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Serial No. 278

D E P A R T M E N T O F C O M M E R C E

U. S. COAST AND GEODETIC SURVEY

E. LESTER JONES, DIRECTOR

VELOCITY OF SOUND INSEA WATER

Commander N. H. HECK

U. S. Coast and Geodetic Survey

and

Ensign JERRY H. SERVICE

U. S. Coaat and Geodetic Surrey

Special Publication No. 108



National Oceanic and Atmospheric Administration

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C O N T E N T S

Introduction-- - - - - - - - - - - - __ - - - - -. . . .. .. .. - - .. .. ~ - - - - - - - - - - - - - - - - -

RBsum6 of existing information on velocity of sound- - - - - ..- - . - - - - - - - - -.

Theory- - - - . .. - - - - - - _ _ _ - - - - - .. . .-. - - - - - - - - - - - ... - - - - - - - - - - - .Method ol preparing velocity tables. ~ - - - - . - - . - - - . - - - - - - -

Adiabatic corrections t o velocity. . ~ .. . . . .. - - .. . . . - . - - .

Accuracy of velocity tnhlc No. 13 _ _ _ _ _ r _ _ _ _ _ _ _ _ - _ _ _ _ _ _ _ _ _ _

CornpariHon of computed velocities with directly niertsured vclocit iex- - -Comparison of surface vclocit,ies_.- - - - - - - - - - - - - - - - - - - - - - - -

Comparison of vertical velocities to great depths- - - - - - - - - - - - - - - - - - .Sources of e r r o r _ _ - _ - - - - - _ - - _ - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - . -Applicability of computed velocities t o acoustic sounding--_- - - - - - - - - - -

ILLUSTRATIONS

1. Map showing oceanographic cruise of steamer G u id e - -____.- - _ _ - - _ _

2. Curves showing variation of M and with depth-________.

_ - _ - _ _ _ _3. Curves phowing variation of vclocity with depth, temperature, and

TABLES

1. Specific volume of sea watcr for all depths, temperatures, and salinities-2. Base values of M _ _ _ _ - _ _ - _ _ _ _ - - _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ __ _ _ _ _ _ _ _ _ - _ _ _ _ _ _3. Salinity corrections to M _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ - _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _4. Temperature corrections t o M _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _6. M for all depths, temperatures, a nd salinities- - - - _ _ - - _ _ _ _ _ _ _ _ _ _ _ _6-10. Tables involved in the adiabatic corrections to velocity - - - - - - - - - - -

11. Computed velocities for soundings of steamer G u i d e - - - - - - - - - - - - - -12. Comparison of measured with computed velocities- - - - - - - - - - - - - -

13. Velocity of sound in sea water for all temperatures, depths, andsalinities- - - - - - - - - - - _ - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - . - .. - - -

I11

psge1

24613161717172425

3

7

14

89101111151822

26



VELOCITY OF SOUND IN SEA WATER

BY

Geodetic SurveyCommander N. H. HECK and Ensign JERRY H. SERVICE,U. 8. Coast and

INTRODUCTION

While the subject of sound has always been recognized as one of theimportant divisions of hysics and certain phases of it have beenthorou hly investigate$ other phases have remained almost un-touche until recent1 . An especial example of this is the transmis-sion of sound throug sea water. Possible application in navigationwas recognized just prior to the World War and some progress wasmade in the design of apparatus, but it was the development of thesubmarine as a menace to shipping and the consequent need fo r meth-ods of counteracting its activities that led to concentrated investi a-tion by the leading physicistv of this and other countries. Suita% emeans of setting up sound waves ca able of transniission through long

them were among the results of this investigation.

z

distances and receivers capable or detecting faint sounds reaching

After the war interest was on the contrary,every effort was made to findknowledge. This is evidenced of organizationscontinuing in or takin u the States the Navy

this addition to

Department develo e8 tEt? sonic depth finder; the War Departmentperfected methods Por accurately determining the velocity of soundalong the surface and made important determinations of velocity; theCoast and Geodetic Survey and tho Bureau of Standards jointlydeveloped the radio-acoustic method for use in hydrographic survey-in

%he British Navy during the same eriod has been at work on

graphic Office has s tu die it he velocity of sound along the surface;the German Hydrographic Office has studied the theoretical velocityof sound with special reference to use in obtaining de th. These

information

acoustic methods for obtainin the deptE of the water and has madedeterminations of velocit aF ng the surface; the French Hydro-

statements are made o n the basis of the latest availab published

1 “Modern navi ational devices ” by F . E. Smith Engineering vol 117 pp 299-300,Mar. 17, 1924,“Acoustical metaods for depth skmding,” Nature.’vol.113 p 4b3- M&. & 1924.“ A ra$io-acoustic method of locsting positions at 888: Ap&&ion to navigation and to hydrographid

surveys, by Dr. A. B . Wood and Capt. H . E. Mrowne, Proc. Phys.8oc. fLondon, vol. 36, part 3, pp. 1s-

194 Anr. 15. I XB__,_ r _ _.“The soundingof the sea by aound,”by P.Marti (hydrographicengInew of the French Navy), La Na-tu50 Au 20,1921, pp. 125-121.



2 U. S COAST AND GEODETIC S U R V E Y

The sonic depth finder was developed by Dr. Harvey C. Hayes,research ph sicist, United States Nav . It is ca able of measuring

the bottom and for the echo to return to the surf aw 2The radio-acoustic a paratus was dcvolo ed by Dr. E. A. Eck-

Survey, in hydrographic work. The function of the apparatus isto measure accurately the time required for a sound wave to travelfrom a bomb ex losion near the surveying vessel to a hydrophone

In both these cases the function of the a parstus is to measure

in one case and distance in the other it is necessary to know thevelocity of sound in sea water under tho existing conditions.

RESUME O F E XIS T ING INFORMATION ON VELOCITY OF SOUND

The subaqueous sound-ranging section of the United States Army,under Col. It. S. Abernethy, Coast Artillery Corps, has made a veryaccurate determinatim of the velocity of sound along the surfacein certain localities. The results are discussed by E. B. Stephenson,ph sicist, who was associated in this

6 o r k of the British Navy resulted in obtaining velocities of soundalong the surface. An empirical formula based Gn their resultsexpresses velocity as a function of temperature and salinity of thewater.6

There is no evidence in existing publications to show that anyorganization, except the United States Coast and Geodetic Survey,has made experimental determinations of the velocity for verticaltransmission to great depths.

From November 17 to December 29, 1923, the Coast and GeodeticSurvey steamer Guide was engaged on an oceanographic cruise fromNew London, Conn., to San Diego, Calif., bg way of Porto Rico andthe Panama Canal. The wide range of conditions encountered isevident from inspection of the map. As the work included an in-vestigation of Nares Deep, north of Porto Rico, the doepest part oft h e Atlantic Ocean, and also the development of a hitherto unex-

lored deep in the Pacific off tho coasts of Central America andbexico, the range in depth and the number of deep soundings wasexceptional. The actual range in depth w a s from 185 fatlioms to4,617 fathoms.

The Guide was equip ed with a sonic depth finder, and was alsoequipped with standarcf ap aratus for taking wire soundings, tem-

at any depth, and for taking specimens of the 1)ottonr. A definitescheme of soundin s was laid out in advanoe. At every fourth orfifth soundin the epth was obtained by wire and the corres onding

accurately tKe time required for soung to travel Pom the surface to

hardt, Bureau of Stan2 rds,for the use of t e Coast and Geodetic

whose position isKn ~ w n . ~

accurately the time interval. It is evident tR a t to determine depth

peratures, and water sampP s (for later duterminntiori of salinity)

Bime intervaPfor the transmission of sound was dotermine by the%

3 “Measuring ocean depths by acoustical methods,” by Dr Harvey C:. Hayes, Journal of the FranklinInstitute. vol. 197. DD. 323-354. Mar.. 1924.



9

sonic depth finder. Temperatures and water samples were obtainedat the surfacc, a t the depth of 200 fathoms, and at the bottom. Inone case in t h e Atlantic and one in the Pacific aerial tern eratureaand water s:emplcs wcre chtained from surface to bottom. 8arrival

VELOCTTY OF SOUND I N SEA R A T E R

at San Di 0 ho water samples were turned over t o the Scripps



4 U. S. COAST A N D G E O D E T IC SURVEY

until the velocities obtained by simultaneous depth and time deter-minations had been studied and a rational basis for applying theo-retical velocities had been developed.

Inasmuch as the piano-wire soundings, which were taken with

s ecial care in recognition of their importance in connection with

observations with the sonic depth finder, taken with 0 ual care, were

made available a reliable series of measurements of the velocity ofsound in sea water under a wide ran e of conditions. Owina to strong

soundings, to faint echoes, to instrumental difficulties, and to othercauses, a few of the determinations are less reliable fhan others, andsuch velocities are given less weight than those obtained under goodconditions.

Early in the cruise of the Guide i t became evident that the velocityincreased with the depth in spite of the fact that the tern eraturo

ested that velocity is a function not only of temperature and salinityf u t also of pressure. Work was begun on the problem of findingthe relation, based upon reliable theoretical grounds, of velocity totemperature, ressure, and salinity. The authors of this ublication,

general ’supervision over acoustic de th and position determinationwork of the Guide, and Ensi n Jerry %. Service, United States Coastand Geodetic Survey, an ogcer of the Guide, who had had previous

experience in physical research, succeededin finding a solution of thisproblem. It is the purpose of this publication to present the resultsob this solution in a form convenient for practical use, as well as toshow how the problem has been solved.

THEORY

The Newtonian equation for the velocity of sound in a givenmedium suggested itself as a logical and reliable foundation uponwhich to work. Sir Isaac Newton first showed rigorously, reasonin

any given medium is given by the-equation

tKe velocity of sound, were direct measurements of depth, and the

direct measurements of time, it is evident tha t the wor% of the Guide

surface currents in a few places a%ecting the accuracy 07 the wire

fell and the salinity remained practically the same. This P ct sug-

Commander E. H. Heck, Coast and Geodetic Survey,wEo exorcised

from fundamentals, that the velocityof transmission of spund throug

v = ;&;ticity ____f the medzmJ density of the medium

By “elasticity of the medium” is meant the ratio:

Increase of pressure applied to the medium

kesdting decrease in volume expressed as a fraction

The “density of the medium” is, of course, the mass per unit

volume, and the mass and volume must be expressed in units corre-s ondin to those of the force and area, respectively, in the pressure.

of the original volume.



VELOCI lb O F SOUND IN SEA WATER 5

It has seemed most satisfactory to make use in the a plication ofNewton’s equation of the opecific-volume data tabulatexin DMeteorology and H drography, art 1, by V. Bjerknes and?%Sandstrorn, publisheiin 1910 by t t e Carnegie Institutionof Washinton. These s ecifio volumes are based upon the very precise wor

of Knudsen, Ekman, and others. The use of these tables wassuggested by Dr. George F. McEwen, of the Scripps Institution,who also gave other valuable advice and assistance. These specificvolumes are probably nowhere in error by more than 1 part in 10,000,and for the most pa rt are correct to 1 part in 100,000. The specificvolume is, of course the reciprocal of the density and can thereforebe used directly in the application of Newton’s equation.

The specific volumes tabulated by Bjerknes and Sandstrom areno t directly measured but are built up as the sum of directly measureds ecific volumes and directly measured changes in s ecifio volume&e to pressure, tern erature, and salinit changes. ?t is possible,

values of the elasticity of sea water, which elasticities are probablynowhere in error b as much as 1 er cent. It will now be shown

of velocity.In the first place it should be stated that as unit of pressure the

bar, which equals lo6dynes per cma, was used in this work. It wasfirst necessary to reduce the depth for which velocities were to becomputed from fathoms to meters, and thence t o dynamic meters bymeans of Table 3H. The dynamic meter is a unit used to take intoaccount the increase in the force of gravity with de th. By means of

were then founb:It is desirable to explain a t this point, the form in wbich the specific-

volume tables of Bjerknes and Sandstrom have been compiled.Seven tables are re uired which are as follows:

O O C . tem erature and 35 (35 parts per thousand) salinity forevery 10Bcibars pressure f om 0 o 10,000 decibars.

Table 9H is a table of salinity corrections to specific volume andhas a range from salinity O& (pure water) to salinity 39&.

Table 10H gives tem erature corrections to specific volume and

’Ifable 11H is a table of combined salinity-temperature corrections.Table 12H is a table of combined salinity-pressure corrections.Table 13H is a table of combined temperature-pressure corrections.Table 14H is a table of combined salinity-temperature-pressure

corrections.It will be noted that each of these tables is designated by a number

followed by H. In what follows i t wil l be understood that tables sodesignated are Bjerknes and Sandstrom tables without mention of thenames of those authors.

It should be understood that the corrections in Tables 9H and lOH

are firsborder corrections and that the corrections in Tables 11H,12H, 13H, and 14H, are additional second-order corrections.

R1;

therefore, by taking d fferences, t o obtain9om the tables satisfactory

how Bjerknes and 8 ndstrom’s tabPs were used in the computation

Table 15H the ressur0 in decibars obtaming at tle various depths

Table 8H gives ghe specific volumes of sea water in cm3/gm at

ran es from - ’ to 29’

e



6 U. 6. C O A S T AND GEODETIC SURVEY

and Sandstrom’s tables.given can be pu t into the form

The definition of elasticity which has been

Elasticity= increase of pressure in dynes/cm a

resulting decrease in sp. vol. in ern ”/gm

specific volume in cm ”gm

Increase of pressure is always taken as 10 decibars or 10” dyneslcmz.“Resulting decrease in sp. vol.” may bc designated by dw. S p e

The elasticity equation then becomescific volume may be designated by w

106 l O 6 vElasticity =- - =-.

dw dv-.

V

Furthermore, in order to have dv a whole number instead of asmall decimal, it is found convenient to use 1o”dw instead of dw,necessitating multiplying the numerator also by lo6,which gives:

10 11wElasticity= dw)

1Since density=u we have from Newton’s equation

Yin m / s e c . = 1 0 3 v J ~ w0

10V in fathoms/sec.-5.468 x 10 2 v d m

I n addition to facility in entering tables, this form lends itselfwell to the use of reciprocal and square-root tables and multiplyingmachines, with consequent ease and speed in obtaining velocities,

METHOD OF PREPARING VELOCITY TABLES

In order that the velocity of sound may bo obtained in accord-ance with equation (2) at any place, the water from tho surface totho bottom is considered in 200-fathom layers and the mean tem-perature and salinity for each layer is obtained from the best avail-able source of information. The velocity for the entire depth isthen taken as the mean of the various layer velocities.

According1 ,Velocity Table No. 13, pages 26-27 gives the velocityfo r the possi le range of temperature and salinity f o r the surfaceand for the depth corresponding to the middle of each 200-fathom

layer.The formation of a table of values of consisted simply of taking



7ELOCITY O F SOUND I N SEA WATER

10sV(Vfv. PEC. VOL. OF SEAWATER IN C M 3 W )

U

-

-UI

2

2::I

‘I0

rr0

SIs k203u

w

w

t



8 U. S. COAST A N D GEODETIC SURVEl

TABLE

[ 08 u ( -spaoinc volume of sc3 water expressed in Igm

Depth

(fathoms)

Surfaceand100.

97,873'97,92397,799 97,Bw97 72797 778

97: a2 97: 3397.510 97,661

97,437 07,480

97' 63497'705

97,781 97,82497 707 97 76197'634 97'67997'Wl 97'00597:488 97:53397,415 97,46097,342 97,388

97,70397,62997,65597,481

2%97,281

97, 46497,39197,31897,24597,17397,101

97,028

97,74097,06697,59397,51997 44697,37397,300

97 m97 43097: 68

2%97,141

97,089

97,67097,59697,52197,44797,373

$E97,42997,35597,28297,20997,13097,083

86,mi

97,641

97,417

97,196

87,39897,32497,251

97,10497,031

96,968

97,177

97,61697,64097,46697,39197,31697,24197,167

97,59697,62097 44597369

97,21997,144

97:294

97,570 97.58197 493 97 60497:417 97:42997 340 97 35297:m 97:27797,188 97,20197,112 97,126

31323334353637

313233343536

37

97 645 97 689 97 639197 6W97'472 97' 617 97) 6697' 61897'400 97' 446 97'495 97' 647

97 266 97 302 97 35297 404

97:112 97: 159 97: I9 97:282

97: 28 97: 373 97:423197: 475

97' 184 97) 30 97'28197'333

300 (554d e c i -bars).

97,31797 241

97,09097,01596940

96: 865

97: 166

977:094701

96,6,723m1

97 Mo

96,87196: 945

97 489'97640

97? 02 97) .54

97:06997:112

97: 4ld97: 48897 34497 39697' 274 97' 326

97'131 97' 183

500 (923d e c i -bars).

97 350

9720497' 132

96:917

97: 277

07'08096'968

97,438

97,22397:284

97:rn

97,31097,23797,16397,091

96, 75

97 01996:847

31 97 16432 97:07833 97 00334 Qd9m35 98'86330 96'77837 983704 96,746

700 (1,293d e c i .bars).

97,24097,16897, 9597,02696,964

97,286

97'00196'930

97,21497 14297' 071

96: 869

97,08497,01096,93696866

96,72196:793

96, 49

97,05396,97996,90696 03496:761

Q 7 9 0 2 796, 53

96180896:733

98, 87

96 878

96,060

31 9698832 98'914

36 96'69130 961617

a3 9B)84034 96'7%

37 98:64a,

Depth(fathoms)

1,100 (2,036deci-bars).

31 86 041 98 056 98 068 98 085 1,900(3,627deci-

33 95'898 9$913 9519% 9$84334 96828 '%:E40 96864 &E7116 96 76.5 96 77 96 784 96 801if3&Ss4 9iee80 9d713 9673137 95,613 9$628 94643 95,881

31 95,880 95,905 95,Q20 96,936 2,100(3,902ded-

33 94748 95:764 94778 9b:7e63 96 677 96 682 96 707 96 724

36 9$636 96.1551 96:EXtI 9 i W37 96466 96:482 96,4971 96615

32 9$969 96.1883 9i696 96'013 bars).

32 95 819 95 834 96 848 95 E M bars).

3; 95.'608 9 im 951637 9dW

96,88896,614

96,64296,46896,39686,32396,261

96,66796,693

96,44696,37396, 00

96, x1

96,

1,300 (2,406dd-bars).

96668os:48596,41396.341~ g ,6996,19796,128

98, 3296,46996,38796,31496,24296,16996,088

96,36396,28096,21796 14496:072

2,300(4,271bars).

ideci-1,500 (2,780ded-bars)

96 7399518879s 6979g:528

9i38695 4.5096:316



VELOCTTT OF SOUND IN SEA WATER

TABLE-Continued

. - - --.94,48894,41894,35294,28594,219

94,34994,28194,21894.15094,084

94,21294,14594,08094,01493,948

94,07994,01193,94793,88293,818

9

3,900 (7,308 deci-bars).

4,100 (7,888 drci-bars).

4,300 (8,070 deci-bars).

4,500 (8,451 dsci-bars).

Depth (fathoms:

93,94493,87793,81393,74893,683

2,700 (5,020 ded .bars).

4,700 (8,834 deci-bars).

2,800 (5,404 deci.bars).

4. 504. 50

4. 604. 49

3,100 (5,780 ded.

bars).

2,5002, 6002 7002: 00

3,300 (8,167 d dbars).

4. 174. 15

4. 144.13%

3,500 (0,647 d e dbars).

5 OOo 3.87 7,500

5 200 3.83% 7,700

5: 100 3.85 7,600

6'300 3.8356 7,800

3,700 (6,927 deobbars).

4.37%4.384. 354. 334 31%

4.304.29

4.27%4.204. 25

Temperature (dggreescentigrade)

s, 500

8,8003,800

2

$E4, 2004,3004,400

a00

4. 003.99%

3.953.93%3.94%

95,44295,37195,30295,23295,10395,09495,026

95,15595,08695,01794,94894, 879

95,01194,94294,87494, XOB94,737

94,86094,79794,72894,661m. 593

94,72394,85494,58794'52094,452

04,68294,514

94,44794,38094,313

4400 3.71 8 , o O

6 500 3.70%6:600 3. 69

6 700 3.68%6800 3.89de00 3.05

9.$ 181 95; 19885,112 95,12995,044 94080

95,174 95,19195, lop 95,12295,036 95,05494,907 94+98594,89Q 94,918

94,888 94,90494,810 94.83594,749 94,78894.881 94,700w.oi4 84,833

94,744 94,78294,674 04,69391,608 94,02794,641 94 . m94,474 94,493

94,004 94,82494,535 94,555

94,409 94,48994,402 94,42294,338 94,355

-I-95,494 3195,423 3295,358 3395,285 3495,217 3595,149 3896,080 37

Temperature (degrees

centigrade) l - - -

. -- ---.94,44394,37094,30894,242m, 170

94,30694,23894,17294,10694,040

94,18794,10194,03593.90993, m3

94, a3393,90893, w193, n3893,770

93,89793, 83183,78093,70193,836

. --. .

. --.

. --.

.-.

-_ -_ -_94,48594,39794,33194,28494,199

94, a2894,26094,19594,12994, w

m, 18094,12394.05890,99283,927

94,05793,98993,92593,86093,795

93,92193, 85493,79093,72593,681

__ Depth (fathoms)

2

TABLE

volume in cma/gm co6espo&ing to 1 bar increase in pressure)]

\

[ fa, ( fts, -lOIdw. a t 3&% alfnitp Oo C and standttrd pressure, where dr-decrease i n specific

Pressure(decibsrs)

0100200300400

500600700800Qoo

::%::E1,400

15001: 000

I, 7001 8001:800

Mas, a, F

3. 80%3. 59

3. 583.57%3.5Ojg

3.553.54%3.53%3. 523.52%

3.51%3. 503.48%3.47 43. 47



10 U. S. COAST AND GEODETIC SURVEY

. -~. _. - ~. __-___--__Decihars 0 10 20 30

__ ___________8,200....-. 93,989 83,986 93,982 93,9798 3O...... ._.._______.__....8:400 __.___3,919 93,915 03,912 93,YU8

70 71 70 71

~

._

40 60 GO 70 80 90

.__--__.-_________

93.975 93,971 93,968 93,964 93,861 93,967. .~.~_._____-_. . ._____-. ---- - - - . . . . - - -__________

93,w)5 83,801 83,697 93,894 83,890 93,88770 70 71 70 71 70

__ ~-.___

Depthswhere Correc-

a plicable tion( h o r n s )

Salinity (O/oO)

~ ___

0-1,300a06

2,500-2,700 +.0531_______..__..__..___....., 5~ ) -2 ,300 +.os

Depthswhere Correcl-

nDplicahle tion(fathoms)

Salinity (O / oO )

0-2, hOO +o. 01%

3,7004,700 +.00%34.._.._.__.__...___..-..._,7o(t3,600 + . n i



VELOCITY O F SOUND I N SEA WATER 11

0-300600703QOO

o300M)o700

Temperature (degreescentigrade)

-0.26-.24-.24-.23

-.n-.24-.%

._____-. -.. -

1...................

0-1, loo1,XO(t2,3002,501t3,3003,,W0-4,1004,3CHl-4,700

2-................ -.05-.04 4- .04 14..................-. 03 1- .03

3. - --. - - - - --.

4-........................

-.-.. 1,900-2,700

0-1, loo1 ,3Wl , 700

@-1,300

0-500700-1,100

0-300

6.. ........................

a.... ......................

-.05% lG..- ....................

-.my,-.oQ I8........................

-.13

--.174(1 m... .....................-.17

-.22o.-. ......................

0looa00600700

TABLE. - -Tetnperat i~re correc t ions to M

- .38-.37-.36-.36-.36

Depthswhere Correc- Temperature (degrw

applicable 1 t ion /I centigrade)(fatboms)

4.434. 42

4. Q4. 374.364.34

4.374. 354. 4

4. 124.314.294.28

4.40

____l ,w3,3001 -0.02 iL...............

3, sw 4,7 oo -. 01>4

4.304. 38

4. 354. 334.324.30

4. 334. 314. 30

4. 284. 74.254. 24

4.30

4. 284. 64. 234. 224.20

4.194. 17

4.224. 214.1Q4. 184.16

4. 154. 13

DepthsCorrec-

0-100 -.351w =:::.33

TABLE

[ M M-lOado, wheredo-decreacie in speciflo volume in cms/gm corresponding t o 1bar increase i n pressure]

Depth (tsthoms)

_ -

l d i ni t Y'O/GU

-

31323334353637

313233

34353037

31323334353637

313233343h

3837

0

_.

4. 5G4. 564. 534. 524.604. 41)4. 47

4.804.484. 47

4. 454. 444. 424.41

4.454. 444. 424.414. 394. 384. 38

4. 94. 38

4. 3b4. 33

4. 24. 0

4.30

-2

4.614. 604.484. 474.454. 44

4. 54.434.4

4. 404.3Q4. 374.36

4. 404. 3Q4.374.364. 344.334. 31

4. 344.334. 314. 304. 28

4. 274.25

4.42

-4.474. 484. 444. 34.414. 404.38

4. 414.394. 8

4. 364. 54. 334.32

4. 384. 354.334.324.304.294.27

4.304.294. 274. 284.24

4. 34.21

Tempera tur e (degrees centigrade)-10

-4.344. 334. 314. 304. 284.274. 26

4. 284. 264. 26

4. 234. 224.204.19

4, 244. 234.214.204. 184.174. 16

4. 184.174. 164. 144.12

4. 114.09

-12

-4.314.304. 284. 274.264. 244. 2a

4. 264. 234. n4. 204. 104. 174.16

4.214. a04. 184.174. 164. 144.12

4. 164. 144. 124.114.09

4. oe4.06

4.23 4.204.21 4.184. 20 I 4.17

4.18 4.154.17 4.144. I5 4. 124.14 4.11

4.O5 I4 o1

-18

-4. 234.224. 204. IQ

4. 174. 164.14

4. 174. 164. 14

4. 124. 114. 084.08

4. 134.124. 104. OB4.074. 084.04

4.084.074. 064.044 02

4.013. QQ

0

-4.214.204. 184. 174.164. 144. 12

4. 164. 144. 13

4. 114.104.084.07

4. 11e 104. 084. 074. 054. 044.02

4.064.054. 034.014. 00

3. 993. 97



U. S. COAS T A N D GEODETIC SURVEY

TABLE-Continued

3 .89

3 .883 .863 .843.82

3.873 .87

3 .843 .833 .823.80

8.86

3.833.82

3 .803 .78

3 .783 .773 .703 .763 .73

3 .743 .723 . 7 13.703 .69

3.81

I3 . 8 1 . _ ._____3.80 _ _ _ _ _ _ _ _3 .78

__._____3.76 __._____3 .78 _ _ _ _ _ _ _ _3 .75 __._____3 .74 __ ._____3 .73 _ _ . _ _ _ _ _3 .71 __._____3 .72 __._____3 . 7 0 - - ~_ _ _ _3 .09 _ _ _ _ _ _ _ _3 .68 __._____3 . 6 7 . . , . _ _ _ _

a . 7 0 . ~ -_ _ _ _qew-____._- -____-________

3,100_ _ _ _ _ _ _ _ _ _ _ _ _ _ . _ _ _ _ _ _ _

3,300-- . _ _ _ _ _ _ _ _ _ _ _ ____.__

3,500-___- ._ . - -___- .____ .__

3,700--__.__- - _ _ _ _ . _ _ _.__

8.853 .843 . 8 3

3.80

3 . m3 . 7 93.783 .773.16

3.703.743 .733 .723.71

3 .723.713.703.69

3.673.683.00

a. 8a

3 .693 .083.673 .06

3 .643.653 . 8 3

__._- - -__ .______ _ . ____--._-_ ___.______ _ . _ _ _ _ _- - .__ -__

Depthfathoms)

1,900

Temperature TBmmmture

-3

4 . 0 44 . 0 24 . 0 14 . 0 03 . 9 83 973 9 6

4.013 . 9 93 . 9 83.973 . 9 53 . 9 43.93

3.953.933.923.913 . 8 93.883 . 8 7

3.613.903. a3.883.863.863 . 8 4

--_

2 4

4.26 4.214.23 4.194 .22 4 .184 .20 4 .164 .19 4 .164.17 4.134.16 4 . 1 2

4.21 4.104 .10 4 .144 .18 4 .134.10 4.114 .16 4 .104 .13 4 .084 .12 4 .07

0

_I4 .304 .284.274 .264 .244. 224.21

4.a54 .234 .22

4 .194.174 .10

4.204. 184.174 .164 .144 .124 .11

4.1s4 .144. 134.114 . 0 94. OR4. OB

4. m

--31 4.0932 4.0733 4. 0834 4.0635 4.033 6 4 . m37 4.01

4.17 4.134 . 1 5 4 ~ 1 14 .14 4 .104 .12 4 .084.11 4.074 . 0 8 4 . 0 54.w 4.04

4.07 4 .064.06 4.034 .04 4 .024 . 0 3 4 . 0 14 .01 3 .994 . 0 0 3 . 9 83.99 3.97

2 . 1 m1 1.M32 4.0433 cw3 4 4 . m36 4.00

37 3.9838 8.88

4.13 ~ _ _ _ _ _ .4 .10 _ _ _ _ _ _ .4 .09 _..____

4.07 __.___

4 . 0 8 _ - _ _ _ _ _4 .04 ...___.4.03 _ - _ __-.

3.98 3,963

3 .86 3 .933.96 3.94

31 4.0032 3.9833 3.9734 3.9636 3.9430 3.9337 3.82

4.16 4.114. 14 4.094 .13 4 .084 .11 4 .064 .10 4 .064 .08 4 .034 . 0 7 4 . 0 2

2.m

3. 89

4 .11 4 .064 .10 4 .064. OB 4 . 0 34 .07 4 .024 .06 4 .004 .04 3 .994 .02 3 .97

I

31 3.8632 3.9533 3 .9434 3.9336 3.9136 3.9037 3.89

3.89 3-693 .93 3 .913.92 3 . 9 03.91 3.893.89 3.873.88 3.863.87 3.86

=======

Depthfathoms)

3

Temperature(degreescantigrade)

-2

_ _

_ _ ^ . _

__-._

3 . 6 23.003.693. 683.67

3.673 . 6 63 . 6 53.643. K

3. M3. g3.6;3. 613. M

3. 613.M3.4(3.4f3.4;

3. 4<3.4:3' 443.42

3.4:. I _ .

..-._.

0 Io3132333436a637

a334363637

333436

37

3334353037

33343638

373334

3-3

... - .__.___

3.063 . m3.623.613.60

3. Bo3 .69

3.573.60

8.673.563.66

3.63

3.643.633. 623 .613. 60

3 .493 .483.473.46

3.45

a. MI

a.M

. _ - _ _ _

._.___

_ _ 3 .923 .913 . 8 9

3.873 .883. ti4

a. 88

3.873 .883. L?43 .833 . 8 23 . 8 13.79

_-.___

3 .043. Ba3 .613.803.59

3 .693 .683.673.663.56

3 .563.663 .643. 6.33 .62

3, -533 .623.613 .603 .49

3.483.473. 483.46

3 .44_____.

~ - - - - -.

1, loo

4,300

4, wo

4 ,700. 713 .703.693 .08

3.663.673 .66



VELOCI CY OF SOUND IN SEA WATER 13

0-13-14-14-15

The salinity corrections tabulated in Table 3 were computed fromTable 12H as the rate of change per bar of the values in that tableat the salinity and pressure in question. The method us'ed in com-puting these values may be illustrated by computing one of the valuessay the correction for 31& salinity applicable between depths 0 and

1,300 fathoms (pressures 0 and 2,400 decibars).TABLE2H

(101x sdnity-pressure correction in o speciflo v o ~ u m e jgm

0

a' 5002: 800

I I

From an inspection of the table one may fairly assume that theexact pressure to which -14 belongs is very approximately 2,450decibars. Since the correction for 0 decibars is 0, the mean changeper bar in the salinity-pressure correction is -14 divided by 245, or-0.06. Since this tends to make the specific volume less a t thehigher pressure, it is additive to M. Hence the salinity correction,

as tabulated in Table 3, to the base M a t 3 1 ~alinity between 0 and

1,300 fathoms is $0.00.

The temperature corrections tabulated in Table 4 were corn uted

per bar of the values in that table a t the temperature and pressure inquestion.

of velocity in Table 13were then computed directly bymeans of equations (1) and (2) from the values of v and M in Tables1 and 5 , respectively.

Tho curves on Plate 2 show how the two quantities from which Vis computed, v and H,es ectively, vary with the depth. The curves

salinity, respectively.

0

from Table 13H, in an exactly similar manner, as the rate of c ange

%

on Plate 3 show how veP city varies with depth, temperature, and

M experimentally determined under isotherma conditions. Grant-

ADIABATIC CORRECTIONS TO VZLOCITY

The values of velocity in Table 13 were corn uted using values of

ing that the condensations and rtlrefactions of the sea water duringthe transmission of sound take place under adiabatic conditions,then the velocities in Table 13 theoretically need to be increased bsmall corrections, which were neglected in computing that table. 8was suggested by Dr. L. H. Adams, of the geophysical laboratory ofthe Carnegie Institution, that these corrections might increase the

velocity by as much as 0.5 of 1 er cent, so it was decided to investi-gate the effect. The theory un Perlying the computation will now be



14 U. 5. COAST AND GEODETIC SURVEY

0,ki the spec%c heat at constant volume, in ergs per gram per

C,, is the specific heat at constant pressure;degree cenFigrade;



VELOCITY O F SOUND IN SEA WATER 15

aa Tand that C, -C,=

aa Twhence C, =C,- ~

B

In other words, the adiabatic compressibility, which probablyobtains durin sound transmission, is less than the isothermal com-

aa Tpressibility, w l ch is what Ekman measured and Bjerknes used in his

are given herewith of

rections to the velocities under various conditions. Since the unitof pressure used for /3 was tho bar, or lo6dynes/cm2,a unit of energyin C, equal to loe ergs, or 1 decijoule, was necessary.

TABLE

[ ola a ( )p-temperature rate of changeof specificvolume, in per degree cantigrade,of BBB wateram

of salinity 35 3

Temperalure in degrees centigrade

6 I 1 0 I 1 6 1 2 0

Depth (fathoms)

The above valueswere computed by means of Tables 10H and 13H

TABLB

[ 0ag ,9- ( )T-isothermal p r a m ate of change of speoifio volume, InEaer bar, of 888 water of

salinity 35k]am

0

Temperature in degrees centigrade

6 I 1 0 1 1 8 1 2 0

Depth (fathoms)

I 1



16 TJ. S. COAST A N D GEODETIC S U R V I P

TABLEI0

metersper second (lower line)][Adiabatic corrections to velocity, in fathoms per second. For the surface corrections are also given in

Depth (fathoms)Temperature in degrees cantigrade

1 0 1 6 1 1 0 1 1 6 1 2 0

The authors are somewhat in doubt as to the advisability of apply-ing this correction. The maximum effect is about 0.5 of 1 per centand the average effect all through the tables is only about 0.2 or0.3 of 1 per cent. Furthermore, in practice the de th obtained by

with the sonic depth finder and the mean velocity obtained fromTable 13 and known physical conditions agrees as closely as can beexpected with the corresponding wire depth.

wire under good conditions is acce ted as the stanBrd. It will be

shown that the depth computedP

om the time interval measured

ACCURACY OF VELOCITY TABLE NO. 13

The accuracy of the velocities tabulated in Table 13 is controlledby the accuracy of the values of M. Jud ing from the records of

values of this quantity, no value of M will be in error by more than1 per cent. Since Nappears under the radical in the velocity equation

this would indicate that no value of velocity will be in error by morethan 0.5 of 1 per cent, which would amount to about 7 m./sec., or

the experimental work of Ekman, which is t%e ultimate source of the



VELOCITY O F SOUND I N S E A WATER 1 7

whether the values of Mused in the table are the true values. Furtherstud is bein given by one of the authors to the possibility of obtain-i n g J ectly Born the results of Ekman's compressibility experimentsmore precise values of M.

COMPARISON OF COMPUTED VELOCITIES WITH DIRECTLY

MEASURED VELOCITIESCOMPARJSON OF SURFACE VELOCITIES

At the surface, at - .3"C. and at salinity 33.5&, E. B. Stephenson,working over a distance of about 15,000 meters, and using veryprecise methods of measuring distance and time, found the velocityof sound to be 1,453 1.5 m./sec. Table 13 gives 1,448 m./sec. forthese conditions.

In connection with the tests of the radio-acoustic apparatus devisedby Dr. E. A. Eckhardt, the subaqeous sound-ranging section of theArmy and the steamer Guide coo erated in a on -distance test of the

were determined with great precision. The distance was about100,000 meters. At the surface, a t 13" C. and salinity 33.5& thevelocity was found t o be 1,492 m./sec. Table 13 gives for theseconditions 1,494 m./sec.

On April 8, 1924, off Encinitas, Calif., the steamer ChLicZc, as a testof the radio-acoustic apparatus aboard ship and at two hydrophonestations fired six detonators in the water near the ship. Theposition of the ship a t each explosion was determined by sextantangles. The time required f o r the sound wave to travel from theship to each hydrophone was measured by the radio-acoustic ap ara-

salinity 33.5 ass close to thesurface. Tahe 13 gives 1,496 m./sec. for these con8tions.

velocity of sound during Novemger, 1923. Bota time and distance

tus. The accom an 'ng table gives the results of the test, and s iwsa mean measureB fe ocity of 1,495 m./sec. at temperature 14°C. and

, the sound wave being assumed to

hydro-phone 1

Detonator No.

Distancefrom

hydro-phone 1

Mela818,43918,4E018 451

14 5618,4bo18,438

- - - -_ _ _ _

M. econds Seconds1.489 I l Z . f l 9

Distance

phone 2

19,010

19, OOO19,00819,013 1,494

1,497

C O M P A R I S O N OF VERTICAL VELOCITIES TO GREAT DEPTHS

For convenience in arisons, computed velocityand measured velocity

by .VF. In every case that V , is determined byderived from Table 13 will be

dividmg a distance measured as accurately as conditions permit bya time interval determined with equal care. The percentage differ-

ence - 100 per cent can properly be regarded as the ultimatevr



bottom

--3.3

3 4 9

2 4. _ _ * - _ _

2.635.1

__ - -_ -_35 1

3.035.2

2.335.0

1.535.1

2.5

35.2

_ _ - _ - _ _35.1

____.__

35.1

1

935

812

1035

814

2036

829

1936828

1936

828

1936

828

2136

831

21

36831

2136

831

2236

833

3udace

13. 934.8

15.034.9

2 2 636.3

21.136.4

21.336.4

21. 73 5 9

23.536.4

25 1

36. 3

25. 136.0

26.335.8

200fathom

6.23.50

6.434.9

17.636.4

17.736.4

17.736.4

17.536.4

17.936.5

17.4

36. 5

17.636.4

17.236.3

35810

35810

1036

821

1036

821

1036

821

1036

821

1036

821

10

36821

1036

821

1036

821

5 7

--5 4

35812

5 435

812

93582a

935822

9358n

935

822

936

822

9

35832

935

822

935

822

11

335

816

35816

35825

35825

35825

35825

35€25

35825

35825

35825

13

--_ _ _ _- _ _ __ _ _ _

4 335

819

7 635

827

7 635837

7 635

827

7 635

827

7 635

827

7 6

35827

7 635

827

7 635

827

- - - _- -- -- - - -

- - - -_ - - _- - -

35837

35837

35839

35839

35841

35839

35839

35839

_ _ _ _. .

_ _ _ __ - _ __ _ _ _- - -

3 335

839

3 335a39

4 335

839

4 335

839

5 435

841

4 3

35839

4 335

839

4 335

839

35825

35823

35825

35827

35825

35821

. - - -

. - - -

35825

35823

35821

35821

--..I

7 6

35827

6 535

824

7 635827

8 735

829

7 635

827

5 435

822

--..- - -._.___

7 635

827

6 635

827

5 535

824

5 535

824

. .___

- - -

. .

--.- - -

-. .

. .

. . .

- - - -

TABLE1

IObserved t e r n e r a -

tures csntigra& andsalinities

dopted temperstures, Salinities, and tabular velocitlesfor depths expressed in hundreds of f a t h o m

Numberof-din1 -

3

-

535

807

535

807

'1536

825

1436624

1436

824

1436

824

1436

824

14

36824

1436

824

1436

824

-

9

35815

435

815

835

824

835

824

835

824

835

824

835

824

8

35824

835

824

835

824

-

15

-

_._.- _ -_._.

335

823

535

828

535

828

535

828

535

828

535

828

5

35828

535

828

535

828

-

17

__.__..

- -_.

335

826

435

829

435

829

535

831

535

831

435

829

5

35831

535

831

535

831

-

19

-_ - -_ - __ _ _

335830

435

831

435

831

435

831

435

831

436

831

4

35831

435

8 1

435

531

-

21

-

335

832

S35

832

435

834

435

834

535

836

4

35834

435

834

435

834

l

I 25

26.

36.

25.35.

25.:36.

w.36..

23.36.l

27. :35.1

26.:

35 :

2 5 . 734. I

2 5 . 735. a

26.83 & 4

26.8S O

27.336.0

m. 834 9

18.:

36.2

16.a 1

17. I36.3

19.236.4

17. 736.4

16.736.3

17. 636.3

17. 63.55

17.036.2

13.436.0

12 536.3

13.538.3

13.835. 6

-0. :

35.

2. <

35.

2 :35.

2. t

36.;

2. ;35..

2.

4. (

35.1

4 . 23 5 . 3

4. 13 5 1

4.035.2

4 035.3

3. 935. 2

z

3483:

213t

831

2:3t

833

z38

833

2136

831

n36833

2235

832

2235

832

2135830

2036

929

1936327

2036i29

2035128

10

36821

1036

821

1036

821

1136

822

1036

821

936

819

'I35

514

1035

320

1035

735I14

735115

7

120

E

3:824

735

822

835

824

935

825

835

824

635

82o

- _ -- _ -.--

835

824

735522

635

320

635

435I15

$20

.__

_ - _-.-

35B

43:9

535

635

331

535328

335124

3m

.--

. ~ -

. _ _

635I31

635I31

535828

53528

_.._ _ .-..

_ _ .__.~ . .

14

36824

1436

824

1436

824

1536

825

1436

824

1336

823

1135

819

1335

821

1335

821

936

316

5

35831

335

826

535

831

535

831

535

831

335

826

_ _ __ _ _

635

834

535

831

435

829

435829

.___

_.__

_...

__._

_ _ _ ___._

4

35834

. _ _ _

. _ _ _

435

834

435

834

435

834

...

._..

.-..

-..

....

.-..

535

836

535838

435

534

._._

_.__

..__

_.__

-.

._._

.___

.._̂

. _ _ _ I

4

35831

335

830

435

831

535833

535

833

..-

__.

__.

-.

--.

--.

635

835

535

833

435

832

435

8 2

_.__

-.-

__..

_.__

_ _ _ _

2 2

35 35844 849

-- - -- - ---.~ - -- --.

3 335 35846 851

3 335 35

846 851

3 335 35

846 851

-.- .-. .

I

3:8%

3:82(

f3:

82:

;I821

93:

821

735

818

435

812

a35

822

835

820

635

516

635

316

535116

._..

.__ .

861%I865%1867% 870%I::::::841

I-. .

36 35116 815

9 1



2 2 234 34

823 828

34 34823 828

2 234 34

823 828

34 34823 828

34 34823 628

34 34825 829

34 34825 8%

3 _.__.

2 2 2

2 2 2

2 2 2

3 3 3

3 2 2

34 .........825 .........

34830

34830

....

.-..

....

34830

34830

34831

34830

.___

34a35

34835

234

835

234

835

...

2 2 234 34

837 wo

2 2 234 34837 840

.............

.............

.............

.............

.............

.............

2 ....

34 ....837 .-..

2 ....34 ....

837 _ - - -

......... ....

2134844

844

. -

. .

. -.

. .

234

848

2 23 4 3 4848

........

........- -.

........

........

........

........

-.

- -.

........

........-.

-. . -

.......

........

~... -

.-__

_-_.

_ _ _ _. .

~ - -. .

.-__

. - -- - -

___.

.__.

_ _ _ _- -- ---.-

.___

........

........

........

........

........................................

................................... 816

.........................................

.........................................

................................... 821

TABLE1-Continued

Adopted temperatures, salinities, and tabular velocities for depth s expressed in hundreds of fathoms)bserved temper a -tures centigrade andsalinlties

. . . . . . . . . veJ l l iumberof sounding c

otton

-

3

_

-..

...

_..

933

814

833

81 1

733809

834

812

934

814

E

3481:

3481:

5

3481'

I3'

81:

5

-.--

-..

..-

734

312

633

810

534808

634

810

734

812

734

811

634

81C

1

3481:

t3'SI(

-

'I

-._-..-..

.__.

634

315

534

434

911

434

811

634

815

634

815

534

813

634

815

c34812

313

c9

-

___.

__.-

_ _ _ _5

34817

434

815

334

812

__.

_ _ __ - -

534

817

534

817

434

815

534

817

434

815

19 21 I 23 25 \ 27 29 31 1 33 j 35 37 3g 41 43 1 45

-20

20

32335

32325

20323 2 5

1833

824

20338%

2034

827

1934

1934

8261934

828

1834

828

am

urfaa

____.

.__-.

2. e34. e

1. <34 t

2 f

3 4 1

.___ .34.t

2

34.1

2. ,34.

2 :

34.

2

84

2

34.

24..................

25..................

26..................

........................... .......... ..........

.............................. ..... ..... .....................

.......... .......... 819

......... ..... .................

..--._._ ..........

...................

.-.-............................. ........ ..... .......... .............. 815

.............. ................... 813

........................

................... ____.I................... ...............-----........................

.............. .................... - - - - L

............................

............................. ...........

.............................

2 ...............................34 .............................._

828 818

.................... _-----..... .................... 8231

2 ....................-34 ............... ....

828 ._._I.............. ..... ..... ..........

_____.

133.6

1 3 53 2 6

9. 933.1

1 2 03 1 3

13.434.6

11.334.4

11.134.7

1 2 734.6

11.634.4

26.831.4

26 431. 1

26.63 2 7

27.832 1

27.333.0

27.133.3

27.13 4 . C

25. 733. t

26. 133 t

3 :3 4 3 '818 82:

3 (

818 82(

3 '

818 82:

3 :3 4 5

818 821

34 3;

3 4 3 .

27.333.8

27.333.8

23.534.1

n.34.0

2 7 .833.8

? s a33.8

28.234.1

23.534.7

19. 134.2

18. 534. 3

16.833.9

16.833.9

15.733.9

1.834.2

12.034.7

ia 934.7

10. 634.7

12 034.7

13. 734.7

10.434.5

11. 134.6

9.634.0

6. 134.4

7.934.0

7. 434.0

a034.1

2. 534.6

2. 434.6

2 334.5

1. 834.6

2 834.6

2 9

2034

827

2034827

1834

825

1934

826

2034827

2134

829

1934826

1734

823

1434

818

1234

816

1234

816

1234

816

1234

816

-

834

812

834812

734

810

834

812

834

812

1034

817

834

812

834

812

734

810

634

808

634

808

634808

634808-

634

810

634810

634

810

634

810

634

810

34812

634

810

634

810

634

810

534

8c41

534

808

534

808

434

807

1

-

534

813

534813

534

813

534

813

534

813

634

815

534

813

534

813

534

813

434

811

534

813

434

811

334809

-

434

815

434815

434

815

434

815

434

815

534

817

534

817

534

817

434

815

434

815

434

815

334

812

..-.

..__

_ _ _ .

-

334

816

334ai6

334

816

334

816

334

816

434

818

434

818

434

818

434

818

334

816

434

818

334

816

- ~ .

.-.

--.

-

334

818

334818

334

81s

334

818

334

818

434

821

434

821

434

821

334

818

334

818

434

821

234

816

._..

._._

.-.-

-

234

820

234820

234

820

234

820

234

820

334

822

334

822

334

822

234

820

234

820

334

872

234820

-

3

...............34 ....................................852 .............................. 828

........................................I I I I H818

......................../................1 _ _ _ _ ................... 819

. ..I .......... ..... .--..I ......

.................... _ . . _ . I ................

................................... 822

.........................................I i / i l........................ . - - - - .............................................. 824i / / I H

834.6

. _ _ _ _ __ _ _ _ _ _

2 434.5

2.434.5

2 434.6

1.534.5

2. 434.3

.............

.............

...~--.................

..............

.____ _ --..-

.............___.I._.̂ _..-

34828

234

823

234

828

2348'23

....._ _ I ..... .... I_ ........ .............................................

.............

.............

... .........



22

Fathoms1,1671,937

U. S. COAST AND GEODETIC SURVEY

Seconds1.4642.382

TABLEo. 12

NORTE ATLANTIC OCEAN

1................2 _ _ _ _ _________.

3................4................5................6................7................8................9................10................1 1 ................12.-..............13................14................15................16.____ _ _ _ _ ___._

11-21 3911-22 3811-22 3711-23 3511-23 3211-24 2911-25 2711-26 2411-26 2311-27 2111-28 I911-30 1912-01 1912-02 2012-03 1912-03 19

333207032944064609234003441 13607

CARIBBEAN SEA

71 3071 0070 0670 2970 3670 2770 3170 1869 1268 0166 5265 056 5 2466 4467 3267 51

...................2,6252,9842,9883.0303 0603’0272:9654,5151,9744,0753,2344,6171,817

I7 5016 5715 1513 231 1 3510 029 36

_ _ _ _ _ _ _ _ -3.5223.6493.6363.7043.6393.6255.4402.3254.8043.9315.5652.154

24................25. ...............26................27. - - - - - -._-.__.28. ...............29. - - -30................31................32.-. - - - - - - - - - _ -33................34................

-. -. - -

83831831838383184182.5837833841823

35.. ..............36. ...............37. -.. . - - -

--.- - -- - - 1.9_ _ _ _ _ _ _ _ _ 1.3_ _ _ _ _ _ _ _ _ _ . 2

. 6 ____._

_ _ _ _ _ _ _ _ . I

1.6 ____.__._

1.4 .........._--______..9_ _ - _ _ _- _ - 1.3

1. 2 ..........

1. 3 .................... 2.4

38................39 - - - _ _ _ _ _ _ _ _ _ _ _40. ...............41................42................43................44................45.. ..............46.. -. -._ _ - - - - -

17................18................19. ...............20................21................22................23................

-___-

12-0312-0412-0612-0512-081%0712-07

Depth Timeby wire intervalI

819831828824823818828

1.2 .........._ _ _ _ .-.--. 0.7.......... 3.4

1. 5 ...........7 ...........2 ..........2.6 ..........

12-1312-1312-14lSl612-1512-16

7 34 78 566 19 79 026 10 81 1 1

6 14 84 267 48 84 068 47 84 55

Fathoms/aec.

797813

825

81581381.5818818818827818828828818819822824

820818A17816821813810

819

67 4168 1571 1674 0277 0579 0879 49

0 . 4 _ _ _ _ _ _ _ _ _ _3.0 ..........

..___..___.1- - - _ _ _ __ _ _ 1.4

3.3 - _ _ _ _ _ _ _ _.......... 1.8.......... .5__._.___. . ?.......... .5.......... 1.4.......... 3.6.......... 2.7.......... 1.I.-.._ .___ 4.......... 1.8

.......... .42.6 ........... I --.__ _ _ _ _

.......... .7

.......... 1.1

.......... 3.5

........A 1.3

2. n ..........

-37.2+ .W

44) -10.4

-0.24

24818301:3M807736

1,7631,8941,9283,1612 0203:4723,4262,0512,1712,5222,660

2,2121,7832,0301,9392,4971,569702

I I

.3022.2971.7161.104.a95

2.2272.2742.3453.7962.4584.1363.9902.4402.8313.0573.174

2.6862.2372.4892.3593.0021.884.E65

8572,8312,3392,2061 9191: 084

1. 0593.3842.7292.7162.3501.329.a28

809837857812817816808

PACIFIC) OCEAN

I I

It is seen from Table 12 that the average percentage differencebetween V and V,, for the entire 44 determinations is 0.2 of 1 percent. Further, it has been computed that the probable error of a



VELOCITY OF SOUND IN SEA WATEB 23

In determining V, the assum tion is made that the echo returns

bottom is sloping, the reflected sound wave which is received willfollow the line passing throu h the vessel normal to tho slope. If

time intervals measured will be too small and Vm mll be too great,

and wcordingly the aver e percentage difference could not possibly

rthle conclusion is thttt if a 6,500-mile cruise with all kinds ofbottom conditions, including several deeps, fails to show the effectof slope, areas of steep slope are of relatively insi Scant extent.

To test this conclusion further, slopes for tf positions wheresoundings 24 to 46, inclusive (Pacific Ocean), were taken, werededuced from the best available information, including the work ofthe Quide and wire soundings by other vessels of the Coast andGeodetic Survey.

from a point vertically below the sB,p. It is of course true that , if the

many of the soundings are t a en a t places of considerable slope, the

be 89 near zero as shown7 the anal-ysis of Table 12. The inevit-

These are given in the following table:

1 0 0 4 2 _ _ _ _ _ _ _ _ _ _ _ _ O M )0 30 43 _ _ _ _ _ _ _ _ _ _ _ _ _ 1 480 60 44 ... _ _ _ _ _ _ _ _ _ 0 000 40 46- . - - * - - - _ _ _ _ _ 0 560 30 40 _ _ _ _ _ _ _ _ _ _ _ 0 120 05

I I I I II I____The mean slope is about 1" with a madmum of 0 .

It must not be inferred that steep slopes do not exist. They are

important geographical features of interest to the eobgist and of

cedure the velocity of sound can be determined without appreciableerror due to slope.

The agreement between V,,and V , has been tested by determiningthe average pe rcen tqe difference and the rohable error of a singlevalue for all the soundings of Table 12. Agetter test is the exami-nation b the wme method of characteristic groups, each of approxi-

Soundings 5 to 10, inclusive, of general de th of 3,000 fathoms,

give an average percentage difference of 0.2 of 1 per cent, with aprobable error of n single value of 0.8 of 1 per cent. Serial temper-atures and salinities were taken a t sounding No. 7.

articularly rigid tost is the a plication to three soundings takenin%res Deep, north of Porto 8100,angin from 4,075 to 4,617fathoms. For these the average percentage iifference was 0.5 of 1per cent, with a probable error for a single value of 1 1 per cent.

For a group of four soundings, Nos. 18 to 21, inclusive, in theCaribbean Sea, with depths from 1,900 to 2,800 fathoms the aver-

e percentage difference was 0.5 of 1 per cent, with a prohable error

For a group of nine soundings, Nos. 36 to 44, inclusive, in the

concern toethehydrographer and ocean0 apher. r he purpose ofthe discussion has been to bring out the Y ct that by proper pro-

mately tKe same physical conditions and general depth.

taken over a level portion of the sea floor o the North Atlantic,

oT a single value of 1.6 per cent.



24 U. 5 COAST A N D GEODETIC SUR'VEY

With differing conditions it should follow that in different regionsvelocities for the same depth should vary. This is found to be thecase. Soundings Nos. 3 n the Atlantic and 44 n the Pacific form anexample of this kind, with velocities 828 and 821 fathoms/sec.,

respectively, the depth at each being a proximately 2,500 fathoms.

depths. Sounding No. 23, depth 185 fathoms, and sounding No.34,depth 3,472 athoms, both have a computed velocity of 828 fathoms/sec.

Also in some cwes the velocities are tEe same for widely differing

SOURCES OF ERROR

The agreement between V , and V, which has been shown by theabove study of Tables 11 and 12 is seen to be remarkably good whenit is considered how many elements enter into a compmson of thesetwo quantities and what sources of error there are in the determi-nation of each of these elements. These sources of error will be dis-cussed in some detail.

Errors in the determination of V , include errors in the determi-nation of depth by wire sounding, and errors in the measurement ofof the time interval with the sonic depth finder.

The accuracy of the determination of depth by wire soundingdepends upon the skill with which the soundin is taken. Thecommanding officer of the steamer Guide, Lieut. mmander R. F.Luce, Coast and Geodetlc Survey, showed exce tional skill in handl-

during every sounding. In only a few cases were the currents

strong enough seriously to affect the accuracy of the wire measure-ment. The accuracy of the registering sheave was tested by run-ning over it a measured length of wire, and the error was found tobe ne ligible. Change in length of the wire with temperature was

weather conditions, fortunately was absent during most of thecruise of the Guide.

The question of the accuracy of time-interval determination undcrservice conditions is of special interest because previously to thecruise of the Guide the apparatus had not been submitted to the testof continuous check against wire soundings in depths such as to make

the time intervals large. The essential precaution is the maintenanceof eriod of disk rotation a t exactly 10 seconds, which the tuning-forR governor usually accom lishes. The depth finder used was ofthe first type developed by Koctor Hayes and had some operatingdefects that have been remedied in later types. One of these was thedifficulty of reducing the loudness, as heard in the phones of theoriginal oscillator sound so as to be com arable with that of the echo.When the oscillator is operated a t fulPpower it is often extreme1difficult to hear the echo and synchronize it with the original s o u n iThe strength of echo also varies with the character of the bottom, so

that in some cases the echo was faint in moderate depths and strongin great depths. Precision of synchronism depends very largely on

ing the vessel, and the wire was kept as nearPy vertical aa possible

also Bound negligible. One common source of error, unfavorable



VELOCITP O F SOUND IN SEA WATER 25

In the studies so far made i t seems to be important chiefly in depthslesa than 500 athoms. It is therefore advisable in a given region ofmoderate depths to take the ersonal equation into account.

consistency is obtained. On one occasion a special effort was madeto determme the ultimate possibilities under exceptionally favorable

conditions. For five soundings in depths rangin rom 535 to 702fathoms the maximum difference of m y value of 5: from the meanwas 1.5 fathoms/sec.

The accuracy of the determination of Vo depends not o n l upon

abilhy of the adopted values of tern erature and salinity. The

it has been brought out that there is a possibility of small errors inthe tables themselves and in the method of deriving M from thetables. The reliability of the ado ted values of temperrtture andsalinity depends on whether they gave been actually measured orinter olated betwcen such measurements as in the case of the Guide

Theanalysisof all the resups indicates t hat a atisfactory degree of

the fundamental corrections of the method but also upon ti reli-

fundamental correctness of the method as been fully discussed, and

or wi ether they have been derived from less reliable sources.

APPLICABILITY OF COM PUTED VELOCITIES TO ACOUSTIC SOUNDING

During the cruise of the Guide depths were determined at 150ositions by the sonic depth finder alone, using computed velocities.

gome of these determinations were in the vicinity of previous wiresoundings obtained by various Coast Survey vessels and the agree-ment was found to be very satisfactory. This brings up the importantquestion as to whether satisfactory soundin s can be made with the

control afforded by wire measurements and determinrttions of tem-perature and salinity. I n this case it would be necessary to obtainthe adopted tern eratures and salinities from the best available pub-lished values. #hem are found in various publications.R

Such a proceduro will give results much nearer the truth than theadoption of a single value of the velocity of sound for all conditions.

It would obviously be of advantage to have tables ex ressing

out that such tables can not be of universal application, but it is

probable that they can be prepared for regions of considerableextent provided that the physical conditions of tHe sea water arkapproxmately the same throughout the region.

sonic depth finder alone, using computed ve ocities, but without the

velocity as a function of depth alone. It has been clearly E rought

“A study of the saltrdty of the surfsoe water inthe North PacIBo Oceanandin the adjacent incloaeci

“bas spezh&e Oewlcht des M e 8 r w ~m NordLt Pacieschen O w n in Zusammenhange mitTemperaturund StrUrnungsewthden,” by Adolph Wadenkohl, Dr. A. Petermann’sQeogr. Mitteilmgen

” by A. Q. Clark, Bmithsonian MiscalleneousCollections, vol. (10, No. 13, Deo. 4, 1912.

-1697. Heft XII.“Expl&atb-d the United States Coast and Geodetic Survey steamer Barhe in the western AtlantiFI

January-Mar& 1a4 under the direction of th e United States Bureau of Fisheries,” “Oceanoby Henry B. Blgelow, App. V to the Report of the U. 8.Commission of Fisheries for 1916. #&au of

hy.

F?$xria Dooument No. 833 1917.The emperaturea s d o ravlties, and aelinftles of the Weddell Sea and of the North and South

Atlantic Ocean I’ b kr. 8. Bruce,Andrew King, and D. W . Wilton, Transactions ofthe Royal 8ooietyof EdInbuwh. h l ,T . Part T. n 71. 1l)lClfi.

G p apMsaher hastalt, heraw bpol b Prof.’Dr.A . 8upm 45 Band 1888 Ootha Justus Perthes



26 U. 8. C O A S T A N D G E O D E T I C SURVEY

Ins ection of Table 12 shows that even under the best conditions '\. -.it is Bifficult to obtain consistently accurate results. Unless wire 1-r

a salinity range of 5.5-& (31 to 36.w a deptr ange from 185 to <%\

measurements are made and physical conditions determined there 3is no way of knowing how accurate the results are. If expeditionsare to continue the practice of sounding by acoustic methods alone, -it is important that there should be further oceanographic work .;similar to that of the Gruide. This vessel during a cruise of 6,500 ~.miles encountered a temperature range of 28 de ees (Oo to 28' C.),

4,617 fathoms, and used computed veiocities ranging from 810 to :.841 fathoms/sec. While future expeditions can scarcely expect to ).

have a wider range they can do much to provide control for acoustic c\r

sounding by detewaining physical conditions and making velocitymeasurements on all the oceans, and especially by fixing more accu- 4rately the places where physical conditions change.

\

U141,488

8141,489

8161,491

8161,402

8171,494

8181,496

8191,497

81781881982082082a823

8ao821

822823824

826

826

823

8%

TABLE3

8161,492

R101,493

8171,496

8181,496

8191,498

am1,488

R211,Wl

am8218228238238%825

822828

825828827

8 2 6 8 3 8

828

828an828

8

an

[Velocityof sound in sea water in fathoms per second. For the surfaco, velocities are also given in meters

aOO.....-.

I

313233

35as37

a4

8urrace ---_.-

and I 31100

500______.132aa34368837

M o _ _ _ _ _ _ 31

aa34aa

Temperature (degrees centigrade)

0

_ _

7801,445

7911,448

7921,448

7821,449

7931,450

793

1,451

7941,452

7Q794795786798797798

79079779878879p800801

801

801soa803

2

795

1,453

7951,454

7961,465

7961,458

7971,458

7981,459

7991,461

79a799

802802

801

803803804804806

805

806807807

wa

4

7981,459

7991,461

8001,462

8001,463

8011,466

802

rn1,488

8028038038048058wi808

804806808807808BOB810

BOB

BOB810811

8021,466

803I 467

8041,488

8041,471

805I 472

m1,473

807I 476

m808807SOB808809810

808808810810812813818

813

814814815

8

-806

1,474

8061,474

8071.476

8081,477

8081,478

BOB1,480

8101,482

808810811812813814814

813814814816816817818

817

810819ai8

10

8111,482

8111,663

8121,686

8131,488

8141,489

8161,480

8151,491

814815816817818819820

8178188198198208al823

821

82282.8824

10

8191,498

8201,499

8211 , 601

8211 m

8221,604

8231,606

8251,607

8238248258%828827sal

827821828828830831832

830

S1

a33saa

18

82L1,

8231.506

8241 , m

8261,ws

8261,510

8261,611

R271,513

827827828828830831

839830831832832833834

g)a

a835836

839

'20

-.-

U2.6

1,WB

82-54 508

8261,611

8271,613

8281,514

8281,516

RW1,618

8

g2Q828830831833833

832aaaa84836838837

836

886837888

aaa

828l 616

8291,518 . \



VELOCITY O F SOUND IN SEA WATER 27

_-

Depth(fathoms)

4 6

TABLE3-Continued

Temperature I Temperature

. .._____. . .__

3,700

- - _ _ _ _ _

- - _ _ _ _ _. _ _ _ _ _ _ _

.-.....

3,900-._.___- . _ _ _ _ __ ~ _ _ _ _ _4,100

.-. _ _ _ _ _

. - ._____- > _ _ _ _ _

.- ._____

.-._____4,300

. I _ _ _ _ _

.- _ _ _ _ _

-

0

803804805805808

an7aG9

806807808809809810R11

808

HI0811812

814814

813814815R18818817817

818817818819820821822

n13

I

852 854854 856855 858

855 857858 858

856 856866 857a57 858857 859858 880

E60 881880 861861 862861 863862 883

863 883883 889868 864864 866

864 866

2

808808SO9810811812813

811812813814814815818

814

814816818817818R18

817RI8819820821822823

820821822823824826826

-.

8588.58858859860

859860861862862

....-..-.. 864 868 888

_ _ _ .--....66 867 8604, ,XKl 886 867 870

_ _ _ . _ _ _ _ _ _68 867 870~ _ _ _ _ _ 867 868 871

__._._..__89 871 873_ _ _ _ _ _ _ _ _ _ 889 872 8744,700 870 872 875

_ _ _ _ --.... 871 873 875_ _ _ _ _ _ _ _ _ _ 872 873 876

-2

843

844R4.5846

84884884985085 1

8518528538548%

853854854855856

n44

- - O

827 31 821828 32 822829 33 823830 34 824831 35 825832 36 825833 37 826

-...- SI 823..... 32 824_ _ _ _ _ 33 825_..._4 825..... 35 828___..6 827_ _ _ _ _ 37 827

....- 31 828

-.... 32 829..... 33 828

._.__8 832_ _ _ _ _ 37 832

.--.. 31 830___..2 831___._3 831..-.- 34 832_ _ _ _ _ 35 833_..__8 834_ _ _ _ _ 37 836

_.._.1 833___._2 834____.3 835.____4 838

____.6 837-__.-7 838

_..__4 a30..... 35 si

_ _ _ _ _ 3s a36

-

1

aa825825828827827828

R25826827827828828828

830

$3 1832832833834834

833833834834835838837

8368378388383 8

839841

-.

-

2

-

825827827828829829830

827828829830831&?1832

832

x33

R35838837837

835836838837838839839

$18839840

840841R42843

a34

-

. _I___

826827828829830831831

828829830831832833833

833

834835R36K37$3 8838

R38837838838839839840

839840841

842843843844

1,900

2. 100

2, 3 w

2 m

2,700

--- 1



vessel for the reduction o f Fehling’s solution in a

hot water bath. The handling o f ordinary contain-

em while hot during filtration is dif6cult and m e w

tain. Comfortable and safemanipulation of the fl astr

by the ring “handle” is possible almost immediately

after removal from tbe bath, if the flask is set into

cold water, or held u d e r the tap for a few seconds.

Rinsing witb hot water is Mxomplished with equal

ease and safety. Nearly six hundred sugar deter-

minations have been *an without a single loss whenthis special “ringed &rak” was used.

C H A ~ L E ~.R o a ~ a sDEPUTXMTOF W A H Y ,

COWMbo AoWtXEATXUL & W E ,

FapT COLLINB, C%QEADo

SPECIAL ARTICLES

CORRECT VELOCITIES FOR ECHO SOUND-

ING IN THE PACIFIC OCEAN

SPECIALublication No. 108, United States Coast

and Geodetic Survey, “Velocity of Sound in SeaWater? gives tablea from which may be derived, by

velocity of sound to use in echo sounding, provided

that the temperature and salinity of the water are

known.If we know the average 8 M d conditions of tem-

perature and salinity for any ocean for all depths,

tables can be prepad which indicate regions

throughout which the same velocities can be used for

given depths without introducing material error. De-termination of the extent of such regions and the

velocities to be used in each is the purpose of t h i s

paper. The resdts show that the information can

be given in a simple and easily used table for theentire Pacific Ocean.Informationas to mean annual temperature at the

surfam and at v r r ious depths was obtained from the

publication %e Warme Verteilung in den Tiefen

des Stilien Ozeans” by Gerhardt Schott and Fritz

Schu. The information was amplified from the Re-port of the Scientific Results of the Challenger Ex-pedition, Physics and Chemistry, Vol. 1. Information

regarding salinity was obtained from an atlas ofthirty-one maps published by the Deutsche Seewarte

in 1896 and from the Challenger report just men-

tioned.

For convenience, a map of the North Pacific waa

selected which gave the outlines of the Innd and

tion the average

to use, the same

Seasonal changes of temperature were neglected, aa

these d e c t only the two upper layers and the secondlayer but Slightly. While the variation of tempera-

ture at the surface during the B B B S O ~ s cons

in the temperate mnes, the average tem

the upper Iayer does not vary much.With the temperature and salinity fixed for each

layer, the proper velocity fo r any desired depth was

obtained ftom the tables of Special Publication No.108, applying the adiabatic correction. The veloci-

ties were tabulated for 600 fathoms, l,zoO, etc., to

5,400 fathoms, the greatest depth known.

The form of Wle adopted as most convenient was

not a velocity t&e, but a percentage convetion table.

In practically all mho sounding now being carr iedon, all soundings re computed for a standard velocity

and all that is needed is the correction to apply for

the proper velocity. The percentage of correction tobe applied is equal to the proper velocity divided by

the standard velocity, minus one. Thus,if standardvelocity is 800 fathoms per sectond and proper veloc-

ity is 824 fathoms per second, the percentage o f cor-

rection is 3.0. The United S t a b Navy and theCoaat and Qsodetio Survey have adopted the above



6% SCZENCE [VOL.LxIv No. 1669

named standard velocity of 800 fathoms (4,800 feet)

per second. So long es the standard velocity is less

than any adopted proper velocity, the correction is

additive.

The percentages of correction were compiled on a

similar map to that used fo r temperature and salinity.The next, operation was to determine the extent of

the region for which the same table might be used

Inspeetion of the map showed tbat for aU inter-

there was little departure from the mean value for5 5 ~ - 1 . - - 0 * 3 lm 3 *o 2'6 3'2 4.0 4'6 5'2

50-40 _____.6 1.0 1.5 2.0 2.6 3.3 4.0 4.6 5.2

35 ....."._13 1.4 1.7 2.2 2.8 3.4 4.1 4.8 5.3he entire region. Mean percentages of correction

were adopted for each layer and the rule was adopted 300 N400 2.0 1.7 2.0 2.5 3.0 3.6 4.2 4.9 5.4

that in general the range of the comted sounding 450 S _......._.._.3 1.4 1.7 2.2 2.8 3.4 4.1 4.8 5.3

should not exceed five fathoms on either side of the 50 .... ....--...... 0.6 1.0 1.5 2.0 2.6 3.3 4.0 4.6 5.2

mean. Fur the r inspection showed that for all inter- 55 ._. _.._.3 0.5 1.1 1.7 2.3 3.0 3.7 4.3 4.9

sections on parallels 40 and 50" N. a seeond table 60 . . -0.0 0.1 0.7 1.5 2.1 2.7 3.5 4.1 4.7

would suace. A still dser en t table was found necea-

sary for the north part of Bering Sea, deep portion For the benefit of those who wish to use metersapproximately in Lat. 60 N. These three tables and a different standard value, Table 6 has been pre-

with interpolation between them cover the entire North pared, giving the computed velocities in fathoms andPacific except the adjacent seas on the west side and meters corresponding to the percentage corrections in

the shoal portion of Bering Sea. Tables 1 o 4.

The area of the South Pacific was then examined,

Table givea 5.2. Correction is 270 fathoms and cor-

rect sounding 5,470.

TABLE 5

PERCENTAGESF CORRECTIONO BE h p p mm TO ECHOSOUNDINGS~ I_

Depth in fathoms0 0 0 0 0 0 0

Lat- 0 ~ 0 0 0 0 0 0without introducing appreciable emr. 8 z- 2- ; 2- 4 2- $- z-=tions from and including 3 0 N. to the equator 60 N ...,_...I..-. 0.0 0.5 1.1 1.9 2.5 3 8 3.9 4.5 5.1

.

_-

TABLE 6

S. The tables follow.

___ . _ _ _________I _____

--Table 1 Table 2 Table 3 Table 4

Fathoms 60" N 50" 8 40" S 60 s50-40" N, 30" N to

600 .....

1,200.....

1,800. ...

2,100 .....

3,000 .....

3,600 .....

4.200 .....

4,800__.__.

5,400 .....

0.0

0.5

1.1

1.9

2.5

3.2

3.9

4.5

5.1

0.6

1.0

1.5

2.0

2.6

3.3

4.0

4.6

5.2

2.0

1.7

2.0

2.5

3.0

3.6

4.2

4.9

5.4

0.0

0.1

0.7

1.5

2.1

2.7

3.5

4.1

4.7

In order that interpolation may be easy, and only

one table be needed, the information has been rear-

ranged in Table 5.

Examples of w e of table: At 35 N., 140 W. an

echo sounding of 2,923 fathoms was obtained using

600 1,097 799 1,461

1,200 2,194 804 1,471

1,800 3,292 809 1,479

2,400 4,389 815 1,491

3,000 5,486 820 1,499

3,600 6,584 826 1,511

4,200 7,681 831 1,519

4,800 8,778 836 1,529

5,100 9,875 841 1,537

805 1,472 815 1,492 799 1,461

808 1,478 813 1,488 801 1,465

812 1,485 815 1,492 806 1,474

815 1,492 820 1,500 812 1,485

821 1,501 824 1,507 817 1,494

826 1,511 828 1,515 822 1,504

833 1,522 833 1,524 828 1,515

837 1,530 839 1,534 833 l p2 2

842 1,539 844 1,542 838 1,532

Salinit ies w e d : 34 ass used from 30" N. to 40 S.,

except 33 at 20 N. rom 160 to 130 W., nd at10 N. from 140 to 120 W. For all other areas,

salinity 33 was adopted. Error introduced by this

practice is small.To show that the m r nvolved in using the tablea

for the large regiom adopted is not great, Table I

was prepared. The equatorial region is selected as

it has a greater range than the others. The reation

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