NATIONAL BUREAU OF STANDARDS REPORT

1896

THE COMPLETE SOLUTIONS OF THE

BALANCED 'INCOMPLETE BLOCK DESIGNS

WITH TEN OR FEWER REPLICATIONS

by

Melicent K 0 Rupp

with an introduction by

W 0 So Connor

<N%>

U. S. DEPARTMENT OF COMMERCE

NATIONAL BUREAU OF STANDARDS
U. S. DEPARTMENT OF COMMERCE

Charles Sawyer, Secretary

NATIONAL BUREAU OF STANDARDS

A. V. Astin, Director THE NATIONAL BUREAU OF STANDARDS

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the divisions and sections engaged in technical work. In general, each section is engaged in specialized research, development, and engineering in the field indicated by its title. A brief description

of the activities, and of the resultant reports and publications, appears on the inside of the back

cover of this report.

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Optics and Metrology. Photometry and Colorimetry. Optical Instruments. Photographic

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Ordnance Development. These three divisions are engaged in a broad program of research

Electromechanical Ordnance, and development in advanced ordnance. Activities include

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® Office of Basic Instrumentation • Office of Weights and Measures.
NATIONAL BUREAU OF STANDARDS REPORT

NBS PROJECT

3737=60-0002 29 August 1952

NBS REPORT

1896

THE COMPLETE SOLUTIONS OF THE

BALANCED INCOMPLETE BLOCK DESIGNS

WITH TEN OR FEWER REPLICATIONS

by

Melieent Rupp

with ~an introdubti-on by

W e So Connor

Statistical Engineering Laboratory

National Applied Mathematics Laboratories

The publication, repi

unless permission iso

25, D, C. Such perm

cal ly prepared If ths

Approved for public release by the

Director of the National Institute of

Standards and Technology (NIST) on October 9, 2015

n part, Is prohibited

ndards, Washington

ort has been specifijort for Its own use,

FOREWORD

This report was prepared as part of a continuing program

of research on mathematical statistics and its applications

carried out at the National Bureau of Standards under the

general supervision of Dr* Churchill Eisenhart, Chief of the

Statistical Engineering laboratory* The Statistical Engineering

Laboratory is Section 11*3 of the National Applied Mathematics

Laboratories (Division 11, National Bureau of Standards), and

is concerned with the development and application of modern

statistical methods in the physical sciences and engineering*

J* H* Curtiss

Chief, National Applied

Mathematics Laboratories

A. V. A3tin

Director

National Bureau of Standards
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INTRODUCTION

by

W. S* Connor

In the balanced incomplete block design v variaties or treatments are compared in such a manner that each treatment is

assigned tp r experimental units* The units themselves are arranged

into b more or less homogeneous blocks, each containing k experlmental units* Any two treatments occur together in the same block

X times, the treatments occurring in a given block being all

different. Hence the design depends on the five parameters, v, b,

r, k, and X* From this definition it is easy to show that the

following conditions are necessary?

bk - vr, r(k-l) = (v-i)^ , Fisher [1] also showed that for the existence of an actual

combinatorial solution it is necessary that

b > v, or k < r * The work of Yates [2], Fisher and Yates [3], Bose [ij.], and

Bhattacharya [£], [6], [7], provided solutions for many of these

designs* Sets of parameters which satisfy the above conditions,

together with brief explanations of how to construct the corresponding designs, are included in Fisher and Yates' tables [8],

All of these sets have r < 10, which is felt to be a practical

upper limit.

The purpose of this report is to write out in full the

solutions for the designs which are listed by Fisher and Yates*

It is believed that making the designs more accessible will

increase their usefulness.

Every solution occupies one or more pages. The reference

number and parameters of the design are given at the top of the

page, followed in some cases by descriptive remarks, and then by

the solution. Treatments are denoted by Arabic numbers, blocks

by Arabic numbers in parentheses, and replications by Roman

numbers * The Index gives the reference number,'* parameters, and

important characteristics of each design. These characteristics

”*No solution is known for those sets of parameters which do not

carry a reference number* All but two of these designs have been

proved impossible.

ii

are abbreviated in a "’Remarks 9* column,, The abbreviations have the

following meanings % "R" denotes "resolvable" , which means that

the blocks are divisible into groups , vh ich have the property that

every treatment occurs once in a groups where i^ and ±2

are positive integers , means that the blocks have been divided

into i^ groups , each of which contains every treatment ±2 times

„

"YoSo" denotes "Youden Square" , which means that the treatments have been arranged so that each column contains every

treatment exactly once 0 This kind of arrangement is always

possible when b = v 8 The first Youden Squares were given in [ 9 ].

"EoYoSo" denotes "extended Youden Square 99 , and means that each

column contains every treatment times, where 1, is a positive

integer , greater than one

„

REFERENCES

[1] Ro A, Fisher , "An examination of the different possible

solutions of a problem in incomplete blocks 3 " Annals

of Eugenics , Vol ,10 , (1940), ppo52»75e

[2] F e Yates , "Incomplete randomized blocks /

9 Annals of Eugenics , Vol o7 , (1936), pp« 121 -X14.0 o

[33 Ro A, Fisher and F e Yates, Statistical Tables for Biological 9 Agricultural 0 and Medical Research , 1st edition,

Oliver and Boyd, Lts 0 , 193S"«

[ip] R„ Co Bose, "On the construction of balanced incomplete

block designs," Annals of Eugenics, Vol »10 , (1939) „ PP. 353-399.

[5] K 0 N 0 Bhattaeharya, "A new balanced incomplete block design,"

Science and Culture , Vol 0 9 , (19144),: p 9 508 o

[6] Ko No Bhattaeharya, "On a new symmetrical balanced incomplete

block design," Bull a Calcutta Math 0 Soc. 9 Vol c 36 9 (1944)

pp 0 91-96o

[73 Ko No Bhattaeharya, "A new solution in balanced incomplete

block design, 99 Sanjdiya , Volo? , (1946), pp 0 423°424°

[8] Ro Ao Fisher and F 0 Yates, Statistical Tables for Biological , Agrieultur al „ and Medical Research, Oliver and Boyd, Ltd, w;

[9] Vi 0 Jo Youden, "Use of incomplete block replications in

estimating tobacco-mosaic virus, 99 Contributions from

the Boyce , Thompson Institute , ^ol 0 9 o (1937 )

0

pPo4l°48 0

- 1 -

1 0 kb v r J

2 6 4 3 1

3 Replications

Rep 8 Blk* Tr P

I

(1) 1 2

(2) 3 4

II

(3) 1 3

(4) 2 4

III

(5) i 4

{6) 2 3

- 2 »

2* k

2

b v r A

io 5 4 i

2 groups; each contains 2 replications;

extended Youden Square

Rep» Blk« Tr„

I

(1) 1 2

(2) 2 5

(3) 3 4

(4) 4 1

(5) 5 3

II

(6) 1 3

(7) 2 4

(3) 3 2

(9) 4 5

(10) 5 l
. 1
A

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3. k b v r

2 15 6 £

5? Replications

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I

II

III

IV

V

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(1)

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( 3 )

(4)

(5)

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3

2

6

5

1 3

2 6

4 5

1 4

2 3

5 6

( 10 )

( 11 )

( 12 )

( 13 ) (14)

(15)

1 5

2 4

3 6

1 6

2 5

3 4

- k -

k. k b v r A

2 21 7 6 1

3 groups s each contains 2 replications;

extended Youden Square

S2£&

I

Blk,

(1)

(2)

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( 5 ) (6)

( 7 )

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1 2

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6 5

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1

2

3

1+ 6

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6 1

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III

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( 16 )

( 17 )

( 18 )

( 19 )

( 20 ) (21)

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2 3

3 6

k 5

5 2

6 7

7 1

- 5 -

Repo

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II

III

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2

b

28

v

8

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7

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7 Replications

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(1)

(2)

(3)

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( 10 )

( 11 )

( 12 )

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(li+)

(15)

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1

3

5

6

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8

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VII

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2

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5

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7

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5

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6 0 k b v r X

2 36 9 8 1

4 groups 5 each contains 2 replications 5 Extended Youden Square

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II

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(7) 7 3 (250 7 9

( 8 ) 8 9 (26) 8 1

(9) 9 5 (27) 9 3

( 10 ) 1 3 ( 28 ) 1 5

( 11 ) 2 5 (29) 2 4

( 12 ) 3 6 (30) 3 8

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(14) 5 8 IV (32) 5 3

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(16) 7 1 (34) 7 2

(17) 8 4 (35) 8 7

( 18 ) 9 2 (36) 9 1

- 7 -

7. k b v r X

2 k5 10 9 1

9 Replications

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,

Rep, Blk, Tr,

(1) 1 2 (16) 1 5

(2) 3 4 (17) 2 4

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(6) 1 3 (21) 1 6

(7) 2 10 (22) 2 5

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(9) 7 8 (24) 4 8

(10) 6 9 (25) 7 9

(id 1 4 (26) 1 7

(12) 2 3 (27) 2 6

III (13) 5 8 VI (28) 3 5

(14) 6 7 (29) 4 9

(15) 9 10 (30) 8 10

Rep. Blk. Tr.

(31) 1 8

(32) 2 7

VII (33) 3 6

(34) 4 10

(35) 5 9

(36) 1 9

( 37 ) 2 8

VIII (38) 3 7

(39) 4 6

( 40 ) 5 io

(4D l io

(42) 2 9

(43) 3 8

(44) 4 7

(45) 56

IX

- 8 -

Rep»

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II

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5 groups; each contains 2 replications!

Extended Youden square

Blk» Tr 0 Rep © Bike Tr o

(1) 1 2 (23) 1 4

(2) 2 11 (21+) 2 3

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(7) 7 1 (29) 7 11

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(9) 9 4 (3D 9 1

(10) 10 9 (32) 10 8

(11) 11 8 (33) 11 5

(12) 1 3 (31+) 1 5

(13) 2 6 (35) 2 9

(11+) 3 5 (36) 3 6

(15) 4 10 (375 4 2

(16) 5 9 IV (38) 5 7

(17) 6 8 (39) 6 10

(18) 7 2 (1+0) 7 8

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(20) 9 7 (1+2) 9 ii

(21) 10 11 0+3) 10 i

(22) 11 4 (44) 11 3

SSE0 Bike Tr o

(45) 1 6

(1+6) 2 5

0+7) 3 4

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Y (50) 6 11

(5D 7 10

(52) 8 9

(53) 9 3

(54) 10 2

(55) 11 1

9

9* k b v r X

3 b b 3 2

Youden Square

Block Treatment

(1)

(2)

(3)

(b)

1 2

2 3

3 b

b i

3

1

2

- 10

k b V r X3 7 7 3 1

Youden Square

Block Treatment

(1) 1 3 6

(2) 2 1 5

(3) 3 7 2

(W U 5 3

(S> 5 6 7

(6) 6 2 4

(7) 7 4 1

11

11 . k b v r X

3 10 5> 6 3

2 groups; each contains 3 replications;

Extended Youden Square

Rep

.

I

II

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( 3 ) (k)

( 5 )

( 6 )

( 7 )

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1

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3

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1

2

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b

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1 $ ^ 2

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3 $

k 1

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1 3

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12. k b

3 10 6^2 v r %

Block Treatment

(1)

(2)

(3)

( k) (5)

(6)

(7)

(8)

(9)

(10)

2 4 6

3 4 5

5 6 1

5 6 2

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6 3 4

13 -

13 , k b v r A

3 12 9 4 1

4 Replications

Rep, Blko Tro

( 1 ) 1 2

I (2) 4 5

(3) 7 8

(4) l 4

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( 6 ) 3 6

(7) 1 6

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< 9 ) 3 5

(10) l 5

( 11 ) 2 6

(12) 3 4

3

6

9

7

8

9

8

9

7

9

7

8

IV

- lij. -

11+. . k b v r X

3 26 13 6 1

2 groups; each contains 3 replications;

Extended Youden Square

Blko

(1) 1

Tr.

3 9

(2) 2 k 10

(3) 3 5 11

(4) k 6 12

(5) 5 7 13

(6) 6 8 1

(7) 7 9 2

(8) 8 10 3

(9) 9 11 k

(10) 10 12 5

(u) 11 13 6

(12) 12 1 7

(13) 13 2 8

(i^) 2 6 5

(15) 3 7 6

(16) k 8 7

(17) 5 9 8

( 18 ) 6 10 9

(19) 7 11 10

(20) 8 12 11

(21) 9 13 12

(22) 10 1 13

(23) 11 2 1

(Zk) 12 3 2

(25) 13 k 3

(26) 1 5 k

- 15 -

15 • k b v r

3 30 10 9 2

3 groups; each contains 3 replications;

Extended Youden Square

Rep, Blk. Tr

.

II

III

(1)

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( 3 ) (4)

(5)

( 6 )

( 7 )

( 8 )

( 9 )

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( 11 )

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( 19 ) (20)

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( 24 ) (25)

( 26 )

( 27 )

( 28 )

( 29 )

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1

2

3

4

5

6

7

8

9

10

1

2

3

4

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6

7

8

9

10

1

2

3

4

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6

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- 16 -

Hep.

I

II

III

16. k b V r X

3 35 15 7 1

7 Replications

Blk. Tr

.

Rep» Blk. Tr o

(1) 1 2 3 (21) 1 10 il

(2) 4 8 12 (22) 2 12 14

(3) 5 10 15 V (23) 3 5 6

(4) 6 11 13 (24) 4 9 13

(5) 7 9 14 (25) 7 8 15

(6) 1 4 5 (26) 1 12 13

(7) 2 8 10 (27) 2 5 7

(8) 3 13 14 VI (26) 3 9 10

(9) 6 9 15 (29) 4 11 15

(10) 7 11 12 (30) 6 8 14

(11) 1 6 7 (3D 1 14 15

(12) 2 9 11 (32) 2 4 6

(13) 3 12 15 VII (33) 3 8 11

(14) 4 10 14 (34) 5 9 12

(IS) 5 8 13 (35) 7 10 13

(16) 1 8 9

(17) 2 13 15

(18) 3 4 7

(19) 5 11 14

(20) 6 10 12

IV

- 17 -

17 o k b v r X

3 57 19 9 1

3 groups; each contains 3 replications;

Extended Youden Square

Blko Tr o ReP« Blk„ Tr o

(1) 1 7 11 (39) 4 6 9

(2) 2 8 12 (40) 5 7 10

(3) 3 9 13 (4D 6 8 11

(4) 4 10 ib (42) 7 9 12

(5) 5 11 15 (43) 8 10 13

(6) 6 12 16 (44) 9 11 14

(7) 7 13 17 (45) 10 12 15

(8) 8 ib 18 (46) 11 13 16

(9) 9 15 19 III (47) 12 14 17

(10} 10 16 1 (48) 13 15 18

(11) 11 17 2 (49) 14 16 19

(12) 12 18 3 (50) 15 17 1

(13) 13 19 4 (5D 16 18 2

(14) ib 1 5 (52) 17 19 3

(15) 15 2 6 (53) 18 1 4

(16) 16 3 7 (54) 19 2 5

(17) 17 b 8 (55) 1 3 6

(18) 18 5 9 (56) 2 4 7

(19) 19 6 10 (57) 3 5 8

(20) 2 3 14

(21) 3 b 15

(22) b 5 16

(23) 5 6 17

(214-) 6 7 18

(25) 7 8 19

(26) 8 9 1

(27) 9 10 '2

(28) 10 11 3

(29) 11 12 4

(30) 12 13 5

(3D 13 ib 6

(32) ib 15 7

(33) 15 16 8

(34) 16 17 9

(35) 17 18 10

(36) 18 19 11

(37! 19 1 12

(38) 1 2 13

- 18 -

18 0 k

bvr

X 3 70 21 10 1

Rep, I

II

III

IVV

10 Replications

Bike Tr o ReP. Blk, Tr

Q

(1) 1 2 3 (36) 1 8 10

(2)

k 5 6 (37) 2 18 19

(3) 7 8 9 (38) 3 15 17

(4) 10 ll 12 VI (39) 4 12 16

(5) 13 14 15 (40) 5 9 21

(6) 16 17 18 (4D 6 11 14

(7) 19 20 21 (42) '7 13 20

(8)' 1 4 15 (43) 1 11 18

(9) 2 5 ll (44) 2 10 20

(IQ) 3 9 16

VII (45) 3 5 12

(id 6 17 20 (46) 4 9 13

(12) 7 12 19 (47) 6 16 21

(13) 8 13 18 (48) 7 14 17

dii-) 10 14 21 (49) 8 15 19

(15) 1 5, 17 (50) 1 12 20

(16) 2 4 14 (5D 2 6 8

(17) 3 7 ii

VIII

(52) 3 14 19

(18) 6 10 19 (53) 4 18 21

(19) 8 16 20 (54) 5 7 15

(20) 9 15 18 (55) 9 10 17

(21) 12 13 21 (56) ll 13 16

(22) 1 6 9 (57) i 13 19

(23) 2 7 16 (58) 2 9 12

(2k) 3 8 21

IX

(59) 3 4 20

(25)

k 17 19 (60) 5 8 14

(26) 5 10 13 (61) 6 7 18

(27) 11 15 20 (62) 10 15 16

(28) 12 14 18 (63) 11 17 21

(29) 1 7 21 (64) 1 14 16

(30) 2 13 17 (65) 2 15 21

(31) 3 10 18 (66) 3 6 13

(32)

k 8 11

X (67) 4 7 10

(33) 5 16 19 (68) 5 18 20

(31*.) 6 12 15 (69) 8 12 17

(35) 9 14 20 (70) 9 11 19

*» 19 “

19 . k b v r X

k £ $ k 3

Youden Square

Blk, Tr

,

( 1 ) 12 3 4

( 2 ) 2 3 k 3

( 3 ) 3 4 5 1

( 4 ) 4 5 12

( 5 ) 5123

20 -

20 . k b v r A

4 7 7 4 2

Youden Square

Blk. Tr

( 1 ) 12 3 4

( 2 ) 2 4 7 5

( 3 ) 3 6. 5 2

( 4 ) 4 5 6 1

( 5 ) 5 7 13 ( 6 ) 6 3 4 7

( 7 ) 7126

21

21. k b v r A

k 13 13 k 1

Youden Square

Blkp Tr,

(1) 1 2 3 10

(2) 2 6 13 7

(3) 3 13 k 8

(4) k 7 1 11

(5) $ 11 8 2

(6) 6 k 10 5

(7) 7 3 5 12

(8) 8 1 12 6

(9) 9 12 2 k

(10) 10 8 7 9

(11) 11 9 6 3

(12) 12 10 11 13

(13) 13 5 9 1

- 22 -

22 , k

4

b

14

v

8

r

7

X

5

7 Replications

ii

hi

IV

v

VI

Blk»

( 1 )

( 2 )

( 3 )

( 4 )

( 5 )

( 6 )

(7)

( 8 )

'(9)

(10)

(It)

( 12 )

Tr

,

1

$

1

3

r

2

1

2

1

3

1

2

1

2

2

6

2

4

3

4

4

3

2

4

3

4

4

3

3

7

7

5

6

5

6

5

s

7

5

6

5

6

4

8

8

6

8

7

7

8

6

8

7

8

VII (13)

( 14 ) 8

7

- 23 -

23 . k b v r A

k 1$ 6 10 6

5 groups?

each contains 2 replications,

which are separable

.

g-elL«

I

II

III

Blk,

( 1 ) (2)

( 3 )

( k

)

( 5 )

( 6 )

( 7 ) (8)

( 9 )

IV

( 10 )

( 11 )

( 12 )

( 13 )

( 111 ) (IS)

Tr,

12 3 4

3 4 5 6

5 6 12

12 3 5

3 4 16

5 6 2 4

12 3 6

3 4 2 5

5 6 14

12 4 5

3 4 2 6

5 6 13

12 4 6

3 4 15

5 6 2 3

V

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24 * k

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r 4 15 10 6

Blk 0 'Tr.

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(2) 136

(3) 1 if 7

(if) 2 3 5

(5) 2 3 if (6) 3 if 7

(7) if 2 9 ( 8 ) 567

(9) 678 ( 10 ) 759 ( 11 ) 5 6 10

(12) 8 9 if (13) 8 9 10

(14) 9 10 2

(15) 10 8 1 X2 89

10

10681123I673

- 2£

-

25 • k b v r

ij. 18 9 8

X

3

2 groups | each contains I4. replications

Extended Youden Square*

Blko Tr,

(1) 1 k 6 7

(2) 2 6 8 9

(3) 3 8 9 1

a) 1+132 ( 5 ) 5718

(6) 6 9 4 5

(7) 7 3 2 6

( 8 ) 8 2 5 4

(9) 9 5 7 3

(10) 12 5 7

(11) 2 3 6 5

(12) 3 4 7 9

(13) 4 9 2 1

(14) 5 19 6

(15) 6 8 13

(16) 7 6 4 8

(17) 8 5 3 4

( 18 ) 9782

» 26

26 * k b v r X

4 20 16 5 1

5 Replications

Rep

II

III

IV

Blk„

( 1 )

( 2 )

( 3 )

( 4 )

( 5 )

( 6 ) (75

(85

Tr

( 10 ) (H5

(125

ak)

,( 15 )

( 16 )

(17)

( 18 )

1 2

5 6

9 10

13 Ik

1

2

3

k

1

2

3

k

1

2

3

k

1

2

3

4

5

6

7

8

6

5

8

7

5

6

8

7

6

5

3

7

11 12

15 16

9 13

10 Ik

11 l£

12 16

11 16

12 15

9 34

10 13

12 14

11 13

10 16

9 15

10 15

9 16

12 13

11 34

V

(20)

- 27 -

27 o k b v r X

4 50 2£ 8 1

2 groups 5 each contains 4 replications

Extended You den Square

Blk 0 Tr

.

Rep o Blko Tr 0

(1)

1 1 2 6 25 (26) 1 3 11 19

(2) 2 3 7 21 (27) 2 4 1? 20

(3) 3 k 8 22 (28) 3 5 13 16

(4) k 5 9 23 (29) 4 1 14 17

(5) 5 1 10 24 (30) 5 2 15 18

(6) 6 7 11 5 (31) 6 8 16 24

(7) 7 8 12 1 (32) 7 9 17 25

(8) 8 9 13 2 (33) 8 10 18 21

(9) 9 10 14 3 (34) 9 6 19 22

(10) 10 6 15 4 (35) 10 7 20 23

(11) 11 12 16 10 (36) 11 13 21 4

(12) 12 13 17 6 (37) 12 14 22 5

(13) 13 14 18 7 II (38) 13 15 23 1

(14) 14 15 19 8 (39) 14 11 24 2

(15) 15 11 20 9 (40) 15 12 25 3

(16) 16 17 21 15 0P-) 16 18 1 9

(17) 17 18 22 11 (42) 17 19 2 10

(18) 18 19 23 12 (43) 18 20 3 6

(19) 19 20 24 13 (44) 19 16 4 7

(20) 20 16 25 14 (45) 20 17 5 8

(21) 21 22 1 20 (46) 21 23 6 14

(22) 22 23 2 16 (47) 22 24 7 15

(23) 23 24 3 17 (48) 23 25 8 11

(21).) '24 25 4 18 (49) 24 21 9 12

(25) 25 21 5 19 (5o) 25 22 10 13

= 28 -

28 o k b v r A

4 63 28 9 1

9 Replications

Rep a Blko Tr 0

(1) 1 3 23 26

(2)

(3)

2 11 20 28

4 Q 15 16

(4) 5 8 10 12

(5) 6 7 22 2?

(6) 13 18 24 25

(7) 14 17 19 21

(8) i 2 24 27

(9) 3 12 21 28

(10) 4 8 23 25

(ID 5 7 13 17

(12) 6 9 10 11

(13) 14 16 22 26

(14) 15 18 19 20

(15) i 4 17 18

(16) 2 6 21 23

(1?) 3 5 11 15

(18) 7 16 25 28

(19) 8 9 19 22

(20) 10 13 26 27

(21) 12 14 20 24

(22) 1 5 20 22

(23) 2 4 10 14

(24) 3 6 16 17

(25) 7 8 21 24

(26) 9 18 2? 28

(2?) 11 13 19 23

(28) 12 15 25 26

Rep 0 Blk«

(58)

(59)

(60)

(61)

(62)

(63)

Rep 0 Bike Tr,

(29) 1 6 12 13

(30) 2 5 16 18

(3D 3 4 19 24

V (32) 7 9 20 23

(33) 8 17 26 28

(34) 10 15 21 22

(35) 11 14 25 27

(36) 1 10 19 28

(37) 2 3 22 25

(38) 4 7 11 12

VI (39) 5 9 24 26

(4o) 6 8 14 18

(4D 13 16 20 21

(42) 15 17 23 2?

(43) i 7 14 15

(44) 2 9 12 17

(45) 3 8 20 2?

VII (46) 4 13 22 28

(47) 5 6 19 25

(48) 10 16 23 24

(49) ii 18 21 26

(50) i 8 11 16

(5D 2 7 19 26

(52) 3 9 13 14

VIII (53) 4 5 21 27

(54) 6 15 24 28

(55) 10 17 20 25

(56) 12 18 22 23

Tr o

1 9 21 25

2 8 13 15

3 7 10 18

4 6 20 26

5 14 23 28

11 17 22 24

12 16 19 27

IX

- 29 -

29 k

5

b

6

v

6

r

5

X

k

Youden Square

Bike

( 1 ) (2)

( 3 ) (k)

( 5 ) (b)

1

2

3

k

5

6

2

3

k

5

6

1

Tr

,

3

4

5

6

k

5

6

1

2

3

5

6

1

2

3

k

- 30 -

30 . k b v r A

5 11 11 5 2

Youden Square

Blk« Tr o

(1) 1 5 6 7 9

(2) 2 8 7 6 10

(3) 3 6 10 11 1

(k) k1 7 11 1 2

($> 5 11 k 8 6

(6) 6 9 3 2 k

(7) 7 k 5 10 3

(8) 8 1 2 3 $

(9) 9 10 1 k 8

(10) 10 2 9 5 11

(11) 11 3 8 9 7

31

°= 31

k b v r \

5 18 9 10 5

2 groups | each contains 5 replications

Extended Youden Square

Rep 0 Blk 0

I

( 1 ) (2)

( 3 ) (k)

( 5 ) (6)

( 7 )

( 8 )

( 9 )

II

( 10 )

( 11 )

( 12 ) (135

(li4-)

( 15 )

( 16 )

( 17 ) (185 -

1

2

3

6

7

8

9

1

2

3

k

5

6

7

8

9

Tr o

2 3 7 8

6 8 4 1

8 5 9 2

3 9 2 6 17 3 1).

1). 2 5 7

9 16 3

5 4 19

7 6 8 5

26518 3 5 9

5 1 ix 6 3287 7924 8735

4 8 9 1

9 4 6 3 16 7 2

- 32 -

32.

k

bv 5 18 10

Blk . Tr e

(1) 123 ( 2 ) 346 ( 3 ) 234 ( 4 ) 3 4 5 ( 5 ) 456 ( 6 ) 356 ( 7 ) 456

(8) 367 ( 9 ) 457 ( 10 ) 678 ( 11 ) 578 ( 12 ) 6 8 9 ( 13 ) 7 9 10

(14) 8 10 1 ( 15 ) 7 9 1 ( 16 ) 8 10 1 ( 17 ) 923 ( 18 ) 10 1 2 K789

10

1011221

102344566 r95789789

10899

10132254

33 -

33 o k b v r X

5 21 21 5 1

Youden Square

Bike Tr.'

(1) 1 2 3 4 17

(2) 2 5 15 19 12

(3) 3 13 12 6 21

(4) 4 7 13 10 19

(5) 5 8 6 17 7

(6) 6 19 1 11 16

(7) 7 21 16 2 9

(8) 8 16 18 12 4

(9) 9 18 5 13 1

(10) 10 12 17 9 11

(11) 11 4 21 5 14

(12) 12 14 7 1 20

(13) 13 11 8 20 2

(14) 14 6 2 18 10

(15) 15 17 14 16 13

(16) 16 10 20 3 5

(17) 17 20 19 21 18

(18) 18 15 11 7 3

(19) 19 3 9 14 8

(20) 20 9 4 15 6

(21) 21 1 10 8 15

° 34 -

34» k b v r X

5 30 2£ 6 1

6 Replications

Rep* Blko Tr »

(1) 1 2 3 4 5

(2)

(3)

6 7 8 9 10

I 11 12 13 14 15

(4) 16 17 18 19 20

(5) 21 22 23 24 25

(6) 1 6 11 16 21

(7) 2 7 12 17 22

II (8) 3 8 13 18 23

(9) 4 9 1

4

19 24

(10) 5 10 15 20 25

(11) X 10 lk 18 22

(12) 2 6 15 19 23

III (13) 3 7 11 20 24

(14) 4 8 12 16 25

(15) 5 9 13 17 21

(16) 1 9 12 20 23

(IT) 2 10 13 16 24

IV (18) 3 6 111 17 25

(19) 4 7 15 18 21

(20) 5 8 li 19 22

(21) i 8 15 17 24

(22) 2 9 li 18 25

V (23) 3 10 12 19 21

(24) k 6 13 20 22

(25) 5 7 14 16 23

(26) 1

7' 13 19 25

(27) 2 8 14 20 21

VI ( 28 ) 3 9 15 16 22

(29) 4 10 li 17 23

(30) 5 6 12 18 24

“ 35 o=

35' o k b v r A

5 82 41 10 1

2 groups? each contains £ replications?

Extended Youden Square

Blko Tr o Bike Tr »

(1) i 10 16 18 37 (42) 1 19 31 32 35

(2) 2 ii 17 19 38 (43) 2 20 32 33 36

(3) 3 12 18 20 39 (44) 3 21 33 34 37

( k ) 4 13 19 21 40 (US) 4 22 34 35 38

(5) 5 14 20 22 41 (46) 5 23 35 36 39

(6) 6 15 21 23 i (47) 6 24 36 37 4o

(7) 7 16 22 24 2 (48) 7 25 37 38 41

(8) 8 17 23 25 3 (49) 8 26 38 39 i

(9) 9 18 24 26 4 (50) 9 27 39 40 2

(10) 10 19 25 27 5 (5D 10 28 40 41 3

(11) 11 20 26 28 6 (52) 11 29 41 i 4

(12) 12 21 27 29 7 (53) 12 30 1 2 5

(13) 13 22 28 30 8 (54) 13 31 2 3 6

(14) 14 23 29 31 9 (55) 14 32 3 4 7

(15) 15 24 30 32 10 (56) 15 33 4 5 8

(16) 16 25 31 33 11 (57) 16 34 5 6 9

(17) 17 26 32 34 12 (58) 17 35 6 7 10

(18) 18 27 33 35 13 (59) 18 36 7 8 11

(19) 19 28 34 36 14 (60) 19 37 8 9 12

(20) 20 29 35 37 15

II

(61) 20 38 9 10 13

(21) 21 30 36 38 16 (62) 21 39 10 11 14

(22) 22 31 37 39 17 (63) 22 40 11 12 15

(23) 23 32 38 4o 18 (64) 23 41 12 13 16

(24) 24 33 39 4i 19 (65) 24 i 13 14 17

(25) 25 34 4o 1 20 (66) 25 2 14 15 18

(26) 26 35 4i 2 21 (6?) 26 3 15 16 19

(27) 2? 36 i 3 22 (68) 27 4 16 17 20

(28) 28 37 2 4

‘23 (69) 28 5 17 18 21

(29) 29 38 3 5 24 (70) 29 6 18 19 22

(30) 30 39 4 6 25 (7D 30 7 19 20 23

(31) 31 40 5 7 26 (72) 31 8 20 21 24

(32) 32 41 6 8 2? (73) 32 9 21 22 25

(33) 33 1 7 9 28 (74) 33 10 22 23 26

(314-) 34 2 8 10 29 (75) 34 11 23 24 2?

(35) 35 3 9 11 30 / 76) 35 12 24 25 28

(36) 36 4 10 12 31 (77) 36 13 25 26 29

(37) 37 5 11 13 32 (78) 37 14 26 2? 30

(38) 38 6 12 14 33 (79) 38- 15 27 28 31

(39) 39 7 13 15 34 (80) 39 16 28 29 32

Ui-o) 4o 8 14 16 35 (81) 40 17 29 30 33

(4D 4x 9 15 17 36 (82) 41 18 30 31 34

36 k

6

- 36 »

b

7

Y

7

r A

6 5

Youden Square

Blko Tr 9

( 1 ) 1 2 3 4 5 6

(2) 2 3 It- 5 6 7

(3) 3 4 5 6 7 X

(4) 4 5 6 7 12

(5! 5 6 7 12 3

((7)

6 ) 671234

7 1 2 3 4 5

CORRECTION

In the designs which are divided into groups, Roman

numbers have been used to indicate the groups 0 The caption

of this column has been mislabelled ”Rep 0 , w instead of the

correct ’’Group . ” For example, the design with reference

number 2, which has two groups, should appear as follows;

Group Blk, Tr 0

( 1 ) 1 2

(2) 2 5

I (3) 3 4

( 4 ) 4 1

( 5 ) 5 3

( 6 ) 1 3

(7) 2 4

II (8) 3 2

( 9 ) 4 5

(10) 5 l

No confusion will arise by observing that such designs

carry a brief description, in which the number of groups is

specified <, Some other designs, such as the design with reference

number 1, are divided into replications, and hence the caption ’’Repo” is correct for therm

- 37 - /

37*

k

b

v

r > 6 11 11 6 3

Youden Square

Bike Tr , ( 1 ) 2 3 4 8 10 11

(2) 3 4 5 9 11 1 ( 3 ) 4 5 6 10 1 2

(it.) 5 6 7 11 2 3 ( 5 ) 6 7 8 1 3 4 ( 6 ) 7 8 9 2 4 5

(7) 8 9 10 3 5 6

(8) 9 10 11 4 6 7

(9) 10 11 1 5 7 8

(10) 11 1 2 6 8 9 ( 11 ) 1 2 3 7 9 10

«* 38 —

38 , k

6

b

12

v

9

r

8

A

5

4 groups; each contains 2 replications

which are separable

Rep,

I

II

III

IV

Blk,

( 1 )

( 2 )

( 3 )

( 4 )

( 5 ) (6)

( 7 )

( 8 )

( 9 )

( 10 )

( 11 )

( 12 )

Tr,

1

4

7

1

2

3

1

2

3

2

3

2

5

8

4

5

6

6

4

5

5

6

4

3

6

9

7

8

9

8

9

7

9

7

8

7

1

4

2

3

1

3

1

2

3

1

2

8

2

£

6

4

5

6

4

4

5

6

i

9

3

6

8

9

7

7

8

9

8

9

7

39.

k

b 6 15

Blko ( 1 ) 3

(2) 2 ( 3 ) 2 ( 4 ) 1

(5) i

(6) 1 ( 7 ) 3 ( 8 ) 2 ( 9 ) 1 ( 10 ) 1 ( 11 ) 1 ( 12 ) 1 ( 13 ) 1 ( 14 ) 1

(15) 2 v

r

A

10 9 5

Tr, 6 7 9 10 5 7 8 10 5 6 8 9 6 7 8 9 7 8 9 10 5 6 9 10 6 7 8 10 4 8 9 10 4 5 9 10 4 6 8 10 3 7 8 9 3 6 7 10 3 4 5 7 4 5 6 8 5 6 7 9

39443452533222234

4o

i^Oo k b v r A

6 16 16 6 2

Youden Square

Blko Tr o

(1) 1 2 3 5 12 13

(2) 2 3 k 6 5 14

(3) 3 4 1 7 10 15

(4) 4 1 2 8 ii 16

(5) 5 6 7 9 16 1

(6) 6 7 8 10 13 2

(7) 7 8 5 11 14 3

(6) 8 5 6 12 15 4

(9) 9 10 11 13 4 5

(10) 10 ii 12 14 1 6

(11) 11 12 9 15 2 7

(12) 12 9 10 16 3 8

(13) 13 Ik 15 1 8 9

(14) 14 15 16 2 5 10

(15) 15 16 13 3 6 11

(16) 16 13 14 4 7 12
-• .r? -
3

Rep

I

II

III

“ I).l «=

4l • k b v r A

6 21+ 16 9 3

groups | each contains 3 replications s which are separable 0

Blk o Tr o

(1) 1 2 5 6 11 12

(2) 3 k 7 8 9 10

(3) 5 6 9 10 13 14

(k) 7 8 11 12 15 16

(5) 9 10 15 16 1 2

(6) 11 12 13 14 3 k

(7) 13 14 1 2 7 8

O) 15 16 3 k 5 6

(9) 1 3 6 8 *13 15

(10) 2 4 5 7 14 16

(11) 5 7 13 15 9 11

(12) 6 8 14 16 10 12

(13) 9 11 2 4 6 8

(11+) 10 12 1 3 5 7

(15) 13 15 10 12 2 4

(16) 14 16 9 11 1 3

(17) 1 4 5 8 10 11

(18) 2 3 6 7 9 12

(19) 5 8 9 12 13 16

(20) 6 7 13 16 1 k

(21) 9 12 1 4 14 15

(22) 10 11 14 15 6 7

(23) 13 16 10 11 2 3

(21+) 14 15 2 3 5 8

= 42 «=

k2 a k b V r X

6 31 31 6 l

Youden Square

Blk<> Tr

(1) 1 2 3 4 5 26

(2) 2 22 2? 17 7 12

(3) 3 13 8 18 23 27

(4) 4 24 9 27 19 14

(5) 5 2? 25 20 10 15

(6) 6 9 7 10 26 8

(7) 7 28 11 3 24 20

(8) 8 4 28 25 12 16

(9) 9 5 13 21 28 17

(10) 10 1 14 22 18 28

(11) 11 14 12 26 15 13

(12) 12 23 20 1 9 29

(13) 13 10 16 2 29 24

(14) 14 17 29 6 3 25

(15) 15 7 18 29 4 21

(16) 16 26 17 19 20 18

(17) 17 15 24 8 30, 1

(18) 18 11 2 9 25i 30

(19) 19 12 10 30 21 3

(20) 20 30 22 13 6 4

(21) 21 25 26 24 22 23

(22) 22 3 31 15 16 9

(23) 23 31 4 11 17 10

(24) 24 18 5 12 31 6

(25) 25 .19 1 31 13 7

(26) 26 29 30 28 27 31

(2?) 27 21 6 16 1 11

(28) 28 6 15 23 2 19

(29) 29 8 19 5 11 22

(30) 30 16 23 7 14 5

(3D 31 20 21 14 8 2

" 43 ~

43 o k78876 b v r X

Youden Square

Blk 0 Tr e

(1) 1 2 3 4 5 6 7

( 2 ) 2 3 4 5 6 7 8

(3) 3 4 5 6 7 8 1

(4) 4 5 6 7 8 1 2

(5) 5 6 7 8 1 2 3

(6) 6 7 8 1 2 3 4

(7) 7 8 1 2 3 4 5

( 8 ) 8 1 2 3 4 5 6

- 44 -

44® k b V p A

7 15 15 7 3

Youden Square

Blk o Tr «

(1) 1 2 3 5 6 9 11

(2) 2 3 4 6 7 10 12

(3) 3 4 5 7 8 11 13

(4) 4 5 6 8 9 12 14

(5) 5 6 7 9 10 13 15

(6) 6 7 8 10 11 14 l

(7) 7 8 9 11 12 15 2

(8) 8 9 10 12 13 1 3

(9) 9 10 11 13 14 2 4

(10) 10 11 12 14 15 3 5

(id 11 12 13 15 1 4 6

(12) 12 13 14 1 2 5 7

(13) 13 14 15 2 3 6 8

(14) 14 15 1 3 4 7 9

(15) 15 1 2 4 5 8 10
'/'

-

*
- 45 - A3

45 o k

b 7 30

Blko

(1) 1 5 ( 2 ) 2 8

(3) 3 1 ( 4 ) 4 2

(5) 3 io ( 6 ) 5 4

(7) 1 4 ( 8 ) 2 8

(9) 3 5

(10) 4 9 ( 11 ) 1 10

(12) 5 2

(13) 3 7

(14) 23

(15) 3 4

(16) 4 7

(17) 5 8 ( 18 ) 5 7

(19) 1 9 ( 20 ) 12 ( 21 ) 1 3

(22) 1 2

(23) 2 3

(24) 34

(25) 4 9

(26) 5 1

(27) 5 2 ( 28 ) 1 2

(29) 6 7 ( 30 ) 11 12

vv

21 10

Tr 0 9 13 18 19

13 14 19 16

14 15 16 17

15 ii 19 17

ii 12 16 18 8 12 17 18 8 11 14 20

15 18 19 20

ii 19 16 20

12 16 17 20

13 19 17 20

14 16 18 20

13 17 18 20 9 12 13 21

14 18 19 21

15 19 16 21

ii 16 17 21

12 19 17 21

15 16 18 21

ii 17 18 21 8 11 12 19 7 12 13 16 8 9 14 17 8 10 13 15

13 14 11 18

10 14 15 12 6 7 15 11 4 5 20 21 9 10 20 21

14 15 20 21 7

1069767

129

1066

156

106

13

10647569

1038

13

46©

kb 7 36

Blko ( 1 ) 1 2

(2) 1 3

(3) 2 4

(41 2 3

(5) 3 4

(6) 4 6

(7) 5 7

(6) 5 6

(9) 6 7

(10) 7 8

(11) 8 9

(12) 9 10

(13) 10 11 ( 14 ) 11 12

(15) 12 13

(16) 13 15

(17) 14 16

(18) 14 15

(19) 15 16

(20) 16 17

(21) 17 18

(22) 18 19

(23) 19 20

(24) 21 24

(25) 20 22

(26) 20 21

(27)

(28)

21

22

22

24

(29) 23 25'

(30) 23 24

(3D 24 25

,(32) 25 26

(33) 26 27

(34) 27 2

(35) 28 3

(36) 28 1 v

r

A

28 9 2

Tr 0 14 20 23 28

15 20 21 24

16 21 22 25

17 22 26 1 9 -18 23 2?

19 23 24 2

24 25 28 3

12 25 26 4

13 20 26 27

21 2? 1 5

14 22 28 6

15 28 2 7

16 23 3 8

2k 1 4 9

18 25

X 10

26 2 5 11 2 3 6 12 3 4 7 13

20 28 4 8

21 5 9 14 5 6 10 15 6 7 11 16 7 8 12 17 8 9 13 18 3 9 10 19 4 10 11 14

2? 11 12 15

12 13 16 20 6 13 17 21 7 14 18 22 8 14 15 19 9 15 16 23

10 16 17 24

17 18 20 25

18 19 21 26

13 19 22 2?

4656785

10

1189

10

11

12

13

17

14

19

27

17

1$

19

221

232

25

26

23

5' 28

26

271

28

11

124

47

47 . k

7

1? 56

v

49

r

8

A

1

8 Replications

Rep,

II

III

IV

Bike TFj> Rep 0 Blko Tr

,

>

(1) 1 2 3 4 5 6 7 (29) l 12 16 2? 31 42 46

(2) 8 9 10 ii 12 13 14 (30) 2 13 17 28 32 36 47

(3) 15 16 17 18 19 20 21 (31) 3 14 18 22 33 37 48

(4) 22 23 24 25 26 27 28 V (32) 4 8 19 23 34 38 49

(5) 29 30 31 32 33 34 35 (33) 5 9 20 24 35 39 43

(6) 36 37 38 39 40 41 42 (34) 6 10 21 25 29 40 44

(7) 43 44 45 46 4? 48 49 (35) 7 11 15 26 30 4i 45

( 8 ) l 8 15 22 29 36 43 (36) 1 11 21 24 34 37 47

(9) 2 9 16 23 30 37 44 (37) 2 12 15 25 35 38 48

(10) 3 10 I? 24 31 38 45 (38) 3 13 16 26 29 39 49

(11) 4 11 18 25 32 39 46 VI (39) 4 14 17 2? 30 4o 43

(12) 5 12 19 26 33 40 47 (4o) 5 8 18 28 31 4i 144

(13) 6 13 20 2? 34 41 48 (4D 6 9 19 22 32 42 45

(14) 7 14 21 28 35 42 49 (42) 7 10 20 23 33 36 46

(15) 1 14 20 26 32 36 44 (43) 1 10 19 28 30 39 48

(16) 2 8 21 2? 33 39 45 (44) 2 11 20 22 31 40 49

(17) 3 9 15 28 34 4o 46 (45) 3 12 21 23 32 4i 43

( 18 ) 4 10 16 22 35 4i 47 VII (46) • 4 13 15 24 33 42 44

(19) 5 11 17 23 29 42 48 (47) 5 !4 16 25 34 36 45

(20) 6 12 lb 24 30 36 49 (48) 6 8 17 26 35 37 46

(24) 7 13 19 25 31 37 43 (49) 7 9 18 27 29 38 47

(22) 1 13 18 23 35 4o 45 (50) 1 9 17 25 33 41 49

(23) 2 14 19 24 29 4i 46

4?

(5D 2 10 18 26 34 42 43

(24) 3 8 20 25. 30 4? (52) 3 11 19 2? 35 36 44

(25) 4 o 21 26 31 36 48 VIII (53) 4 12 20 28 29 37 45

(26) 5 10 15 2 ? 32 37 49 (54) 5 13 21 22 30 38 is

(27) 6 11 16 28 33 38 43 (55) 6 14 15 23 31 39 kl

(28) 7 12 17 22 34 39 44 (56) 7 8 16 24 32 40 48

k.Q -

ij.8 « k b v r X

8 9 9 8 ?

Youden Square

Blko Tr 9

•t

( 1 ) 12345678 ( 2 ) 23456789 ( 3 ) 34567891 ( 4) 45678912 ( 5 ) 56789123 ( 6 ) 67891234 ( 7 ) 78912345 ( 8 ) 8 9 1 2 3 4 5 6

( 9 ) 91234567

49

- 49 “

k b v r .A

8 15 15 8 4

Youden Square

Blk„ Tr

„

(1) 4 7 8 10 12 13 14 15

(2) 5 8 9 11 13 14 15 l

(3) 6 9 10 12 14 15 l 2

(45 7 10 11 13 15 i 2 3

(55 8 11 12 14 i 2 3 4

(6) 9 12 13 15 2 3 k 5

(7) 10 13 14 1 3 4 5 6

(8) 11 14 15 4 5 6 7

(9) 12 15 l 3 5 6 7 8

(10) 13 1 2 4 6 7 8 9

(11) 14 2 3 5 7 8 9 10

(12) 15 3 4 6 8 9 10 11

(13) 1 4 5 7 9 10 11 12

(14) 2 5 6 8 10 11 12 13

(15) 3 6 7 9 11 12 13 14

“ So «

50 » k

b

vp

A 8 57 57 8 1

louden Square

Blko

(1) 1 2 3 4 5 6 7 50

(2) 2 51 16 23 30 37 9 44

(3) 3 10 51 24 31 38 45 17

(4) 4 11 18 5i 32 39 46 25

(5) 5 12 19 26 51 4© 33 47

(6) 6 13 20 2? 34 51 48 41

(7) 7 14 21 28 35 42 49 51

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(32) 32 42 55 6 9 19 22 45

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(45) 45 4 57 20 28 29 12 37

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(54) 54 33 37 48 22 3 14 18

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( 7 ) 7 9 11 12 13 14 17 1 2

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(68) 5 11 26 33 39 54 58 64 79

(69) 6 12 27 31 37 52 59 65 80

(70) 7 13 19 35 41 47 63 69 75

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61 -

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Rep e Blk e Tr,

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(74) 2 16 24 31 39 53 63 68 73

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(2) 2 4 9 10 12 13 16 17 18

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(16) 16 18 4 5 7 8 11 12 13

(17) - 17 19 5 6 8 9 12 13 14

(18) 18 1 6 7 9 10 13 14 15

(19) 19 2 7 8 10 11 14 15 16

18

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(2) 2 3 12 9 10 17 16 19 5 22

(3) 3 k 20 10 17 13 6 18 ll 23

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(8) 8 11 17 25 16 23 29 7 26 5

(9) 9 12 24 29 27 18 1 26 17 6

(10) 10 13 18 19 29 25 2 27 28 7

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(12) 12 8 27 23 20 29 4 22 21 2

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(15) 15 24 26 5 2 27 ii 10 30 20

(16) 16 25 6 30 3 28 12 11 27 21

(17) 17 26 28 7 30 22 13 12 4 15

(18) 18 2? 23 1 5 30 14 13 22 16

(19) 19 28 30 2 6 14 8 24 23 17

(20) 20 22 8 3 7 24 9 30 25 18

(21) 21 23 10 4 l 26 30 25 9 19

(22) 22 21 11 17 24 1 25 2 31 13

(23) 23 15 3 18 25 2 26 31 12 14

(24) 24 16 19 31 26 3 27 4 13 8

(25) 25 17 14 27 31 4 28 5 20 9

(2.6) 26 18 5 21 28 31 22 6 8 10

(27) 27 19 31 15 22 6 23 9 7 11

(28) 28 20 16 24 23 7 31 1 10 12

(29) 29 30 2 6 4 5 7 3 1 31

(30) 30 31 9 13 11 12 10 8 14 29

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66 -

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(68) 68 69 74 78 91 3

(69) 69 70 75 79 1 4

(70) 70 71 76 80 2 5

(71) 71 72 77 81 3 6

(72) 72 73 78 82 4 7

(73) 73 74 79 83 5

(71+) 74 75 80 84 6 9

(75) 75 76 8l 85 7 10

(76) 76 77 82 ' 86 8 11

(77) 77 78 83 8? 9 12

(78) 78 79 84 88 10 13

(79) 79 80 85 89 11 14

(80) 80 81 86 90 12 15

(81) 81 82 87 91 13 16

(82) 82 83 88 1 14 17

(83) 83 84 89 2 15 18

(81+) 84 85 90 3 16 19

(.85) 85 86 91 4 17 20

(86) 86 8? 1 5 18 21

(87) 8? 88 2 6 19 22

(88) 88 89 3 7 20 23

(89) 89 90 4 8 21 24

(90) 90 91 5 9 22 25

(91) 91 1 6 10 23 26 )

85 6 8

86 7 9

8? 8 10

88 9 11

89 10 12

90 11 13

91 12 14 1 13 15 2 14 16 3 15 1? 4 16 18 5 17 19 6 18 20 7 19 21 8 20 22 9 21 23

10 22 24

11 23 25

12 24 26

13 25 2?

14 26 28

15 27 29

16 28 30

17 29 31

18 30 32

19 31 33

20 32 34

21 33 35

22 34 36

23 35 37

24 36 38

25 37 39

26 38 40

27 39 41

26 40 42

29 41 43

30 42 44

31 43 45

32 44 46

33 45 47

34 46 48

35 47 49

36 48 5o

37 49 51

38 50 52

39 51 53

40 52 54

41 53 55

78

79

80

81

82

83

84

85

86

87

88

89

90

91123456789

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

25

26

27

28

29

30

31

32

33

34

6

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

2k

25

26

2 ?

28

29

30

31

32

33

3k

35

36

37

38

- 68 -

INDEX BY NUMBER OF UNITS IN A BLOCK

(k) (b) (v) (r) (A) Remarks

2 6 4 3 1 R

2 10 5 4 1 2Gs2 jE 0 Y«,S

2 15 6 5 1 R

2 21 7 6 1 3G?2|E»YoS

2 28 8 7 1 R

2 36 9 8 1 4Gs2|EoYoS

2 45 10 9 1 R

2 55 11 10 1 5G?2|EoYoS

3 k 4 3 2 YoSo

3 7 7 3 1 Y.S,

3 10 5 6 3 2Gs3|EcY 0 S

3 10 6 5 2

3 12 9 4 1 R

3 26 13 6 1 2Gs3?EoYeS

3 30 10 9 2 3G?3|E.Y 0 S

3 35 15 7 1 R

3 57 19 9 1 3Gs3;e 0 y 0 s

3 70 21 10 1 r

k 5 5 4 3 YoSo

k 7 7 4 2 Y 0 S „ k 13 13 4 1 YoSo

k 14 8 7 3 R

4 15 6 10 6 50?2

4 15 10 6 2

k 18 9 8 3 2Gs4?E 0 YoS

k 20 16 5 1 R

k 50 25 8 1 2G?4|E.YoS

k 63 28 9 1 R

5 6 6 5 4 YoSo

5 11 11 5 2 .. YoSo

5 18 9 10 5 2Gs5;EoYoS

5 18 10 9 4

5 21 15 7 2

5 21 21 5 1 YoSo

5 30 25 6 1 R

5 82 41 10 1 2Gs5jEoYoS

6 7 7 6 5 YoSo

6 11 11 6 3 YoSo

6 12 9 8 5 4Gs2

6 15 10 9 5

6 16 16 6 2 YoSo

6 24 16 9 3 30? 3

6 28 21 8 2

* 69 -

INDEX (Cont'd)

Reference

number W (b) (v) (r) (A) Remarks

42 6 31 31 6 1 Y.S.

6 69 46 9 1

6 85 51 10 1

43 7 8 8 7 6 Y.S

.

44 7 15 15 7 3 Y.S.

7 22 22 7 2

45 7 30 21 10 3

46 7 36 28 9 2

47 7 56 49 8 1 R

48 8 9 9 8 7 Y*So

49 8 15 15 8 4 Y.S 0 8 29 29 8 2

8 45 36 10 2

5o 8 57 57 8 1 YoS 0 51 8 72 64 9 1 R

52 9 10 10 9 8 Y»S.

53 9 13 13 9 6 Y.S.

54 9 19 19 9 4 Y.S.

55 9 25 25 9 3 Y.S.

56 9 37 37 9 2 Y.S

57 9 73 73 9 1 Y.S.

58 9 90 81 10 1 R

59 10 11 11 10 9 Y.S 0 60 10 16 16 10 6 Y.S.

61 10 19 19 10 5 Y.S.

62 10 31 31 10 3 Y.S.

63

10 46 46 10 2

10 91 91 10 1 Y.S.

THE NATIONAL BUREAU OF STANDARDS

Functions and Activities

The functions of the National Bureau of Standards are set forth in the Act of Congress, March

3, 1901, as amended by Congress in Public Law 619, 1950. These include the development and

maintenance of the national standards of measurement and the provision of means and methods

for making measurements consistent with these standards; the determination of physical constants and properties of materials; the development of methods and instruments for testing materials,

devices, and structures; advisory services to Government Agencies on scientific and technical

problems; invention and development of devices to serve special needs of the Government; and the

development of standard practices, codes, and specifications. The work includes basic and applied

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or program. Published papers appear either in the Bureau’s own series of publications or in the

journals of professional and scientific societies. The Bureau itself publishes three monthly periodicals, available from the Government Printing Office: The Journal of Research, which presents

complete papers reporting technical investigations; the Technical News Bulletin, which presents

summary and preliminary reports on work in progress; and Basic Radio Propagation Predictions,

which provides data for determining the best frequencies to use for radio communications throughout

the world. There are also five series of nonperiodical publications: The Applied Mathematics

Series, Circulars, Handbooks, Building Materials and Structures Reports, and Miscellaneous

Publications.

Information on the Bureau’s publications can be found in NBS Circular 460, Publications of

the National Bureau of Standards ($1.00). Information on calibration services and fees can be

found in NBS Circular 483, Testing by the National Bureau of Standards (25 cents). Both are

available from the Government Printing Office. Inquiries regarding the Bureau’s reports and

publications should be addressed to the Office of Scientific Publications, National Bureau of Standards, Washington 25, D. C.
I