DEOEYBBR, 1914, MONTRLY WEATHER REVIEW. 66t
In thie memoir Hanu thmwe (Jut a new thought toward the exphna- tion of the conetant eemidiurnal wave of atmospheric piemure. He seka whether pneeibly the abeorption of the radiant heat from the Bun by the upper atrata of the air can be the eource of this wave and of ita conetancv.
It ls ass; to perceive that by the periodlc d i m 1 influenre of the solar rays on the upper layers of the atmosphere occurring similarly day after day, periodic motions of great re larity must arise in the up er strata of the atmThere, vis, an osclllatlon of the wrole mass of the atmosphere. %h- motions can ex am the typical rharacter of the diurnal oscillations of the barometer. whereas the loc$ differences reDresent the h i s of the element that m o u e s the result.
We here Bee that Ham had correctly appreciated the amplitude of the double wave of preaaure. In t h i e elegant little memoir it is interesting to perceive the demon- stration that the magnitude of the amplitude of this wave has nothing to do with eun-spots, whence Ham correctly drawe the following conclusion :
Thls diurnal oscillation of the pressure can not depend on the electricit of the sun as was thought by Lamont. for in that case it must certainly have a p e r d i n common with the magnetic variatiom which evidently depend upon the sun-spot period.
On page 311 he eaye:
(25) T t . Etude eur la marche diurne du baromhtre. [See (II).]
An examination of the figures in Table 4 shows that the aemidiumal wave is a com- plex wave resulting from the interference 01 two distinct waves. One of these which we shall call the mondarq semidfurnal maw. presents one maximum and one mihimurn in the coursa 01 the year like the diurnal wave and, like it also. is influenpj b local conditions. * * This secondary wave is then certainly due like the diurna?wave to the diurnal variation of the tem erature of the lower layers 01 the atmosphere. Th; second wave whlch we shall call t f e prinripal rcmidiurwl wave dlRercmt charactaristlfs its amplltude experiences a double variation in &a rourseTthe year it is a moximtim at the two equinoxes and a minimum at the solstices. * * On; cen indeed already foresee that the phase of this second wave for one and the same station is constant throughout the year.
Amin on wee 338 Anmt save:
respmts v
The diurnaic&e of the b&me& can be considered w the rennltant d the s u p e wition of two waves havin very different origins and characters. One 01 these wavm
e independent 01 the s p e a f geoqaphic conditions of each station: it depends only on the posltion of the sun in its orbit and on the latitude.
After Angot has remarked that erhape it may be poanible that thia eemidiurnal, principal wave afeo hae a term containing the 4-fold angle (#+42), but in that caw ita amplitude certainly can not be even 0.02 to 0.03 mm., he then proceeds to say:
The second wave can be represented by a series such as
ai ws(z+h)+m cos(*+9r)+ap C O S (~Z +~) . . . This wave Iscaused at least in great part bv the diurnal variation of temperature in the lower layers of air h d consequently aU :tshoefflrients de end not ody on the latitude and the season b;t e ually on the particular situatlon oreach station: the coefRcients c h a r y their values Ath every change of condition and erery local iduence that c n
modi the diurnal variations of temperature; we me thercIore justified in calling this s?coudg wavo by the name thermal wave.
(26) Margules. Ueber die Schwingungen periodiach erwiirmter Luft. Situngab., IC. Akad. d. Wiee., math.-naturw. Kl., Wien, 1890,
fianslated in- Abbe, C. Mechanics of the earths atmosphere. Washington, 1891. (Smithaonian miac. coll. No. 843.) pp. 296318.
(27) Thomson, Sir W. On the thermodynnmic acceleration of the arth 8 rotation. Proc. Royal aoc., Edinburgh, 1882, 11: 400. See
Margulea (26), page 207.
99: 204-227.
I1 I. wind.
(28) Pernter. Die Windverhdtniaae auf dem Sonnblick und einigen anderen Gipfelstationen. Denkschr., Kak. Akad. d. Wies., Wien, 68: 209, ffg.
(29) Pernter. Idem, page 206 and 207.
(30) Helmholtz. Ueber atmm hihiache Bewegungen. Sitzungeb., Kgl. preum. Akad. d. Wisa., Berin, 1888. Reproduced an Meteorolo- giache Zeitechrift, 1888, 28: 329.
Translated in- Abbe. Mechanice of the earthe atmosphere. Waehington, 1891. (Smithaonian miec. coll., No. 843.) pp. 75-93.
(31) Ktippen, in hie remarks on Hanne Die tiigliche Periode der Geschwinxgkeit und Richtung dee Windea. Sitzungsb., d. &is. Ak. d. Wise., 2 Abth. Wen, 89: 11 ffg: also in Meteorologiechen Zeitachrift, 14: 343; and more extenaively in Annalen d. Hydrographie, 11: 635.
(32) Sprung. Lehrbuch der Meteorologie, page 341.
(33) Almoet every trace of variation in the diurnal curve ie lacking
(34) Sprung. Deuteche Meteorologieche Zeitechrift, 1: 15.
(35) The many additional items added by Sprun by counting the rotation of the windvane, are baaed in eneral on ogbeerwtione made only three times a day and thie inaufkient obeervational material may certainly explain the reault attained by him.
eat work:
on the ocean.
ON THUNDER.
By WILHELM SCHHIDT.
IDaM K.k. Zentralan$talt fUr Ibetemulogie u. Qeadynamik, Vlenna, lolr.]
1. From earliest times a thunderstorm, and particu- larly the thunder and lightning, has made tbe greatest impression on man. It is, therefore, all the more strange, that precisely these phenomena have remained
so little studied, and that our knowledgo of the sound phenoniena has not been increased by more ex erimenta that are something more than malo 8s. An1 yet it is
tions that may be made when it thunders, themselves point tho way to such experiments. Beside the extremely violent, usually deep-toned peals-though they some- tima have a clear ringing or a rushing sound-one may also hear the ringin or breaking as of window panes
can even be perceived by the sense of touch, and some timcs by the trembling of the $ound. Thus phenomena whose intensity far exceeds t at producible by sound, demonstrate that other vibrations than the audible ones are also present. The very depth of the tone leads to the assumption that there are yet deeper toned pressure variations of such few vibrations that they are inaudible and the direct cause of the effects mentioned. We shall, therefore, endeavor to demonstrate these vibrations which are something quite novel in nature, as well as to complete the picture by recording the audible vibrations.
not a t all difficult to secure results in i f is field. Observa-
accompanying some % eavy thunder crash; the vibrations
,
METHODS FOR RECORDING THE VIBRATIONS.
2. Instrument I.-Two different instruments, I and 11, serve to acconiplish these two urposes. The instru-
use a niechanicill registration since there was considerable energy available and the velocities to be recorded were not too great. In its final form, I consisted of a wooden box of 210 liters capacity, having all its joints carefully sealed, and with a hexagonal a erture of more t.han 250
sq. cm. in one of its sides. h i s aperture was almost closed b a very light aluminum late suspended by
freely in and out. Thus every atniospheric coinpression- wave falling upon the box must also compress and reduce the Folume of the air within the chamber and the aluminum plate, acting as a iston, swing inwards. The
A simplo train of levers was sufficient to transmit these vibrations to a recording pen writin on the moving sheet
running over a motor-driven cylinder upon which rests the recording oint of the pen ami. The band of record aper is stretc i ed b a free roller suspended in the lower Lop and set tat a s&ht angle with the driven cylinder thus causi a lateral shifting of the record strip and a spiral recor 3 . With a slight friction it was possible to secure recording s eeds of 5 to 8 miii. per second. The
usual way. 3. Standar&zation of instrument I.-It would be a
mistake to assume that the displacement of the pen is proportional to the variations in pressure. The inertia
nient, I, designed to record the P onger vibrations could
means o ? two long threads, so that t E e plate could swing
reverse process was caused t y a rarefaction of the air.
that t.he best 2 evice is the endless strip of of a chronogra h. Experience wit seismogra
record was fixed g y means of a shellac solution in the
I Authors abstract (Oerman) of the two Ipllowin papers: Analyse des Donner~,~
I<Le&ser has Wesen des Donners Tmrulolcd/rom Metsorolo(lische) Zeit.chrllt, BraunschweIg, 0% 1914, SI: 487-4DB.-
Sitzun b. K. k. Aknd. d. \Visseq~~IIa, Wien, lBl! 131: 2045.
ibid., IIa, 1914, iY8.
C.A.1.
666 MONTHLY WEATHER REVIEW. DECEMBER, 1914
due to the mass of the aluminum plate and of the air bands tlnd the known speed of the paper permits the itself, the period of vibration of the whole system, the determination of the time interval between two individ- partial e ualization of pressure within and without the u d successive condensations. The rough surface of the chamber % y means of the open interval around the plate, paper used held the soot so firmly that one could "fix" and finally friction, all these induce a delay and particu- the important portions of the record at a later time. larly a change in the magnitude of the pen displacement The advantages of this device are: the absence of which can, of course, be computed from the measure- coarse inert masses,. a minimum frictional effect, the
ments but are much better determined empiricall For possibility of expandmg the time scale with a consequent
this purpose a hole is bored in the wall of the c h a d e r and more detailed analysis of the processes studied, and
a closed glass tube,fitti it quite close1 is inserted and final1 the small cost which removes any limits to the pushed in or withdrawn 5 y hand. If t%le stroke of this lengti of the record strip used (e. 1700 meters for a
ass iston is regulated b means of collars fitted to it, thunderstorm). The only appreciafd disadvantage lies
fnd i! one limits himsel 9 somewhat to producing the in the fact that while instrument 11 permits qualitative gentler waves, then the changes in volume produced by observations such as the duration of vibrations, it is the piston stroke may be converted into pressure changes possible to make 0111~ rough quantitative gradations which may be compared with the curves simultaneously according to the intensit of the coating.
of being able to pick out only those wave8 of r&m form devices were set up and in running order in the lahora- recorded by the instrument. There is here the advantage
and having the period of vibration simultaneously re- tory of the Ii. k. Zentrdanstalt fur Mcteorologie u.
corded. Indeed the latter primarily determines the Geodynmik in Vieu 1% On the approach of a thunder- magnification. For example, a pressure wave whose amplitude [corresponds to a pressme change] of 1 plm. in the motor, and light the turpentine lamp.
5. InstauaEion; Time B etermination.-For a time both
storm it was mere +* y necessary to open a window, switch An im-
! portant matter here, however, was the time-recording I device for it wit8 only b its aid that one could correlate
I the simultaneous recor ?i s of the two instrument.s, and the contemporaneous notes on the character o the audible sound phenomena, the distance of the lightning, etc. To secure the time record the anchor esca ement, or lever, of a simple aInm clock was so mod' I! ecl that a single oscillation of the lever closed and opened iiii elec t i c circuit, thereby making time marks alongside both the curve of instrument I and the soot band of No. 11. A4n additional key inserted in this time circuit permits the time marks to be interrupted at any instant, thus fur- nishing r i ready meana of distinguishing them. The latter rocedure was Used on instrument 11 Only when it wm -ked to test the speed of the pa ier bawd; other- wise the slightly confusing succession o time marks on tbh record was replaced by consecutively numbered little pnsterd stuck on the strip rcmi itly after each thunder-
in portions of tshc record.
Secords with instrunient I were secured during the summer of 1912, and both instruments simultaneously recorded some thuiiderstoims during the summer of 1913.
In the follo~vhig p:%ges :%re fi1st discussed tho results of studies of sound vibrntioiis due to thunder, which are in art known to the ear; afterw:irds I consider the more
which present something fundamen tally new.
mercury shows-
Defle$tion of Time of vibra-
tion. =* Pen. Bseadr. YQB.
0.2 ...______._._....... 41
.4...... ....-.-----... 79 .8. ....._...._._____.. 53 .8 ......._._._________ 29 1.0 ...-.--._.._._...... 20
3.1 ..I...-......-.._-._ 5
slow vibrations are least pronounced; the period of vi l! ration of the system md conse uently the strongest men& cation lies in the nei hbor ood of 0.4 second. The con- version of the recor s; ed vibrations is carried out by the
~d of the above values. This method of stmdardiza- tlon brings the specid advantee that the numbers do not hold true in the case of the deflections produced by
of the involuntary variations in t h e wave lengths pro-
duced during the standardization, hold only for isolated deflections such as are significant in thunder.
4. Instrument II.-The second instrument, 11, designed to study the sound vibrations of thunder, employs a method somewhat apprombg the smoke-fing method used by Marbe (1). A gaphophone horn of 57 conti-
with its mouthpiece (repn>ducm end) applied laterally to a short upright chimney of leas than 4 quare centl- meters cross section. All com ression wavw (Dichte- wellen) that strike the lar e en of the hoin are propa- gated with much magnifiei a m litude into the chimney and induce vibrations in a m a l f smoky turpentine flame. The upper end of the flame, extending beyond the top of
! the chimney, was intercepted at about 5 =. from tha chimney top b a moving strip of t,&gra h paper driven at the rate 0 9 about 145 111111. per Becon f; by an electric motor. Appropriate screens caused the smoky flame to deposit a uniform band of soot when the flame wm a t
rat; but e v q jump of the flme, every condensation or rarefaction of the air, caused a heavier or lighter deposit of soot so that transverse bands were deposited upon the paper strip. The measured internal between two such
Whence it appears that very rapid and ver
tl B 1
an infinitely long series of similar WaVeE but, by reason p d , thereby giving iendy i hi! ent cation of the correspond-
meters aperture stands a t right angles to the window, vi0 F ent prcseure variations of somewhat longer duration
BESULTS OF THE RECORDS.
sound me8.
6. G e n a l r&ew.-Instrument 11, iii its ha1 form, be- gan its records with the two thunderstorms of August 6
and 12, 1913, and approsimatdy 20 audible thunder peals. In each cast? the r f f d i of the air vibrations was
recorded as a pronounced rapid altmiation of light and dark bands across the record paper in placc of the other- wise uniform gray soot coating. T1.e time of tluration of each could be siniply clctcrmmed from t h inkrval be- twecn two adjacent bands. Tlie general ap earance of the record showed that the most diverse kin i s of vibra-
B
DECIEMBER, 1914. MONTHLY WEATHER REVIEW. 667
s m 23-86 36-46 466s
6546 86-76 7s-w 8686 *1(u
llxi-115 115-1211 1361a6 la5-146 14&lM
lS5-166 105-176 17sl86 la-195 1*m
tioiis succeed one mother in a thunde eal; beginning
readily perceived) and ranging up to more than 100.
These vlbrations formed ai1 uninterrupted series, but pronounced roplarity was not to be remarked except in the later portion of the thunder; most cases showed a
merry mixture of series of shorter and longer vibrations, particularly immediately after the first impact and later a t the occasional pronounced intensifications. It thus appears that only individual ortions of the thunder can be rc arded as a tone. Tfe other ortioiis are at the
larity of the time intervals alone a.nc. not made to include the usually wholly arbitrary iniplication that one here has primarily to do with specidly rapid vibrations. Now generally irregular pressure fluctuations must change and weaken much more rapidly during their prop- agation than do regular fluctua.tions, and this is intensi- fied as the interval shortens. If these records of thunder that has ahead traveled a considerable distance (in all
and the f i t sound) enable us to infer the procedures in the vicinity of the lightning path, then we here have to do with a series of very violent, irregular, tuations taking place in particular1 rapii succession; there the (klirrencle, knatternde) rattfing, clanking thun- der has a much higher, almost metallic Klanefarbe (tone color). The appropriateness of the term clanking (klirreiide) is shown by the experiment where the closed window was smartly struck; the ap aratus than re- corded vibrations that were in generi quite similar t,o those of thunder.
The h e variations in the shades of the smoked record of instrument I1 unfortunately are not adapted t,o clear reproduction. The were therefore translated into num-
and grays, the highest numbers (plotted as ordinates) indicating the deepest blackenin or the most violent pressure waves. In this way has 6 een constructed figure 1 [omitted], which shows the translated record obtained on August 6, 1913, during the first seconds of the thunder
at 2:44 p. m. In this very carefully executed twofold copying the regularities were invqluntarily emphasized ; however, i t is clearly shown that immediately after the first somewhat slower vibrations, very rapid changes set in at once and that the same procedure takes place after the first node of the thunder.
7. StatistkZ summq.-Of course such a detailed tmatment was not possible for all the caaes of thunder. I n its place I attempted to characterize the variations b
a statistical method, by determining the duration of eac i
thunder and then to compute the frequenc of occur- rence of the peals of various durations. In t6s way was
obtained column 2 of Table 1, from the three most com- pletely recorded thunders, the numbers of waves bein grouped by equally spaced intervals of the number c?
vibrations per second. Rut one is not to assume that in speaking of the number of vibrations per second we ever merrsumd a long, regular series of them. Even two successive vibrations seldom had exactly the same dura,- tion. The concept tone is here in mind, since this name is at times also applied to single waves.
with about 25 per second (a lowcr num T er was not so
P
best % ut noises, if this nanie is a pted to the irregu-
caaes I observe B a marked interval between the lightning
7 flu*
bers with tlie aid o 9 a numbered scale of shades of black
9
f
10 s6Q.6 62 1m.1 40 76.0 24 a. 6
22 17.8 18 10.0
4a 19.6 66 20.6 69 l a 6
n 17.7 46 0.6 15 4.5
!a S. 6
16 21
14 1.6 12 1. S 0 0.8 6 0.6 5 0.8
According to this table the most likely tones to hear in thunder are those with 15 to 40 vibrations per second (E, the second E below the bass clef); those of 40 to 75
are less frequent, while hi her tones, 75 (D# in the bass) to 120 or A are again of f requent occurrence. Tones of
music, are again uite rare.
As only those vi B rations were measured that exceeded
a definite intensity, the above figures do present the distribution of intensities to a certain degree; neverthe- less they are not to be re arded as an espression of the distribution of ener y. %alum are indeed given, and
as one of shorter duration. If it is desired to pass to energies then the intensities am to be multiplied by. the times of their duration, i. e., by the reciprocals of the vibration numbers (given in column 1); thus are secured t,he values in column 3 of Table 1, where the generally uniform character of the distribution gives articular emphasis to the estriiordinary prominence of $e longest waves with vibration nunihers below the limit of sound. Tlio manner of recording is less favorable to the register- ing of yet longer vibrations, and as a matter of fact the contrast is really much greater than our table can express.
Pressure vibrations of longer duration.
8. General review.-The whole distribution of the ermits one to antici ate that yet slower vibra- ~~F p i  ?~ a large part. f o r various reasons these slower VI rations cou d not be adequately recorded by mkaiis of instrument 11; but it was otherwise with in- strument I, which was designed to reveal precisely this cl.?ss, and which furthermore permitted quantitative determinations. As early as the summer of 1912 records
of thiq kind had been secured, but the much more reliable standardization was not carried out until 1913, and we shall therefore restrict this discussion to the four thunder- storms a t the end of July and be innin of August of that year, embracing 47 thunderpeL. A n of the peals were vigorous enough to yield well developed records throughout.
yet higher vibrations, such as those usually met with
for these a wave of P o q e r duration had the same value
668 MONTHLY WEATHER REVIEW. DECEMBER, 1014
Seed. 0.32
.24 -38 .16
. 1s
.m
.!a .18 .34 .18
a22
In general the strongest pressure variations uniformly showed relatively long periods lying between 0.2 and 0.5 second with a masimum of 0.54 second. Even when the were far below they coincided with the limits of audib&ty: points of the greatest sudiblo loudness, the beats and nodes of t.he thunder indeed bricfly preceded them; so that in every case the first vibrations to arrive were slow ones even though slightly later accom anied and followed by more rapid ones.
9. A e c i s e evaluation-Energy content.-In the case
of those 8 thunde eals where the pen did not jump
able), the records were evaluated by measuring and computin the duration and amplitude of the strongest waves. the case of the thunder of August 6, 2:46
y. m., all the plainly distinguishable variations were thus measured. The results of this lastrnientioned case are presented in Table 2. The eatest durations of vibrat,ions are fair1 uniform accor r ing to their mag-
and 0.54 second, and if the change were repeated regu- larly mi h t be regarded 8s tones 1 ing one or two octaves
maximum variations in pressure measured between the extreme positions are far more contrasted. The highest value of the pressure is 0.017 mni. of mercury, which is
Fery considerably above that of the strongest sound.
TABLE 2.-Detminations of 17 of thc stronger waver, of tlu thunder at
V?.enna on Aug. 6, 1915, at 6:46 p . m.
over the paper too 7 ast (this was not altogether avoid-
nitudes; as mentione B above, they range between 0.20
below t % e limit of audibility. d n the other hand the
dfm.olHg 0.017
.w .004
.m .m .004
.m .013 .014
.003
am
0.24
.38 .24
.22 .14 .28
am .on2 .OM .OM
.M)4
.m
Intensity of wave.
##fIt.SGC
1.63
.09 .00
.oa
0.01
. 11 .92
1. M 0.06
. 01
.ffi .OD
.oa .04
a 11
. is
affi
Energy oi wave :internal).
mE4 .026 .034
.m . ai2 .Ol5
0. om .OH
. 166 .31i
.m
.w .ol3 .Ol9
. 011 .025
a 013
One can now ca1culat.e by means of the pressure changes, the intensity, I, of the sound, i. e. the amount of energy passing in 1 second through 1 square centi- meter of a lane perpendicular to the direction of propa- gation of t E e sound. I n the formula (1)
= 0.304 X 10OP
the velocity of sound, c, a t 18C. and the mean pressure 743 mm., was taken as 342.8 meters per sccond and the spec& gravity, p, as 0.001186. Tho ratio of the specific heat of air, K, is put at 1.402; the pressure amplitude 8 in the first expreqsion is in absolut? measure, b in the second expression is measured in millmeters of mercury. Thus are derived for this one thunder, the figures given in column 3 of Table 2, and multi lying those by the
converted into the energy-amounts given in the last duration in time of each indiridua Q vibration they are
*In extreme casea the IImlt ol audibility is aboutO.05 second duration of vihtlon, yet in suoh casea the hearing Is regarded w very sensitive.
column. It is now possible to compute the total ener embodied in the pressure variations of this thun F er peal. By adding the values in column 4 there results 1.27 erg/cm2 for the evaluated vibrations which occupied a time interval of 4.1 seconds. Now if it is .assumed that the total duration of the thunder was 13 seconds, which is probably close to the actual facts, and that the mean intensity during the missing 8.9 seconds which was too small to measuro, was approximately 0.01
erg/cm2sec., then the total ener y amounts to about 1.4 erg/cm.2 Further, suppose t 5 at the origin of the disturbance had the form of a point and was 5 km. (which is too far) distant from the point of observation then, disregarding losses due to friction and other causes, the tota2 energy of the thunder amounted to 22,000
meter-kilograms (2).
Energy loss.--For comparison we may deduce the approximate value of the energy of li htning. Riecke gives. 95
the stronger discharges; the tension is proba ly over- estimated at loD volts; whence the energy is approxi- mately 1O1O meter-kilograms, a value quite dispropor- tionately in excess of that of the computed energy of
thunder. Although the necessity of making arbitrary assump- tions in the calculations greatly impairs the reliability of both values, neverthleess it is quito certain that then magnitudes are widely different; hense it is ceitajn that at a short distance away only the smallest fraction of the energy of lightning is still present in the form of pressure Vibrations. There are two lausible causes for this perhaps some-
of energy is consumed in the nonmechanical forms of heat and light at the time of the dischar e; (2) the
greater than those of ordina.ry sound and ais0 of irregular character, causes a considerable loss in intensity. But this second cause must also find ex ression in t,he fact that the individual thunder peals, wfkh generally origi- nate at different widely separated li htning bolts, show
vealed much better by the oii inal records than by the evaluated cuives and tables. sigure 2 [omitted] shows a proximately the first four seconds at the beginnings of
once with o m of the most pronounced pressure vibra- tions, in one case the vibrations increase more gradually to the maximu . But one may distinguish similar differen- ces in the t r under sounds that come to our ears: Some begin at once wit.h a heavy crash after which t,he intensity decreases (we need not here consider the cases of occa- sional later temporary increase), others increase gradu- ally. This feature is so pronounced that we may at once classify thunder into Grou,p A, the sudden crash, and Group B, the gradually developed crash. Figure 2
[omittcd], shows that these are essential differences.
singlo wave (impubc) succeeded by ot rp ers t.hat show are a
The strongcst vibrations in the former
ecarccly worth mentioning; tho latter group have, as a
rule, a rather regular scrim of waves whose amplitudes sliow a steplike increase and then a dying out. Upon computing the mean maximum amplitude of vibration of the more accurately evaluated four peals of Group A it is found to be 0.43 erg/cm2 and that of the four in Group B is 0.14 crg/cma sec. Considering tho known fact that the thunder in tho vicinity of the flash always sets in with the heaviest crash so that the observed interval
10. Compriaon d h . the energy of Zightning.
t
coulombs as the quantity o f e1ectricit.y trans orted in
what unexpecte c f result,: (1) A considerable amount
propagation of such pressure vibrations fi 0th much
corresponding mutual departures. 9 hese facts are re-
t f: ree thunder records. Only one of them starts off at
DECEMBER, 1914. MONTHLY WEATHER REVIEW. 669
between the first noise and the heaviest crash must develop during the propagation of the sound, one must conclude that the main vibration becomes separated from the beginning of the thunder after a considerable path has been traversed. One can ala0 cite ear observa- tions in this connection. Thus it appears that the thunders of Group A are generally to be considered the original, earlier vibrations; after traveling some distance they would transform themselves into those of Grou B.
the preceding that any coriclusions regartlin tho origin
records leads to the first and most surprising result that the strongest dcflection always indicates a rarefaction. It, is preceded by only a very brief og t.hat might indicate
little reflection, indicates that in tho apparatus the mag- nification of vibrations closc to the period roper to the
tions, ancl that in the case of vibrations of brief duration the magnification is quits smdl. It. is, therefore, not altogether out of the question that the amount of the actual condensation represented by the first small jog should exceed the rarcf action of the succeeding vibration. I t is certain that none of the following deflections even a proximates in intensity thnt of the maximum; perha s
t E en the latter with its antecedent compression IS to ge regarded as a lund of isolated warn (Einzelwelle). This wave always introduces the vibrations in much the same manner, and is followed by the irrcgular deflections. Experiments had already revealed a kind of condensa- tion wave that bears much the same characteristics, viz, the percussion or explosion wave. Whcn a compression or rarefaction of the air takcs place with extraordinarily great speed (suddenly) at one point, there arise cliffer- ences in density that no longer can be called snidl as com- pared to normal pressure, even when they have traveled considerable distances. In such a case i t is not pcrniis- sible to disregarcl the usual theory of the propagation of sound; with mcrcasin contrast in clensity tho velocit of
tho parts of the wave having the greateat pressures acl- vance more rapidly than those of lcsser pressure and soon are in the van; so there arises here something approxi- mating a discontinuity, a sudden jump in density. The instant this condition is established the front becomes a source of wave motion which, according to Tudirz (3),
who has further developed t.hese oints alon the lines of a rcflec- tion and thus consunies some of the intensity of the per- cussion wave. In this way the density contrast in the latter finally become so far reduced that i t travels only with the velocity of sound ancl loses its special charac- teristics. Experiments with release by explosions, cases where such wm-ea may be observed and studied to special ad- vantage: showed that here tho total amount of energy expmlcd is of secoitdar iniportanco, while the prime
12. Phenomena clue to spark waces; exdanation of
quickest phenomena that we know. I t y t e s tre- menclous corn ressions alon its path, as s own, among
a pressure of 64 atmop heres was developed in a spark
11. Si~miZarity with e.cploosion waves.-It follows P rom
of thunder will be based, by reference, on t % e facts re- lating to Group A. A more s etailed comparison of these
a compression. The empiricd ca 1 ibration, as well as a
system is considerably greater than that o P other vibra-
propagation considera % ly exceeds that of sound. gere
the Riemann theory, travels bac i ward ns toes f
esslmtial is the mannw o P rolvasc?, its suclrlcnncss.
thunder.-No doubt the electric spark bc 1 ongs to the
others, by H. E ache & E. B aschck (4), who found that
gap of 3 millimeters, a s though the pressure was siniul-
: The sudden production of a rareIaction, such as results from the sudden collspse 01 an exhausted lass sphere will produce the corresponding phenomenon with a rarafac- tion in p l s ~e oi a cow-tlon.
taneously increased by the presence of subdivided elec- trode material. For this reason E. Mach (5) naturally found the spark a simple method for studying the phe- nomena in point b tho aid of tmhe Schlieren and interfer- ence rnet,hods. E& presentation reveals all the above essential phenonicna, tho quick rise in pressure at the hcginning of the wave, the following slower rarefaction, and the a pearance of su e osed waves after the highest pressure {as passed. mpF 01 s experiments in explosions on a grand scale show similar features (6).
Let us now imagine the tiny spark magnified to the trr- mendous dimensions of a lightning flash, all the sequential phcnomrna will also show a very considerable magnifi- cation. The extraordinarily great electric repulsion be- tween the similarly charged particles in the lightning path seems to be the princi a1 cause of a sudden very stron
part, and electrostriction or %fornation due to electric stress would act in the opposite direction. A percussion wave due to this suddon stron pressure rise advances
cylinder wave. Primarily the total energy of the alter- nations in density is united in this wave gmlually, how- ever, waves set out backward from it. o original sini- ple detonation, which L u m e r (7) thinks is the form iii which we hear an explosion wave, grows weaker while variations in density of longer duration follow, the rum- blin sets in. In the course of time the energy content of the 8 etonation is no longer essentially diff erentiatsd from the more usual sound waves, the primary vibration no longer plays a special r81e and on occasion may become quite lost among the various disturbing influences or even previously change its form, so that it is introduced by a rarefaction. Though the isolated wavcs dieout, there long ersist all the accictnntdly formed regular wave series. b.nally, t.he latter alone are essentially in existence. Other details of the records agree with the above de- duction. Short waves set in, in Group A, after the first strong deflections; furthermore, instrument I1 yields a record here that agrees essentially with that produced by bursting paper bags. Regular series of waves occur
mostly in the later portions of the thunder.
13. Explanation, qf the longer dura.tion aid the repeated beclts.-The increasing breadth of the density changes due to an e s losion wave niay explain the increasing
niust be sought for the repeated beats or nodes that often ogcur several times in succession in the same One is here involuntarily led to the idea-perhaps the longer duration of the thunder-that every point
source of disturbance, whence the first sounds to reach the ear are from the points nearest thereto and succeeding souncls are from increasingly distant sources. Aside from the consideration that according to this theory the lightnings nearest the point of observation would gener- ally give the longest endurin thunder, which is contrary to our experience, the laws o f physics would require that in such a case the thunder would be heard as a single simple sound, because the disturbances along the whole of the spark path are practicauy simultaneous and set free in the same form. A comparison with the salvo from a firing squad disregards the essential components just mentioned, and therefore leads to a quite false conclusion. Since the idea of uniform disturbance along the whole s ark path does not support the explanation of the longer &ration of the thunder, then the ossibility of the occur-
logical result from the fact that we have to do with
rise in pressure. Here ?l eatin seems to play but a sma fi
from it in every direction in the f orni of something near a
duration of t E e thunder; but some other esplanation
spark path is to be regarded as an independent.
rence of a finite series of intensi g cations or beats is the
670 MONTHLY WEATHER REVIEW. DECEMBER, 1914
I
neither a straight-line path nor a precisely simultaneous release at all points along it. Experiments with sparks following sharply bent paths (8) showed that the distinct wave series originated by the &fferent sections of the spark path show but imperfect mutual fusion, and in part intersect one another even when they have become very weak. The same may be predicated of sharply-bent lightning flashes, which after all are seen not to be so very frequent if one makes proper allowance for the deceptive a pearances due to perspective shifting. The second set o r circumstances also tends to produce these more or less independent centers of disturbance separated by longer intervals, smce experiments here dso have shown that
%
the same s ark produces quite different effects accordin to the d erent conditions and resistances encountere along its ath. Thus oints that have already been traversed IY y the predisc R arge (prelinzinary) offer better
conductivity than others. Probably the most important r81e is that of the cur- rents of the atmosphere. There is no essential difference between them cleflective and other effects upon ex losion waves and o r h a r y sound waves. The greater t 1 e dis-
tance between the source and the observer, the more diverse are the aths to the observer traveled by the dif- ferent parts of t R e wave, the longer does the thunder seem to endure, and the larger the number of beats  (Schliige) it shows. These experiences are in agreement with the results J. N. Dorr (9) has obtained from the stud of the effects of the great explosion in the quarries a t Giener- Neustadt. He found that as it traveled the originit1 simple detonation broke up into a series of separate sounds that were in part of a different character,viz,
haps this doas enable them to have some influence u on the sound phenomenon, for it is readily conceivable t 1 iat
their somewhat pronounced psrioclicity is of mechanical origin. Thus, supposing all the air particles are hurled apart by the first partial discharge, then in the nest instant they will swing back to their positions in the spark path thereby generating a condensation that of course causes a new rarefactlon which eatly assists the further discharge through the same ciannel, Y of the electsicity that had accumulated in the interim. This rocess may be repeated until the. supply of electricity !ecomes too small. NOW every time this occurs com- pression waves are sent out and all in all these may well roduce upon the observer the impression of a mora or
Lss regular-series. In countin up the time intervals of the partial discharges recor d ed in Walters unfortu-
nately very small number of photographs! I found 5 cases which would correspond to 15-40 vibrations per second, 4 cases between 40 and 66, 2 cases between 65 and 90, and 1 case of 90-115 vibrations. This distribution reminds one so strongly of that in the sound waves from the thunder revealed by instrument I1 (see Tab13 1) that one is inclined to see here a fundamental relationship. It is simply necessary to imagine that at least one portion of the wavm separating from the discontinuity, originated simultaneously at the be inning and even favored tlie discharges t-hat threw off &e others. E. Mach has shown that explosion waves may carry others superimposed upon them.
SUMMARY.
The records made by appropriate1 designed recording
alternations of pressure vibrations of very various Iura- tioiis; but these are so i r r e d a r (86) that one can not here speak of tones, althoua the time interval separat-
ing two vibrations is partly short enough when they come regularly to niake tones of a rattling, clanging kind whose records are quite similar to those of the The evaluation of the records of clanking windo three thunderpea (87) revealed that intervals of 1/75 to
1/120 second were somewhat more frequent and that at first longer intervals were of less frequency, until coming
to those above 1/40 second (tones lower than E), there was an increased frequency that multiplied as one ap roached the vibrations too long to be audible. h e essential constituent of thunder, however, were the yet longer vibrations, certainly far below the limits of audibilit , which were rather violent pressure variations
half second) that were accompanied by the beats os
nodes in the thunder ($8). In one case the deflec- tiom of these pressure variations amounted to 0.017
mm. Hg., or considerabl more than that due to the
showed it was certrtinly a vel? insignificant fraction- less than 0.00001 -of the energy of 1ight.nin One must therefore conclude that the latter is most con-
that theyyave not t r a d e very great distances are characterized by a single initial masimuni deflection of rarefaction, in no case preceded by more than a very brief condensation (810). Their form close1 simulates
very suddenly produced condensations or rarefactions ($11). Their velocity of ropagntion is a t first much greater t.han that of souuj, but approaches this as the intensity of the density disturbance rapidly decreases on account of the retrogressive waves sent out from the discontinuity itself. Laboratory experiments show that such explosion waves arise at an electric spark gap, where it has been possible to demonstrate there exists an extraordinarily marked pressure rise. Their roperties are thus all the more evident in thunder. $bus are to be explained
($812, 13) the rapid decrease in intemity, t.he change in tone color, while the irregular air currents are r-espon- sible for the increasing duration as the point of ongm of the thunder retreats and for the recurring beats. The isolated (susgelosten) waves are most probably due to the intermittent discharges that occur so fre- quently in lightning (814).
instruments (8 $ 1-5) show that thun B er presents fre uent
. wpane
(the hig E est observed duration being more than one-
highest sound im ulse. !F he determination of the total energy content o P the strongest recorded thunder ($10)
%
Thun B e eals whose stren th justifies the assumption
that of the percussion or explosion waves ra 3 iating fToni
sumed b other fornis of energy, such as heat an t light.
NOTE8 AND REFEBENCES.
(1) Marbe i n Phys. Xtachr., 1906, 7: 543.
(2) The magnitude of this energy when consldered a8 energy of mund i e shown by the following comparison. Webster estimates that that 107 trumpeters can generate a tone of 1 HP. Thus the power of
a trumpeter at the distance of 1 meter is still 0.02 erg/cmzsec.; i. e., oven leea than 1/300 of the f i r 3 wave as measured in Table 2. If, therefore, it were desired to equal tho total energy-content of the thun- der by means of trumpeting we would need 2X1O8 trumpetere blowing in a uniformly sustained manner for 13 m n d s . (3) Riemann-Weber. Partielle Differentialgleichungen der mathe-
Marbe & Seddig, in Annalen d. Phys., (4) 1909, &O: 579.
mathhen Pbysik. Tumlin, in Lotoe Jahb. I. Naturw., Bag, 1880, 2s; and
Sitzungab., K. A M . d. biaeenech., Abt. IIa, Wien, 1687, 06: 307.
- -
DEOEMBEE, 1914. MONTHLY WEATHER REVIEW. 671
(4) Made, H. Ueber den Druck in Gasen unter dem Einfluss atarker elektromotoriacher Kriifte. Sitzungsb., R. Akad. d. Wieaen- ach. Abt. IIa, Wien, 1898, 107: 708. Easchek, E. L Mache, E. Ueber den Druck im Funken. ibid., 1898, 107; Annalen d. Ph aik (Wied.), N. F., 3899, 68: 740. 15) Mach. E. & Weltrubskv. f. v. Ueber die Fornieu von Funken- weh& Sitzunib., 6. Akd.'!. Wie-aensch., Wien,-1878, 78: 551. (6) Wolff in Annalen d. Phyeik (Wied.), N. F., 1699, 69: 339. (7) Lummer. Ueber dieTheoriedes Kmllee. Schlesischeu Geeells. f. vaterl. Kultur, 11. Abt., 1905, 83. Jhrb. \8) Mach, E. L Gruss, G. 0 tische b%ersuchung der Funken- we len. Sitzungab., R. Akad. 8. Wiaseua., Abt.IIa, Wen, 1878, 78: 479.
(9) Dljrr, J. R. Ueber die Fernwirkung der Explosion am Stein- felde bei Wiener-Neuetadt (1912, Juni 7). Sitzungsb., K. Akad. d. We- sens., K1. Ha, Wien,. 1913, 1% O : 1683.
(10) Walter, B. (n Phys. Ztschr., 1902,8:168; also Hamburger wiwene. Anatalt-a, Jhrb. 1503, BO
. 3.
*', 3 ; ." - ,. *'j 1 2 t. THE PUCE OF FORESTRY AXONC) NATURAL SCIENCES.'
By HENRY 5. GRAVES, Chief, United States Forest Service.
[Extracts from an address delivered before the Washington Academy of Scicnres, Dec. 3, 1914.1
Forestry as a natural science deals wit.11 tahe forest as a community in which the individual trees influence one another and also influence the character and lifc of the community itself. As a comniunity the forest, has indi- vidual charac.ter and form. It has a definite life 1iist.oi.y; it grows, develops, matures, and propngatcs itself. Its form, development, and find total product inay be modi- fied by external influences. By.el)use it mtiy be gmatly injured, and the forest as H, living ent,ity may even be
destroyed. It responds equally to care, and niay be so molded. by skillful treatment as to produce n high quality of product and in greater amount and in a shorter t,iiue than if left to nature. The life history of this forest community vanes accordin to the species composing it,
of different a es are grou ed, the climatic and soil factors
The sim lest form of a forest c.ommuiiity is that coni-
When several species and trees of different ages occupy the same ground, the forni is more coniples, the crowns overla pin and the roots occupying different layers of the sol. 'fhus, for instance, when the ground is occupied with a mised stand of Douglas fir and hemlock, tho former requiring more light occupies the u per stor , and he-
strata of the soil. The hemlock, on the other hand, which is capable of growing under shade, occupies the under sto , and having shallow roots utilizes largely the top sox * * * In a forest there is altogether a different climate, a dif- ferent soil, and a different ground cover than outside of it. A forest cover does not allow all the precipitat.ion that falls over it to reach the ground. Part of the pre- cipitation remains on the crowns and is later evaporated back into the air. Another part, through openings in the cover, reaches the ground, while a third art runs down along the trunks to the base of the trees. &any and exact measurements have demonstrated that a forest cover interce ts from 15 to SO per cent of recipitation, accorrl-
forest, and other factors. Thus pine forests of the North intercept only about 30 per cent, spruce about 40 per cent, and fi nearly 60 per cent of the total precipitation that falls in the open. The amount that runs off along the trunks in some species is ver small-less than 1 per cent. In others-for instance, {eechbit is 5 per cent.
the density of the stand, t E e manner in which the trees
which affect t % e vigor an T; growth of the individual trees.
posed o P trees of one species and all of t,he same age.
cause of its deeper root system exten t; s to the r ower-lying
ing to t R e species of trees, density o P the stand, age of the
1 Reprinted from Journal, WE&. Acad. Ed., Jan. 19,1915,641-50.
Thus if a certain locality receives 50 inches of rain, the ground under the forest will receive onl 40, 30, or 20
from the totnl circulation of moisture over the area occu- pied by the forest. The forest cover, besides pre~eiit~iiig all of the precipitation from reaching the ground, simi- lmly keeps out li ht, heat, and wind. Under n forest
light chiate xiid a different relative humidity tlinn in the open. * * * The effect which trees in a stand have upon each 0 t h is not confined merely to changes in their external form and growt,li; it extends also to their internal struct,ure. The specific gravity of the wood, its composition, and the
differ in the same species and on the same soil an in the matonicd structure which determines its specific
same climate, according to the position which the tree occupies in the stand. Thus in a 100-year-old stand of spruce and fir bhe specific gravity of wood is greatest. in trees of the third crown class (intermediate trees). The ratio of the thick wall portion of the annual ring to the thin wall of the spring wood is nlso different in trees of
different crown classes. The difference in the size of the tracheids, in trees of different crown classes, may be so reat that in one tracheid of B dominant tree there may f e placed three tracheid cclls of a suppressed tree. The amount of lignin per unit of weight is greater in domi- nant trees than in suppressed trees. * * * Forestry, unlike horticulture or a iculture, deals with wild lants scarcely modified by cu ff' tivation. Trees arc
also !&-lived plants; from the origin of a forest stand to its maturity there may pass more than a century. Foresters therefore operate over long periods of time. They must also den1 with vast areas; the soil under the forest is ns a rule unchanged by cultivation, and most of the cultural operations applicable in arboriculture or
agricblture are entirely impracticable in forestry. For- est,s, therefore, are largely the product of nriture, the re- sult of the free lay of natural forces. Since the foresters had to deal wit.[ natural plants which grew under natural conditions, they early learned to study and use the naturitl forces affecting forest growth. In nature the least change in the topogritpliy, exposure, or depth of soil, etc, means n change in t.he composition of the forest, in its density, in the charactcr of t,hc ground cover, and so on.
As a result of his observat,ions the forester has developed definite laws of forest distribut.ion. The forests in the diffnreiit regioils of the countr;p have been divided into natural typcs wit.h corresponding ty es of climate and site. These iiotural forest types, whici, by the way, were also developed long before the modern conce tion of lant formations came to light, have been laig at the foundation of nearly all of the practical work in the woods. A forest type became the silvicultural unit, which has the
same physical conditions of growth throughout, and therefore requires the same method of treatment. The manlier of rowth and the met,hocl of nt~turd re ener&
same type no m:itter where it occuis.
After the relation between a certain natural type of forest and the climate and topography of a region has been established, the forest growth becomes the living espression of the climatic and physical factors of the locality. Similarly, with B given type of climate and locality it is possible for the forester to conceive the t of forest which would grow there naturally. The sp" OF
ester, therefore, ma speak of the climate of the beech
pine forest. Thus, if in China, which may lack weather observations, we h d a beech forest similar to one found
inches. Thus 10, 20, and 30 inches wi 9 be withdrawn
cover, therefore, t P iere is altogether a different heat and
tion, oncc f ercloped for n forest t,ype, hold true f or the
forest of the Engemann 9 spruce forest, of the yellow-