SP-58 Supplement to H.O. Pub. 614

SPECIAL PUBLICATION

TABLES OF SOUND SPEED IN SEA WATER

Oceanographic Analysis Division | Marine Sciences Department

AUGUST 1962

OC e 228.8 U.S. NAVAL OCEANOGRAPHIC OFFICE 3S WASHINGTON, D.C. ek.

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SP-58 Supplement to H.O. Pub. 614

SPECIAL PUBLICATION

TABLES OF SOUND SPEED IN SEA WATER

Oceanographic Analysis Division Marine Sciences Department

AUGUST 1962

-8 U.S. NAVAL OCEANOGRAPHIC OFFICE WASHINGTON, D.C.

Mey CO

ABST RAG.

Sound speed tables have been computed from W.D. Wilson’s equation (Journal of the Acoustical Society of America, Vol. 32, No. 10, October 1960). The tables cover temperature, salinity, and pressure ranges from —2.5° to 34.9°C, 0 to 41.9°/,., and 1.03 kg/cm2 to 1260 kg/cm2. A pressure-depth relationship is established whereby the tables may be entered with either depth in meters or pressure in kilograms per square centimeter.

A sound speed nomogram developed from values in the table is

_ presented for purposes of rapid calculation.

FOREWORD

It has become increasingly evident that the accuracy of the Kuwahara equation for computing sound speeds in sea water is not sufficient for present day needs. In situ measurements of sound speed in sea water indicate that at some depths the speed calculated by the Kuwahara equation is 3 to 4 meters per second too slow. To remedy this inade- quacy a conference of interested parties, heldatthe Hydrographic Office in May 1961, concluded that the sound speed equation of Kuwahara should be replaced by the empirical equation developed at the Naval Ordnance Laboratory by Wayne D,. Wilson. Since that time this Office has been recomputing available sound speed data onthe basis of Wilson's equation, The tables presented here have beendevelopedfrom the Wilson equation to facilitate hand computation of sound speeds from tempera- ture and salinity data.

Although continuing research may yield more accurate equations, these tables are individually accurate to the nearest 0.1 meter per second and the total error in any computation within the normal range of oceanographic variables should be less than 0.3 meter per second.

Rear Admiral, U. S. Navy Commander

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CONTENTS

Page Part I, Discussion AS A Wiel DLS Bie, Mise cle ots Najves oe aintet fects 56 0 6) Opec ay ciated cars 2 B_sound speed) Nomograrns sg ve eile fe =) eels i ies 3 RUGS 5 6 6004 ¢ 9906000005 5 Rep Eseiamee 4 Part II, Sound Speed Tables Examples of Use Of Tables c.h jes 6 <i ter = tei (esi te aller 7 Table 1. Sound Speed, V, (1449.1 m/sec), corrected for changes in Pressure (kg/cm4), Vopr cece 8 Table 2, Sound Speed, V, (1449.1 m/sec), corrected for changes in Depth (meters), pressures derived assuming 35%, 0°C), Vp Ste hes - 9 Table 3. Correction to Sound Speed, V, (1449.1 m/sec), for changes in Latitude-Depth, Vy .......- ) Table 4. Correction to Sound Speed, V, (1449.1 m/sec), for changes in, Salinity (%e); Veo 2 5 - =: 2 © = 10 Table 5. Correction to Sound Speed, V, (1449.1 m/sec), for changes in Temperature (°C), Vz. .... ~ 20 Table 6. Correction to Sound Speed, V, (1449.1 m/sec), for simultaneous changes in Salinity, Temperature, and Pressure, Vstp AGO 10h Go. co 28 Table 7. Sound Speed Conversion - Meters/Second COSMECENOECONGd Santis se we «hs 5. a aha 47 FIGURE sound Speed INomogram 2.9. i. 656. s+ s « Hap ultée Oh Seon O- Chee 5

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PART I. DISCUSSION INTRODUCTION

The sound speed tables presented in H. O. Pub. No. 614), after Kuwahara2, present sound speed as a function of temperature, salinity, pressure, and latitude. His tables were developed from mathematical analysis of specific volumes rather than empirical sound speed meas- urements, Actual measurements of sound speed in sea water indicate Kuwahara's speeds are approximately 4 meters per second too slow.

With the development of progressively more complex weapons systems it became necessary to have more accurate sound speed information. As a result of this recognized need, a conference? of interested parties was held at the Hydrographic Office in May 196l for the purpose of resolving whether or not a new equation for the calculation of sound speed should be adopted, It was generally agreed that Wilson's equation4 (shown below) should be adopted for Naval applications. This decision was reached with the knowledge that research presently being conducted may yield equations which are somewhat more accurate.

V m/sec. = 1449.14 +Vp +V +Vy +Vetp

Where: Vp") ='160272 > -10=" PhO268"x 107° P24'sH216 « 1059.P8 — 3.3603 x 10-12 p4 V, = 1.39799 (S—35) + 1.69202 x 10-3 (S—35)? od ss =e ahh og tg 24 V4 572, Aaba2 se 10e- i = 2 6045. .q 10 1° + 729851 sc 10 ° 1 Veg = S35) (244 100s 7 7711 XO’ T+ 7.7016,% 10, P

— 1.2943 x 10-7 P? +3.1580 x 10-8 PT+1.5790 x 10-2 PT?) P(2{1e607 10 2 -P a7ae12' 10-8 1 4.4.5 283 a0 BT) 4+ P*(—2.5204 x 10-” T +1.8563 x 10-9 T*) +P°(—1.9646 x Oj. TD:

The tables presented herein are computed from the above equation and should be used in lieu of those in H. O. Pub. No. 614, 1951 edition.

A. TABLES

According to Wilson, the mean standard deviation of the error between his equation and measured speeds over the range of variables (temperature -4°C. to 30°C., salinity 0% to 37%, pressure 1 to 1,000 kg/cm“) is 0.30 m/sec. With temperature as the dependent variable, the maximum standard deviation is 0.74 m/sec at salinity 0.00% and surface pressure, and the minimum standard deviation is 0.08 m/sec at 36.55% salinity and 420 kg/cm% pressure.

The accuracy of the equation at values higher than those shown above has had some limited evaluation by Wilson. The difference between the measured and computed velocities at some sample extreme values are:

Temperature Salinity Pressure Difference 30 513°C. 42.15% Surface 0.13m/sec 39.85 34.99 Surface 0.06 39.85 42.15 Surface 0.85 39.85 42.15 381 kg/cm2 0.65 20.11 34.99 1,150 kg/cm2 0.21

Tables 1 through 6 were developed using the Wilson equation programmed for the IBM 7070 computer. The speeds were computed to the nearest 0.01 m/sec and for convenience were rounded to the nearest 0.1 m/sec for presentation.

Although Wilson's equation is entered with pressure as a variable, by assuming a uniform water column of 0°C. temperature and 35% salinity, a depth-pressure relationship is established; therefore, the tables are presented so that they canbe entered with depth or pressure. A convenient depth interval from 1 meter to 11,500 meters in the depth (pressure) correction, Table 2, is used in order to minimize interpo- lation; however, if it is desired to use in situ pressure to obtain the pressure correction, Table 1 is to be used, Table 3, converted from the original Kuwahara table, is to be applied to correct the sound speeds for variations in gravity with latitude and depth. Tables 4 and 5 may be entered with salinity to the nearest 0.01% and temperature to the nearest 0.01°C., thus eliminating interpolation. The simultaneous cor- rections for temperature, salinity, and depth (pressure) are presented

in Table 6 at standard oceanographic station depths assuming the above pressure-depth relationship. Again, if it is desired to use in situ pressures instead of depth to make the simultaneous correction, the pressure value is presented at each depth. Some interpolation may be required in these tables; however, for depths less than 3,000 meters, the difference between tables for identical temperature and salinity values is usually less than 0.2m/sec. Table 7 is presented for ease of conversion of meters/second to feet/second if desired.

The assumption that the sound speed at a particular depthisa weak function of the temperature and salinity structure above that depth is supported by NEL”. Inaddition, direct comparisons were made at the Hydrographic Office between the speeds presented here and those computed by using the actual pressures. Sound speeds were computed at standard depths, in one case using computed in situ pressures and in the other using computed pressures resulting from an assumed water column at 0°C. temperature and 35% salinity. In the Gulf of Alaska and the Philippine Trench, this method indicated differences of less than 0.1 m/sec or less above 4,000 meters depth. In the Philippine Trench at 8,000 meters, the difference was less than 0.2 m/sec. These computations indicated that the change in pressure attributed to differences in temperature and salinity from 0°C. and 35% have only a minor effect on the sound speed at any depth.

B. SOUND SPEED NOMOGRAM

The sound speed nomogram and structure form was drawn from the values of sound speed giveninthe tables. As in the tables, the pressure- depth relationship is based on a 0°C. and 35% water column, The main body of the nomogram presents sound speed as a function of tempera- ture and depth with salinity held at 35%. Values are plotted to the nearest tenth of a meter per second and can probably be read to the nearest 0.5 m/sec. An inset is provided to correct for salinities other than 35%; for salinities less than 35% the correction is negative, for salinities greater than 35% the correction is positive. For the normal range of salinity, temperature, and depth for oceanic and nearshore waters the salinity correction is accurate to the nearest 0.1 m/sec. For anomalous oceanographic conditions but within the range of variables covered by the tables, the error may increase to 0,3 to 0.4m/sec; i.e., for fresh water at 2,000 meters depth or 32% (or 38%o) salinity at 11,000 meters.

Sound speeds from the nomogram can be determined to within one meter per second; if greater accuracy is desired, the tables should be used,

The temperature structure at an oceanographic station may be plotted on the nomogram to determine an approximate sound speed structure. Large errors in absolute speed will occur in nearshore areas or enclosed seas where the salinity may deviate radically from 35%0; the general shape of the speed structure may be easily determined for the normal oceanographic environment,

REFERENCES

1. U. S. HYDROGRAPHIC OFFICE. Processing oceanographic data,by E. C. LaFond, H. O. Pub. No. 614. 114p., 1951.

2. KUWAHARA, S. Velocity of sound in sea water and calculation of the velocity for use in sonic sounding. Hydrographic Review, vol. 16, no, 2, pp. 123-140, 1939.

3. U. S. HYDROGRAPHIC OFFICE. Summary of the conference on sound speed equations. Enclosure to HO ltr ser 9233 of 24 Oct. 1961.

4, WILSON, W. D. Equation for the speed of sound in sea water, Journal of the Acoustical Society of America, vol. 32, no. 10, pp. 1357, Oct. 1960.

5. PEDERSEN, M. A. NEL sound velocity program. Informal draft enclosure to NEL ltr to USNHO SF001 03 01 (NEL L15) 2233-13 of 10 May 1961.

DEPTH (THOUSANDS OF FEET)

SP 58 4700 4800 4900 5000 5100 5200 FEET/SEC 1430 1440 1450 1460 1470 1480 1490 1500 1510 1520 1530 1540 1550 1560 1570 1580 1590 1600 METERS /SEC 0 ;, 100 0.5 as at aoe =a 40° 45° 50° 55% 60" 65° 70' 75% 80% 85'y TEMPERATURE (°F) 200 | al i 1.0 300 T | 400 nes 0°! > 4 6° 8° 10° 12° 14° 16° 18° 20°)-KY-22°-\ 24°-h+ 26° 28°] 30°} TEMPERATURE (°C) 1.5 ! 64 300 2 - 3 1000 | 4 BB | | : | 4 | T ! 6 | Ty | t T . 2000 7 | Tt | | T 8 if it it i ; | | = h im @ | 1 wn i 1 i-4 | w 9 | + t Ww 10. - i - i 3000 = t col & 11 SALINITY CORRECTION t t Le 3 ‘a SALINITY (°/, ,) a Fa) } an a 13 30 5 | LI 4000 t = 14 t 40 ie om ta T 15 H ~ 5 Eo 16 = | i H | a It i | £ 50 - {31 $3345] 37439f 41 10 O ‘ C 5000 179] wo Z LAS 5 ots 10 155 20 25++11 30} 32}34136}38}40 2 i 18K] = pie & 60 a if rH 1) Fi ; t 19 = : Lue i 4 + I a - t i 6000 20 20F} 70 } : t t t T T 21 ea | 25 CI i 22 80 [ | | [ i 7000 23 —50 —45 —40 —35 —30 —25 —20 —I5 —10 —5 0 5 Tom ~ T METERS /SEC + 24 ol or ro ott ~150—140 -130 -120 -110 -100 -90 —80 -70 -60 -50 -40 -30 -20 -10 fo) 10 20 30 25 FEET/SEC SOUND SPEED CORRECTION FOR SAUNITY it }_} 26 T

SOUND SPEED NOMOGRAM (BASED ON WILSON’S EQUATION)

HO.N29167@2-c35

FEET/SEC

: 8000 1430 1440 1450 1460 1470 1480 1490 1500 1510 1520 1530 1540 1550 1560 1570 1580 1590 1600 METERS/SEC 4700 4800 4900 5000 5100 5200

5

DEPTH (THOUSANDS OF FEET)

SOUND SPEED NOMOGRAM (BASED ON WILSON’S EQUATION)

SP 58 4700 4900 5000 5100 5200 FEET/SEC 1430 1490 1500 1530 1540 1550 1560 1600 METERS/SEC i) | 100 0.5 +-|50° 55 70 804 85%¢ TEMPERATURE ("F) 200 1.0 300 T 400 15 105 12° 18° 20° aay 24° 26° 28° 4; 30°} TEMPERATURE (°C) 64 500 2 =: sh 3 if 1000 4 5 I l I 6 + 2000 i, if if if T | 1 | 8 t t an T T a T 9 ; w w 10 3000 = 7 oh a = * SALINITY CORRECTION f a 196; qf S 12 25 October ) y) SALINITY eZ. ) ~ : : uw ie c | 4000 14 ri i 15 16 L h f —+— o - 5000 17 = iz t = It 18 5 2 < é | [ A T I 19 2 i | j = I 20 zs , 6000 4 21 | 22 I 23 7000 25. —20 24 METERS /SEC 25 -160 —150—140 —130-120-110-100 ~90 -80 ~—70 -60 -50 -40 -30 -20 -10 © 10 20 30 ~ FEET/SECOND | SOUND SPEED CORRECTION FOR SAUNITY 1 26 ; I 8000 1430 1440 1450 1460 1470 1480 1490 1500 1510 1520 1530 1540 1550 1560 1570 1580 1590 1600 METERS/SEC 4700 4800 4900 5000 5100 5200 FEET/SEC

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SALINITY, TEMPERATURE, AND PRESSURE, Vetp

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TABLE 6, CORRECTION TO SOUND SPEED, V, (1449.1 m/sec), FOR SIMULTANEOUS CHANGES IN

9.9 9.7 6.5 6.3

9-5 |10.1

9.7 |10.3 |10.9 9.5 |10.1/10.7 9.3 | 9.9 /10.5 9.2) 9-7 (10.3

9.3

9.2

6.1

5.9

5.3

Sa2 || 55

6.5 | 6.9

8 6 el

8.6

7.0

5.7

5.6

5.2

8.9

Ail

5-9 | 6.3

e

8.2] 8.8

8.8

8.6

8.1

Te)

6.6

6.4

5-4

5.2

5.1

4.9 4.4] 4.7] 5.0 4.2), 4.5 14.8

9.1 9.0 7.9 | 8.5 8.3 8.2 8.0 7.9 | 8.4 | 9.0 te 7.5 6.6 el 6.0 5.8 5.7 sry) S108) 5.2 5.0 4.9 4.7 4.6

t.7 726 To4 1-3 7.1 7.0 6.1 Seif 5-4 5.3 SI 1 4.8 4.5 ue 4.2 4.1 3.9

0

otf 6.3 6-9

7.8| 8.5 T.7| 8.3

6.7 6.6 6.5 Bet 5.3 5-0 4.4 | 4.8 4.3 | 4.7 4.6 44 4.2 4.0 3.9

otf |) hoe! 6.2 6.0 5.9 4.6 Toe | Sie!

6.5 5.6 5.5 4.0 Sid, 3-8 | 4.2 3.7 364 3.3 | 3-6

5.9 5.8 See 5.1 4.9 3.5 3.4 3.3 3.0 2.9

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369 | 4.5 3-8 | 4.4

4.0 | 4.6 2.9 2.8 2.7 2.7 2-2 | 2.6 2.5 2.4 2.4 Des

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-0.8/-0.4 -0.8 -0.8 -0.8 -0.7 =Ol57 -0.7 -0.7 -0.6 -0.6

28

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-0.5/-0.5/-0.6

-0.4 -0.6/-0.7

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1.4

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1 1 1 | 1 0.7) 0-9 0. 0. Os 0.8 0.7 0.6 0.5 0. 0. O. 0.4 Ons 0.2 0.2 (hr 0.1 0.0

0.6 0.5 0.4 O.4 0.3 0.3 0.2 0.2 0.2 0.1 0 0.1 0.0 -0 -0 -0

0.5 O4 0.4 0.3 Oss 0.2 0.2 0.2 0.0 0.0

0.1 0.1

1 1 1

2 2 onl

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0 0 0.1 0 0 0 0.1 0.1 0.1

-0.0 -0.0 0. 0. -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0} 0.1

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0

0

0

-0.6/-0.3 -0.6|-0.3/-0.0 -0.5 -0.3 Si- Si- -0.5/-0.2 -0.4/-0.2 -0.4)-0.2 -0.3/-0.2 -0.3/-0.2 -0.3/-0.1 -0.3/-0.1 . 0 ° 0 -0.2/-0.1 -0.2/-0.1 -0.2 -0.1 =O |—Olen -0.1/-0.1 -0.1 -0.1/-0.0 -0.0/-0.0 -0.0]-0.0 0.0] 0.0

22.0 22.5 23.0 23

24

24

25.0 26.5 27.0 27.5 28.0 28.5 29.0 29.5 30

30.5 31.0 31.5 32.0 32.5 33.0 33-5 34.0 3425 35.0 35.5

29

-0.1 -0.2

0.0}-0.0/-0.1 -0.2

0.0 0.1

0.1

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=0.2

-0.1/-0.1

0.0

0.1

37.5

O.1] 0.1

38.0

0.0/-0.1/-0.2]-9.2)-0.3|-0.4/-0.5/-0.6)-0.6

0.1

0.2

38.5

39.0

-0.7/-0.8

-0.2|-0.3/-0.4|-0.5|-0.6 -0.2}-0.3})-0.5|/-0.6/-0.7/-0.8|/-0.9

0.0/-0.1

0.2} 0.1

39.5

0.0/-0.1

0.1

0.2 0.2 0.3 0.3

40.0

40.5 41.0

-0.3}-0.4|-0.5|-0.7

-0.1

0.0

0.1

41.5 42.0

0.0/-0.2|-0.3|-0.5/-0.6|-0.8|]-0.9]|-1.1

0.2

0.3

TABLE 6. CORRECTION TO SOUND SPEED, V,, (1449.1 m/sec), FOR SIMULTANEOUS CHANGES IN

500 METERS (52.47 kg/cm?)

SALINITY, TEMPERATURE, AND PRESSURE, Vetp - Continued

Se eee EEE:

36

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2-3) 2.4 ASW AG "2 Ve Tiie2e0 1.7) 1.8 1.0 0.8] 0.8 0.6 0.6 0.0; 0.0 -0.2/-0.2 -0.4)-0.4 -0.6)-0.6 -0.7 -0.8 -1.0 SU iS Un7 -1.9/-2.0 Die -2.4 6

-2.1 —-2.3

1.9 1.7 1.6 1.4 0.7 0.5

2.1 -1.3/-1.3/-1.4

-0.9|-0.9 —1.2/-1.3]-1.3/-1.4 |-1.4{-1.5/-1.6

-0.0 =Olez -O0.4 -0.6 —-0.7 Soil -1.8 -2.0 Oe -2.3 =.

0.8] 0.9 0.6 0.4 0.3 0.1

1.6 -0.1

1.9 1.8 1.4 1.3 0.9

2.) —1.6/-1.6/-1.7/-1.8

-0.2 -0.4 -0.6 -0.7 -0.9 =1.1 -1.2 aie U5 -2.1 2.2

1.9 1.8 1.6 1.5 1.3 1.2 1.0 0.8 0.7 0.5 O.4 0.2 0.1 (05.1) -0.2 -0.4 -0.6 -0.7 -0.9 -1.0 —1.2 Sos) -1.6 —ynits! -1.9 -2.1

1.9 1.8 1.5 1.2 1.0 0.9 0.8 0.6 0.5 0.3 0.2 0.0 -0.1 -O0.4 —0.7 -1.0 -1.1 -1.5 -2.0

1.3 1.1 0.9 0.8 (O}e57/ 0.5 0.4 0.3 0.1 0.0

-0.1 =0%35)|—0.3

-0.4 -0.7 -0.8/-0.8 -1.1 -1.3)/-1.4 —-1.5 -1.6/-1.7 -1.8

Wave 1.0 0.8 0.7 0.5 O.4 One 0.1

-0.0

0.6 =(0/55)\—O0)e 5) Oe

SVWots|| SGT eats}

-0.1] -0.3 -O.4 -0.6 (0)5 U/ -0.9|/-0.9 -1.0 Vell =e -1.4 So) SVots

1.4 1.1 0.9 0.7 0.6 0.5 0.4 0.3 0.2 0.1 -0.0 -0.1 -0.3 -0.4 -0.5 -0.6 -0.7 -0.8 -0.9 -1.0 -1.1 Nia -1.4 05) -1.6

0.7

0.4

0.2

0.1 -0.0 -0.1 -0.2 -0.3 -O.4 -0.5 -0.6 -0.7 -0.8 -0.9 -1.0 -1.1 =U =ileis -1.4

0.6

0.0 {5 -0.1 -0.2 -0.3 -0.4 -0.5 -0.6 -0.7 -0.8 -0.8 -0.9 -1.0 -1.1 -1.2 =a!

0.6

0.0 -0.1 -0.2 -0.3 -O.4 -0.4 -0.5 -0.6 WSU -0.8 -0.8 -0.9 —-1.0 -1.1 -1.1

-0.1

0.4] O25 -0.0; 0.0 -0.1 -0.1 -0.1/-0.1 -0.2/-0.2 -0.2)/-0.3 -0.3/-0.3 -0.3/-0.4 -0.4/-0.5 -0.4)-0.5 =-0.5 -0.6 -0.6|-0.7 -0.7/-0.8 -0.7/-0.9 -0.8/-0.9

-0.7/-0.8|-1.0

0.5

0.3

0.1

0.0 -0.0 -0.1 -0.1 -0.) -0.2 -0.2 =Os5 -0.3 -0.4 -O0.4 -0.4 -0.5 -0.6 -0.6

0.1 0.4 0.1 0.3 0.1 0.3 O.2] 0.3 0.2) 0.2 O.1} 0.2 O.1} 0.1 0.0] O.1}) 0.1 0.0; 0.0] 0.1 0-0} 0.0; 0.0 -0.0| 0.0} 0.0 -0.0/-0.0}]-0.0 -0.0}-0.0]-0.0 -0.0/-0.1/}-0.1 -0.0}/-0.1/-0.1 -0.0/-0.1/-0.1 -0-1}-0.1}-0.2 -0.1/-0.1}-0.2 -0.1/-0.2]-0.2 -0.1/-0.2/-0.3 -0.1)-0.2]-0.3 -0.1}/-0.2 -0.3 -0.1/-0.2}-0.4/-0.5|/-0.6/-0.7 -0.3)-0.4 -0.1/-0.3})-0.4 -0.1/-0.3)-0.5 —0.2j-0.3|-0.5

-0.0 -0.0} 0.0 -0.0 -0.0 -0.0 -0.0 -0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0

el

(53) 0.2| 0.0/-0.1

0.0} 0.0

-0.3 =Ols2)||\—Olet -0.2|/-0.1 -0.1/-0.1 -0.1}/-0.0 -0.0);-0.0 -0.0/-0.0 -0.0/ -0.0 0.0}; 0.0 0.0; 0.0 0.1} 0.0 0.1 0.2} 0.1 0.2} 0.1 0.2 0.3 0.3} 0.2 0.3 0.3} 0.2 O.4} 0.2 O.4} 0.2] 0.0

28.5 29.0 29.5 32.0 32.5 33.0 33.5 34.0 34.5 35.0 35.5 38.0 38.5 39.0 39.5 40.0 40.5 41.0 41.5 42.0

TABLE 6. CORRECTION TO SOUND SPEED, Nia (1449.1 m/sec), FOR SIMULTANEOUS CHANGES IN

1000 METERS (104.09 kg/cm?)

- Continued

SALINITY, TEMPERATURE, AND PRESSURE, Vetp

ANODWDANODODWOANODWANODWOANCDVWANOD 6 © © 6 10 fo 6 © ie K0)\"0. ie ie, ete ie) te, foe Je) se. te ‘ste. @ 6's 8 ee m~mr ROCCO OCoOoOoOenDnnnamaanrnnrrrwowooowon

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9.9 9.2

20 8.9 ae 7.8 726 7.5 Wares "or 7.0 6.9 5.9 5.8 5-6 5-5 5-3 5.0 4.9 4.7 4.6 4.4

9.6 9.5 8.7 8.6 8.4 8.3 6.7 6.6 604 6.3 6.1 5.2

10.9|11.7/12.6/13.5 8.1

10.7/11.6 |12.4 113 10.6)11.4 {12.2 )13.1

10.4)11.2 |12.1

10.2 9.3|10.1

9.9 9.7 9.6 Deh 9.2 9.0 8.9 8.7 8.6 8.5 8.3 8.2 8.0 7.9 Te? 726 7.5 te3 7.2 7.0 6.9 6.7 6.6 6.5 6.3 6.2 6.0 5.9 5.7 5-6 5.5 5.3 5-2 5.0 4.9 4.7 4.6 4.5 4.3 4.2 4.0 3.9 | 423

9.2 |10.0

9.0 8.9 8.8 8.7 Bed 8.4 8.3 8.1 8.0 Mon? Tel 1.6 7.5 1.3 1.2 6.9 6.8 6.7 6.6 6.4 6.3 6.2 6.0 5.9 5.8 5.6 5.5 5-4 5.2 5.1 5.0 4.8 4.7 4.6 4.5 4.3 3.8 | 4.2 3.9 3.8 3.7 3.5

7.5] 8.4 8.2 8.1 8.9 T29 7.8 T26 7.5 To4 1.3 7.2 7.0 6.9 6.8 6.7 6.6 6.4 6.3 6.2 6.1 6.0 5-8 5.7 5.6 BiG 5) 5.4 5-2 5.1 5.0 4.9 4.8 4.6 4.5 4e4 +e | 4.0

SIGS) |) SiGe) 3.7 SiS) 364

Teh 7.3 1.2 Te.) 7.0 6.9 6.8 6.7 6.4 6.3 602 6.1 6.0 5.9 5.8 5.7 5.6 5.5 5e4 5-2 5.1] 5.0 4.9 4.3 4.7 4.6 4.5 44 4.3 4.2 3.6] 4.0 369 3.8) 4.3 3.6 3.4 Ses Ss 3.1 3 2

6.7 6.6 6.5 6.4 6.3 6.2 6.0 5.9 5-8| 626 5.7 5.6 526 Sve 5.4 5-3 5.2 5.1 5-0 4.9 4.8 4.7 4.6 4.5 4.4 4.3 4.2 ye] 4.0 3.9 3.8 Sieilt 3.5 3.4 Sadi Set 3.2 3.1 3.0 2.9 2.8 2.7

6.1

5-9 5.8 Sole 5.7 5.6 3)0 3) 5-4 5.3 5-2 5.1 5.1 5.0 4.9 4.7 4.6 4.5 4.5 4o4 4.3 4.2 4.) 4.0 3.9 3.8 3.8 3.7 3.6 355 3.4 3.3 Sa2 Sine 3.1 3.0 2-9 2.8 2.7 2-6 2-5 Aka '5} 2.4

5.1 5.1 5.0 4.9 4.8 4.8 4.7 4.6 4.5 Koy Key 4.3 4.2 4.1 4.1 4.0 3-9 3.8 3-8 3.7 3.6 3.5 3-5 3.4 3-3 322 3.2 3.1 3.0 2.9 2.9 2.8 2.7 2.6 2.6 POPS 2-4 2-3 2.3 Dae 2.1 2.0 2.0

) 1.6 1.8 1.7 1.6 1.6

3-6} 4.3 365 | 4.3 3e5| 4e2 3-4 | 4.1 4.1 4.0 4.0 3.9 OW We sinks} Sel | sa8 3.7 3.6 3.6 3605 3.4 3.4 3.3 3.3 3.2 3.1 3. 3.0 2.9 2.9 2.8 2.7 PT 2.6 2.0} 2.4 1.9 | 2.4 Ta? | 2635 1.8 | 2.2 1.8 | 2.2 TaZionh 1.7 | 2.0 1.6 | 2.0 1.6 | 1 1.5 1.4 1.4 3 1.3

3.3 323 3.2 322 3.0 3.0 2-9 PP) 2.8 2-8 2.7 2.7 2.6 2.6 2.5 2.5 2-4 2-3 2.3 262 2-2

2.1 2.1 2

2.8 2.7 2.7 Ziel 2.6 2.6 2.5 2.5 2.5 2-4 2.4 263 2.3 2.2 2-2 2.2 2. 2.1 2.0 2.0 2.0 1.9 1.9 8 1.8 7 1.7 lot 1.6 6 1.5 5 1.5 1.4 1.4 1.3 1.3 1.2 1.2 1.2 ] ] 1.0 1.0

1.9 1.9 1.9 1.8 1.8 1.8 1.8 1.7 1.7 1.7 1.6 1.6

6 1.5 1.5 1.5 1.4 1.4 1.4 1.4 1.3 1.3 1.3 1.2 1.2 1.2

1 1.0 1.0 1.0

2.0 2.0 0.9 0.9 0.9 0.8 0.8 0.8 0.7 0.7

1.3 | 2.0

1.2 1.2 1.2 1.2 1.2 1.2 1.0 1.0 1.0

0) 1.0

0.9 0.9 0.9 0.9 0.9 0.8 0.8 0.8 0.8 0.8 0.7 0.7 0.7 0.7 0.6 0-6 0.6 0.6 0.6 0.5 0.5 0.5 0.5 0.5 0.4

1.1 1.1 1.1

0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2

Ole -0.2 0.2 -0.2 -0.2 -0.2 -0.2 -0.2 -0.2 -0.2 -0.2 -0.2 =Olee -0.2 -0.2 -0.2 -0.2 -0.2 -0.2 -0.2 -0.2 -0.1 -0.1 -0.1 -0.1 -0.1 -0.1 -0.1 =O -0.1 -0.1 -0.1 -0.1 -0.1 -0.1 = iva =Orea -0.1 -0.1

-1.0 -1.0 -0.9 -0.9 -0.9 -0.9 -0.9 -0.9 -0.9 -0.8 -0.8 = Olt -0.7 -0.7 -0.7 -0.7 -0.7 -0.7 -0.6 -0.6 -0.6 -0.6 -0.6 -0.6 -0.5 -0.5 -0.5 =O'5 -0.5 =Oiss -0.4 -0.4 -O0.4 -0.4 -O.4 -O.4 -0.4 -0.3

=lWert Weill -1.7 -1.6 —166 -1.6 =ie5 =—1.5 -1.5 -1.4 =1.3 =11.3 = lies =Ne2 -1.2 Were =le2 =iienl Ee =ilet =61 -1.0 -1.0 -1.0 -1.0 -0.9 -0.9 -0.9 -0.8 -0.8 -0.8 =Oleit =Olsir, =O\.7 =O -0.6 -0.6 -0.6

0.0 0.5 1.0 le 2.0 Ze5 3.0 365 4.0 4.5 6.5 7.0 7.5 8.0 8.5 9.0 9.5 10.0 10.5 11.0 11.5 12.0 12.5 13.0 13.5 14.0 14.5 15.0 15.5 16.5 17.0 iar 18.0 18.5 19.0 19.5 20.0 20.5 21.0 21.5

32

4.8 4.5) 4.8

4.5 4.0 3-8] 4.1 3.6

4.1 3.9 3.8 3.6 3.5 SoS

3.7 3.6 3-5 Ses 3.2

3.4 3013 3.1 3.0 2.9 2.7 2.6 2.5

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Oe KO «725°?

Doe 2.1

2.5 264 eteS

2-4 A250)

2.) 2.0 1.9 1.9 1.8

1.8 1.7 ote 1.6 1.5

1.5 1.5 os! Was)

1.2 1.2 1.0

1.1

1.0 0.9 0.8 0.8

0.7 0.7 0.6 0.6

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24.0

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1.7 1.6 1.5

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0.5| 0.7 0.5| 0.7 0.5) 0.7

0.3 0.3 0.3

0.1 0.1 0.1

-0.1 -0.1 =(lenl

-0.3 -0.2 -0.2 -0.2 —Oia2

-0.4 -O.4

24.5 25.0 25.5

4.0 324 3.2 3.0 2.8 2.6 2-4 2.2 2.0 1.8 1.2 1.0 0.8 0.6 0-5 0.3 0.1 —0.1 -0.5 -0.7 -0.9 -1.1 Ves S58)

3.3 Sle2. 3.0 2.8 2.6 2-4 (2572 2.0 1.8 1.7 1.3 1.1 0.9 0.7 0.5 0.3 0.2 -0.0 -0.2 -0.6 -0.8 -1.0 = 1115 —1.3 55 -1.7|-1.7

-l 226) 2e9 2.7 29) 2-4 2-2 1.8 1.7 1.5 1.3 1.0 0.8 O.4 0.3 0.1 -0.1 -0.3 -0.6 -0.8 =e0 S52 =e = 41.555) Silote

3.0 2.8 2.5 2.3 2-2 2.0 1.7 1.5 1.3 1.2 0.8 0.7 0.3 0.2 -0.2 -0.3 -0.6 -0.8 -1.0 ihe ie sss Soe

2.7 2-23] 2.6 2-3 2.1 1.9 1.8 5 1.3 1.2 1.0 0.9

222 760)

2.9 2.4 0.7 0.6 0.3 0.1 =0.2 -0.4 -0.7 -0.8 -1.0 Sou Nise} -1.4 Saw

2-6 205 1.9 1.8 1.6 1.5 1.3 1.2 1.0 0.9 0.8 0.6 0.5 0.3 0.2 0.0 -0.2 -0.4 -0.7 -0.8 -1.0 —iliett Nis. —1.4

2.4 2-2 2.1 2.0 1.8 1.7 1.6 1.4 1.3 Were. 1.0 0.9 0.8 0.6 0.5 0.4 0.3 0.1 -0.0 —Olef -0.8 -0.9 tou aia = eS) Sas aes

—Oles -0.4

2.0 1.9 1.7 1.6 1.5 1.4 1.1 1.0 0.9 0.8 0.7 0.5 0.4 0.3 0.2 0.1 -0.1 -0.3 -0.4 = O)ent -0.8 -0.9 -1.0 =I" 1 leet -1.4

1.9 1.8 1.7 1.5 1.4 1.3 1.2 1.0 0.9 0.8 0.7 0.6 0.5 0.3 0.2 0.1 0.0 -0.1 -0.3 -O0-4 -0.7 -0.9 -1.0 Alkan] = 5° Nis

-0.6

1.6 1.5 1.4 1.3 1.3 1.2 1.1 0.9 0.8 0.7 0.6 0.5 Q.4 0.3 0.2 0.1 -0.0 -0.4 -0.7 -0.8 -0.9 15 (0)

=o i -0.3 -0.6 =jholl —1.2

1.4 1.3 1.3 Wer2 1.1 1.0 0.9 0.8 0.7 0.6 0.6 0.5 0.4 0.3 0.2 0.1 U.0 =-0.0 -0.1 -0.3 -0.4 -0.6 5 7p l0)5 Tr -0.8 -0.9 1.0 =i

1.2 1.1 1.1 1.0 0.9 0.8 0.8 0.7 0.6 0.5 0.5 O44 0.3 0.2 0.1 0.0 -0.1 -0.1) -0.3 -O.4 -0.5 -0.6 AVE 7f =(Olow, -0.8 -0.9 -1.6

1.0 0.9 0.9 0.8 0.8 0.7 0.6 0.6 0.5 0.4 0.4 0.3 0.2 0.0 -0.0 -0.1 -0.1 -0.3 =(0}.55) -0.5 -0.5 -0.6 -0.7 -0.7 -0.8 -0.8

0.8 0.8 0.7 0.7 0.6 0.5 0.5 0.4 O.4 0.3 0.3 0.2 0.0 -0.0 -0.1 -0.1 -0.2 -O.4 -0.5 =O -0.6 -0.6 -0.7 =O

0.6 0.6 0.5 0.5 0.5 0.4 0.3 0.3 0.2 0.2 0.2 -0.0 -0.0 -0.1 -0.1 -0.2 =O)s2-|—055 -0.3 -0.4 -O.4 -0.5 -0.5 -0.5 -0.6

0.4 0.4 0.4 O.4 0.3 0.3 0.2 0.2 0.1 0.1 0.0 -0.0 -0.0 -0.1 -0.1 -0.2 -0.2 -0.3 —( 053) =()5 3} -0.3 -0.4 -0.4 -0.4

0.3 0.2 0.2 0.2 0.1 0.1 0.1 0.1 0.0 0.0 -0.0 -v0.0 -0.1 -0.1 -0.1 -0.1 -0.2 -0.2 05 -0.2 -0.2 -0.3 -0.3

0.1 0.1 0.1 0.1 0.0 0.0 0.0 0.0 0.0 -0.0 =07.0 -0.0 -0.0 -0.0 -0.0 = (Ost =001 -0.1 -0.1 -0.1 =0.1 10) | -0.1 -0.1

-0.1 =O -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0

-0.2 -0.2 -0.1 -0.1 -0.1 -0.1 -0.1 -0.0 -0.0 -0.0 0.0 0.0 0.0 0.0 0.1 el 0.1 0.1 0.1 0.2 0.2 0.2 0.2

-0.4 -0.3 -0.3 -0.3 -0.2 =0.2 -0.2 -0.1 =1)5 1 -0.1 -0.0 -0.0 0.0 0.1 0.1 0.1 0.2 0.2 0.2 0.3 0.3 0.3 0.3 0.4 0.4 0.4

26.0 26.5 27.5 28.0 28.5 29.5 30.0 31.0 31.5 32.0 32.5 33.0 3325 34.0 34.5 35.0 35-5 36.0 36.5 37.0 37-5 38.0 38.5 39.0 39.5 40.0 40.5 41.0 41.5 42.0

1500 METERS (155.81 kg/cm“)

TABLE 6. CORRECTION TO SOUND SPEED, V, (1449.1 m/sec). FOR SIMULTANEOUS CHANGES IN

SALINITY, TEMPERATURE, AND PRESSURE, Vetp - Continued

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*(Lg61 paqutaday) $19 “GNMd *"O “H 0} juauratddns ke se peystiqnd ‘pequeseid st ureadourou paeds punos vy ‘aanssaid zo y3dap arayzra yzIM pesn aq Aeur satqez

Aqaiaym payst{qejsa st drysuoejer yydap-aansseid y BS-dS “HH * WUD. /BH 09ZT OF COT PUL “MHE"TH OF 003 ‘D6 FE OF65°2- wioiy saduer aansseid pue Ajruryes ‘aanjeraduraz I2A09 satqel “19}3eM eas ut punos jo paads zo;

uotjenba s,uos{tm ‘q eudeM uo paseq aie saltqey

"1272M Bas ut paads Panos jo Sage (2H *r

peeds - punos - 193em—PaG

¢ sao0uerazay

*(8S-dS) *satqe7 2 “315 1

‘dip "7961 ysn3ny ‘uotstatq stshyeuy d1yderZ0ue300 ‘UGLVM WAS NI qaads GNNOS JO SaTaVL

ao0ujO 2tyderdoue| 20 [RAEN “SN

SOsNOOY Ia}emiapuyn *7

peads - punos *|

8S-dS ‘tr

*13ay2M Bas ut paads punos jo saqqey tay *t

peads -punos -1ajem—vasg ‘¢ SOIJsNO IY Jajyemiapuy *7

peads - punos *|

8S-dS ‘tr

*12j8M Bas ut paads punos JO saTqel +21) “tT

peads - punos - 193em—kasg *¢ SOIWSNOIY IajJeMIapuy “7

peads - punos ‘|

“(L661 paqutaday) #19 “QNd “O “H 0} qauralddns e se paystiqnd ‘pajuasaad st weadoulou paads punos y *aanssaad zo yjdap azayita yyImM pasn aq Aeur salqez Aqaitaym paystiqeysa st diysuoejaa yydap-ainssaad vy UPR 09ZI 92 EDT PU HL OF 093 ‘Deb HE 0946°2- wior1y saduexr aanssaid pue Ajtuijes ‘aanjerodura} IdAOD salqey, ‘193eM Bas ut punos jo paads doy uotenba s,uos{tm “GQ audeM uo paseq aie salqey

saouatajay

*(gs-ds) s9tqey 2 “815 1 “dip “2961 ysnany ‘uotstatq stskteuy 21yderdoues00

‘YaLVM WAS NI GaadS GNNOS AO SA TAVL ao0jO 2tyderdouesdO [RAPN “S “N

“(L661 paqtadey) $19 “aNd “O “H 0} quauratddns e se peystiqnd ‘paquesead st urerdsouiou paads punos vy ‘aanssaad 10 yjdap iayyIe qyIM pesn aq Aeur satqeyz Aqaiaym paystiqejse st drysuorjejas yydap-aanssaid y 7g 8 09ZT 03 EOI PUL “"H61F 93 093 ‘D.6°FE 9345°2- wioi1y saduer aansseid pue Ajruiyes ‘ainjeradura3 I2A0D satqey “19}e4 eas ur punos jo paaeds zo;

uoyenba s,uos{ImM “q auAeM uo paseq aie salqey

saouarayay

*(g¢-das) “s919e3 2 “3 1

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20130 21ydead0uesz0 TRARN *S ‘“N

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*(LS61 pewutadey) #19 ‘GMd ‘O “H 0} queuratddns e se paystiqnd *pazuasead st urerdourou paads punos y ‘aanssaid 10 yjdap rayjta yyIM pesn aq Aeur salqez Aqaiaym paystiqeisa st diysuorejar yydap-aanssaad y 8S-dS “HH *{W19/BA O9ZT 0} COT PUL ‘%6 Th 03 009 'D.6"FE 0365°2- uiorty saduer aainssaid pue Ajrutpes ‘aanjyeraduraz I2A0D salqey, “1a3e" eas ut punos jo paeds oz

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*I372M 2S ut peads punos jo SaTqel 'e9nn “tr

peeds ~—punos ~lajem—eas ‘¢ saouetTajay

SoWsNooy 1azeMrapun *7 *(gS-ds) “s91qe1 2 “301 ‘di ‘7961 ysnd3ny ‘uotstatq stskleuy styderZ0ue3s0Q ‘UAaLVM VAS NI Ga3ads GNNOS JO SaTAVL

20130 otyderZoue|acO [BARN ‘SN

peads - punos *|

“(LS61 peqatadey) #19 “GNd ‘O “H 03 quouratddns e se paystiqnd ‘pazueseid st wreidourou pasds punos y ‘aanssaaid io yjdap rayj3ta yyIM pesn aq Aeur salqe} Aqaiaym paystiqejsea st drysuoyelaa y3dap-aanssaad y 119/34 09ZT 0F €O°T PUL '™%H6"1H OF 093 D.6°FE 0345°2- uiozy saduer aainsseid pue Ajrurtes ‘aanjeradura, I2A09 salqey “1a3e" eas ut punos jo paads 0; uo1enba s,uos[tm *‘q audeM uo paseq aie salqey

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"I372M 2S ut paads punos jo saqqey 7a ‘rt

pads - punos - 193em— ag sa90Uerazay

SOSNOOY IazeMmzapuy *(gg-dS) *s91qei 2 “8 1 ‘d)} "7961 ysn3ny ‘uorstatq stshTeuy 2tyderZ0ue|0Q ‘UGLVM VAS NI GaadsS GNNOS 4O SaTAVL

291330 D1yderd0ue|sz0O [eARN ‘SN

peeds - punos ‘|

8S-dS ‘tr

"13JBM BAS ut paads punos Jo salqey :ap3ta *t

peads - punos - 1a3em—Pag ‘¢

SO1sNooy TayemMitapuy

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paads - punos *{

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*12}72M Bas ut paadg Punos jo SeTqeL +2131) “tr

peads - punos ~ 1aj3em—P ag “¢ SO1}SNOOY I9a}eMIapuy “7

peads - punos *{

‘(LS61 payutaday) $19 “Qnd “O “H 0} quauatddns e se peysttqnd ‘pajuasead st weadsoulou paads punos y *aanssaad 1x0 yjdap rayita yyIM pasn aq Aeu satqrz Aqaiaym paystiqeisa st dtysuoejaa yjdap-aanssaad vy * {W192 /34 09ZT OF EO" 1 PUL SLE 93 099 ‘D6 HE 0345°2- uio ry saduei aanssaid pue Ajruijes ‘aanjeraduiay I9AOD salqey, ‘1azeMm eas ut punos jo paads zo;

uotjenba s,uos[ImM "q auAeM uo paseq aie salqey

saouatajay

‘(gs-ds) satqes 2 “85 1

‘dib ‘2961 3snsny ‘uotstatq stshjeuy 21ydeas0ue|a0Q ‘WGLVM WAS NI GaadS GNNOS AO SATAVL

20730 Dtydeadoue|scO TRARPN “SN

*(Lo61 paqutadey) $19 “aNd “O “H 0} Juauratddns e se peyst[qnd ‘pajuesead st urer30u1ou paads punos yw ‘aainsseid 10 yjdap reyjIa yIM pesn aq Aeur sa[qe} Aqearaym paystiqgeysa st drysuorejer yjdap-ainssaid y yar BA 09ZT OF EOL PUL “HTH 03 093 ‘DHE 07.45°2- uioi1j saduer aanssaid pue Ajuiyes ‘aainjeraduraz I3A09 sajqey, *193e" eas ut punos jo paads 0; uotjzenba s,uos[tmM ‘qd aukeM uo paseq aie salqey

soousTajoy

*(gg-ds) "setqe 2 “31 T ‘d)} “7961 ysn3ny ‘uotstatq stshjeuy Ityderso0ueasQ ‘YGLVM WAS NI Gaads GNNOS 4O Sa TAVL a0jO Dtyderd0uP|DDO [RAPN “S ‘N