28 ~ 4M 

I 3V 3W 4K SP 2U 2S ~ 4Y 3 

0 2H 2J 2X 3Z :5C 4J SC lH 3A SD 

l!'2A~38~00~~6B~~~~~§Q6BW 

P lL 10 4F 6J 6M ,!L 2G 2C 2Y 3R 30 3J 3X 4X 

0 3S 4Q 5E SQ lJ lD ~ 2N 2J 3Y 4G 6R 6I 6Y 

X lC 2Q 3R 4T 5S 6V 10 lA lZ :5K 4C §Q 5P 5E 6E 

Z lP 4W 4C SZ lE 2X 5H §I m 

B 1 T lZ 2I 4L 40 58 5G SL SR lC lR gQ 2P 

V~IB~~~4X4H9~&~~2A4L4F~~~ 

L 2T4D5QW4W6W 

Y lB lF lI ~ 2F 3H gQ ~ 3Z 5S 6N 

W lM2U~SY6ClK2F:5D3N4K58505N6Z60 

U 2Y 2E 2G :5E 5D 60 !Q !Q 2H 2Z 3U 4A 5G 5R 

T ~~&A.5D6V6L 

BHW~~~~~~~~~2L~~~~S~~~ 

G lD 2D 3J 4Y ~ 4N SX 6N ~ 3H 4Z ~ 

D~~m$fil~~~Ha~3V~4E~~ 

K lG 2W 3Y :5K 4E 5C SW lP 2E 9 ~ ~ .§Q §A 

B 

8 

N 111 2K :5D 4M 4P 4W lF 2V 38 5X 5V 

Underlined type denotes wheela in reveraed poaitlona. 

'11888---~Jll 8 
126 

TABLll N 

B lX 2L 3E 4N 4Q 4X lE 2U 3A .§! 5U 

lU~~3Y~~~HIBll~~~~~~~~ 

M: lB lK 211 2Q 3M 58 2H 3H 4U 4M 4C 6W 6E 60 es· 

A 10 lS lR lY 2P 2A 4J 5N 50 5U lS 4R 4I .§.K 5Z §l 

Q 2D2C3Q4S4C5S6U§H 

I lF 2N 3N 4A 5I 6H lR lX 2C 2A ~ ~ 

0 3W 3X 4L 6Q 2T 2R 2J ~ §! 

Ji' 2I 2K 2Y 3A 3D 4K SD lG 3Z SC 

P~~~~~~~oo~afil~~~~~ 

C lM lP 4G SK SN lK 2F 2B 2X ~ 3N 3I 3W 4W 

X 3T 4R 5F SR lI .!Q lW 2M 2I 3X 4F §Q 6H SX 

Z lD 2R 3S 4U 5T SW lN lZ 1 Y ~ 48 5P 50 5D SD 

B lQ 4X 4D SA lD 2W 5G 5X SG 

V lU lA 2J 4M 4P 5C 5H 611 SS ll !Q 2P 20 

L lT lI 30 3R 3U 4Y 4I 5X 5L S8 6J lL 2Z 4K 4E 4S ~ §f 

Y 2U 4E 5R SV 4V §! 

W lC lG lJ 2S 2G 3I 2N 3F 3Y 5R 6M 

U lN 2V 5K SZ SD lJ 2E 3C 3M 4J 5A 5N 5M 6Y 6N 

T 2Z 2F 2H 3F 5E SP lF lP 2G 2Y 3T 4Z 5F fill 

B SI lM 2S 5C SU SK 

Gll~R~~~~~~~~2K~~~~e4N~g 

D lE 2E 3K 4Z ~ 40 SY SO 3P 3G 4Y ~ 

K~~3H~~9~~W~~3U~4D~6J 

111 lH 2X 3Z 3L 4F 5D 6X 10 2D 3V 3L 4A §I ~ 

B 

N 

Underlined type denotes wheels in reversed positions. 

APPENDIX VI 

SUMMARY OF RESULTS 

By using the values derived from a study of the "V" and "Z" messages it was possible 

to find messages in which three values of the indicator were known-the first, second, and fifth 

letters. A little experimentation soon yielded the value of the remaining two indicator letters 

and also values for the "dog setting" square. 

The lines d and r indicate which letters correspond to direct and reversed setting respectively, 

of the wheels. 

Figure 1 gives the dog setting corresponding to the various combinations of the first two 

wheels. There are no values entered in row 5 or in column 5 because in the messages submitted 

wheel 5 was not used. 

Figure 2 gives the plain-text equivalents for the enciphered indicators. 

Figure 3 gives the complete settings of those cipher messages which were read. No attempt 

was made to read any further messages since it appeared th.at a complete solution would be a 

matter of time only. 

d ___ A C F G J K L 0 R S T X Z 

r ___ B D E H I M N P Q U V W Y 

1 

1 

2 ABY 

3 8CZ 

4 

5 

~1 ACZ 

2 I a 

4 ~ 6 

8CZ 1 CDV 

BDV BDZ 

ADW BEX 

CDV. 

BDV 

F1auu 1 

(127) 

CEV 

ACZI 

ADW 

~ I 

• 
128 

Plain 

Clphm 1 3 3 ' 5 - - A T ,___ 

B v A 

c 0 M ,_ 

D F K T u 

E L 0 

F 0 

G I E 

H 

- I ,___ - - - - - J A D 

K c w 

L c x c Q 

II D K 

N N Q ,___ - 0 c 

p z F p B 

Q J I v 

R I A J ,_ 

s G v H J 

T N K 

u E A ,_ - ,_ - ·-- v H ,. D H ,_ - w E 

x 

~I~ 

- ·-

- Q 0 

L J 

F:tGUBll 2 

129 

Ellelphend Dee111berecl M1111111 

Indicator lndleator No. 

ZRZPP=YALPB (156) 

6l8G 

VDLSU=HKXJA (162) 

Hiil 

MRLDO=DAXUC (179) 

3111'3 

BSKVF= VVCDZ (186) 

MUlll 

LPDUU=CFTEA (189) 

Hl3l 

SSSVJ=GVHDE (196) 

36'12 

VGBKL=HIAWQ (210) 

3318!1 

F1ouu 3 

0 

BJJC!Phend DeelJlhend Jl....-

lndlaatar Indator No. 

SCRLT=GOJCK (218) 

81' 

DRTUV=FANEH (252) 

3111lH 

NNBQU=NQAIA (253) 

"183 

DDJQP=FKDIH (229) 

3111CI 

QRPCP=JAOMB (206) 

llltl 

PSYLV=ZVQCH (177) 

llW3 

RNTLE=IQNCO (165) 

81'