76 



WORK OF THE CARNEGIE AND SUGGESTIONS FOR FUTURE SCIENTIFIC CRUISES 



component perpendicular to this direction. The last two 

 quantities can be measured directly from the record. 

 The average total rate of change of amplitude of the fic- 

 titious pendulum is first measured over an interval 

 chosen so that the average of a2 sin (0 2 -<t>) is zero. 

 Thus by virtue of equations (15) and (16), the effect of 

 amplitude and isochronism is zero. This allows k in 

 equation (14) to be computed. When this has been done, 

 another interval is chosen (perhaps on a different rec- 

 ord), so that the average of a2 sin {<t>2 - <t>) is as large 

 as possible. For this interval the rate of change of am- 

 plitude due to damping and amplitude is calculated by 

 equations (14) and (15). The average total rate of change 

 of amplitude is measured from the record; the differ- 

 ence between this value and the sum of the effects due 

 to damping and amplitude is owing to the deviation from 

 isochronism and may, therefore, with the aid of equation 

 (16), be calculated. A similar procedure gives (T2 - 

 T3), the lack of isochronism in the other pair. 



In this way (T2 - Tl) was found to be about -250 x 

 10*'' second, whereas (T2 - T3) was less than about 40 x 

 10-7 second. Considerable uncertainty in these values, 

 particularly in the latter one, results from the errors in 

 the actual measurements of the total rate of change of 

 amplitude used in their determination. Unfortunately, in 

 all the Carnegie records which were used in determin- 

 ing gravity, the second factor in the correction for devi- 

 ation from isochronism was small [see equation (5)], so 

 that the possible error in this correction due to the un- 

 certainties in (T2 - Tl) and (T2 - T3) probably is not 

 greater than about 10 x 10-7 second even in the most 

 unfavorable record. The deviation of isochronism in 

 each pair, however, was known to be not greater than 50 

 X 10" ' second when the pendulums were adjusted in 

 Europe. The large value of -250 x 10-7 second for (T2 

 - Tl) obtained at the base station in Washington indi- 

 cates that some accident occurred to pendulum no. 1 be- 

 fore the base station observations were made. In view 

 of this, it seems likely that Ti might, with use, have 

 been subject to further changes apart from changes due 

 to variations in gravity. 



If no change in either Ti or T3, apart from change 

 due to variation in gravity, had occurred after the Wash- 

 ington observations, the values of (Ti - T3) should have 

 been constant. An inspection of the last column in table 

 1, however, indicates that they show variations which are 

 much too large to be due to errors in their determina- 

 tion. These variations in (Tl -T3) therefore have been 

 attributed to changes in Ti in view of its probable incon- 

 stancy. 



Table 1. Gravity results on K Xm by Meinesz (1926) 

 and on the Carnegie (1929) 



Station 



Kxm 



Carnegie 



T3 only Tl only 



Carnegie 

 difference 

 (Tl - T3) 



cm/sec^ cm/sec^ cm/sec^ sec X 10" 



For this reason those values of gravity derived 

 from Tl are given no weight except to provide some 

 check on the values derived from T3. A glance at table 

 1, which gives the values of gravity in centimeters per 

 second for each separate determination, shows that the 

 values of gravity obtained in San Francisco and Honolulu 

 are in much better agreement with those previously de- 

 termined there by Dr. Vening Meinesz when T3 is used 

 for the calculation than when Ti is used. This seems to 

 indicate further that Ti was subject to erratic changes. 

 The values in the second colunm were obtained by Dr. 

 Vening Meinesz on board the Dutch submarine K XIII 

 during a cruise from Holland to Java in 1926. 



A further inspection of table 1 shows that for the 

 last three stations, which are the only new ones deter- 

 mined on the Carnegie , the values of gravity derived 

 from Tl and from T3 are in fairly good agreement. 

 Practically then, it is not important whether the values 

 derived from Ti are rejected or not as far as the new 

 stations are concerned. 



Table 2 gives the latitude and longitude for each of 

 the five stations. 



Table 2. Geographical positions, Carnegie 

 gravity stations 



Station 



Latitude 

 (<^) 



Longitude 

 (A) 



San Francisco 

 Honolulu 

 Pago Pago 

 Penrhyn 

 At sea 



37 47.6 N 

 21 18.5 N 

 14 16.6 S 

 8 59.7 S 

 27 44.8 N 



122 23.4 W 



157 52.0 W 

 170 41.0 W 



158 03.8 W 

 135 22.1 W 



The results of the computations for the isotatic re- 

 ductions of the last three stations as made by the U. S. 

 Coast and Geodetic Survey are given in tables 3 and 4. 

 The methods used in calculating the reductions were 

 those elalxDrated by Hayford and Bowie (6 and 7). 



Remarks on Anomalies 



The last line in table 3 gives the values of the iso- 

 static anomalies, according to the Bowie formula of 

 1917, at the three Carnegie stations. The first of these 

 stations, marked "at sea," has a positive anomaly ac- 

 cording to the Bowie formula of 1917 of 0.036 cm/sec^. 

 This value agrees with the average anomalies obtained 

 by Dr. Vening Meinesz for stations in this approximate 

 neighborhood of the Pacific. The positive anomaly of 

 0.040 cm/sec2 at Penrhyn is not unusual. Dr. Vening 

 Meinesz is of the opinion that the large positive anomaly 

 at Pago Pago--0.110 cm/sec^ according to the Bowie 

 formula of 191 7- -probably has some connection with the 

 neighboring Tonga Deep, since up to the present practi- 

 cally all the deeps where observations have been made, 

 show a strip of negative anomalies over or near the deep, 

 bordered on both sides by fields of positive anomalies 

 which in several instances attain rather large values. 

 He considers quite unlikely the possibility that this 

 anomaly is owing to the fact that the island is composed 

 largely of a heavy basalt or to the fact that the station, 

 although made in the harbor of Pago Pago effectively 

 was not far from the center of the island. A detailed 



