GRAVITY DETERMINATIONS ON THE CARNEGIE 



75 



sea. The upper record was obtained in the open sea 

 between San Francisco and Honolulu, the middle one off 

 West Passage, Penrhyn Island, and the lower one off 

 Tauhunu Village, Manahiki Island. Because of the large 

 amplitude of the middle pendulum, the lower curve on 

 each record is indistinct. On the originals it was clear 

 enough to insure a satisfactory reduction of the upper 

 two records. The vertical blank spaces in the upper 

 record are due to the observer's having momentarily 

 thrown the recording spots, by means of a reflecting 

 prism provided for the purpose, on a special ground- 

 glass screen to insure that the apparatus was function- 

 ing properly.. This in no way disturbs the record. 



The sudden change in the amplitudes of the fictitious 

 pendulums near the left end of the lower record indi- 

 cates that the middle pendulum slipped on its knife edge. 

 Other unsuccessful attempts to obtain gravity records 

 at sea failed either for the same reason or because it 

 was feared that slipping would occur. 



Several factors may operate to increase the ampli- 

 tudes of the pendulums to the point where slipping may 

 occur. One is the unavoidable horizontal acceleration 

 due to the rolling of the ship. Another, and this Dr. Ven- 

 ing Meinesz from his long experience with the apparatus 

 considers quite important, is the effect of surface waves 

 on the hull of the ship to produce horizontal accelera- 

 tions apart from those due to rolling. Finally there are 

 the elastic vibrations of parts of the apparatus or its 

 support. If the period of such vibrations is near to the 

 period of the pendulums, there will be a resonance ef- 

 fect which will cause the pendulum amplitudes to get 

 large. 



Some experiments were made in Honolulu harbor to 

 determine whether the gimbal frame supporting the pen- 

 dulum apparatus had a period which would produce large 

 amplitudes in the pendulums. These experiments con- 

 sisted in starting the pendulums swinging in the same 

 way as for a gravity observation and then displacing the 

 whole frame slightly and allowing it to vibrate. These 

 vibrations, though small in amplitude, caused a large 

 increase in the pendulum amplitudes. The frame then 

 was temporarily braced so that it was impossible to 

 cause the whole apparatus to vibrate in such a way that 

 it would affect the pendulum amplitudes. With this same 

 bracing further attempts at sea were made to obtain 

 gravity records, but without any obvious improvement. 

 Possibly the cause for the large effect on the pendulums 

 originated not in the vibrations of the main supporting 

 frame of the apparatus but in vibrations of one of the 

 several subsidiary members necessary for the gimbal 

 suspension. This must be taken into account when it is 

 considered that the frame of the apparatus was made of 

 brass, in order not to introduce unnecessary magnetic 

 material on the Carnegie , and that the members were 

 not of sufficient size to insure rigidity. 



Dr. Wright, under whose direction the first obser- 

 vations were made on the Carnegie in San Francisco 

 harbor, is of the opinion that the lack of rigidity in the 

 platform on which the apparatus was mounted is a factor 

 which should be strongly emphasized in attempting to 

 explain just why the pendulum amplitudes got too large 

 for the instrument to function properly. 



This experience indicates the necessity of making 

 experiments on land before installing such an apparatus 

 on a ship to insure that no part of the apparatus has a 

 period of vibration which can materially affect the pen- 

 dulums. These experiments also should include tests to 



determine whether the period of the apparatus in the 

 gimbals has any effect on the pendulums. In these tests 

 it must be observed that any effect which causes a vari- 

 tion, apart from that due to damping, amplitude, and 

 isochronism, of the amplitude of the fictitious pendulums 

 will have an effect on their periods. The causes of any 

 such variations then must be removed. 



It seems also, from the writer's experience on 

 board the Carnegie , that the friction in the bearing points 

 of the gimbal suspension caused the movements of the 

 apparatus to be somewhat jerky. This was overcome 

 only partly by adjustments of the size of the damping 

 vane which was attached to the apparatus and immersed 

 in oil. 



The Carnegie experience suggested, and the experi- 

 ments of Dr. Vening Meinesz on board some passenger 

 vessels confirm, that orienting the apparatus so that the 

 plane of oscillation of the pendulums is parallel to the 

 ship's keel instead of perpendicular to it, considerably 

 increases the probability of obtaining a successful grav- 

 ity determination. It now seems quite possible that, had 

 the apparatus on the Carnegie been so oriented, a large 

 number of successful determinations would have been 

 obtained. 



Remarks on Reductions 



It should be borne in mind that the Meinesz gravity 

 apparatus does not determine the absolute value of grav- 

 ity at any station, but only the value at that station rela- 

 tive to a base station. The base station for Carnegie 

 observations was that of the U. S. Coast and Geodetic 

 Survey in Washington. Since the correction for deviation 

 from isochronism depends on the difference in the peri- 

 ods of the middle pendulum and that outer pendulum 

 from which the fictitious pendulum is derived (see equa- 

 tion 5), it is obvious that this difference must be knov/n. 

 Observations at the base station under somewhat special 

 initial conditions (5, p. 28) are needed for determining 

 this deviation of isochronism. Unfortunately, in the ob- 

 servations made at the base station in Washington, the 

 phase relation between the pendulums was such that the 

 deviation from isochronism in the two pendulum pairs 

 could not be obtained. It was possible, however, to ob- 

 tain approximate values of (T2 - Ti) and of (T2 - T3) In 

 another way. The rate of change of amplitude of each 

 fictitious pendulum depends on the damping, the ampli- 

 tude, and the deviation of isochronism. The following 

 equations (taken from 5, p. 21) determine the effect of 

 each factor: 



Damping: da/dt = -ka 



(14) 



Amplitude: da/dt = (tt/IBT) a a2 sin (02 

 [a + 2a2 cos {'t>2 + <t>)] ■ ■ • • 



(15) 



Deviation of isochronism: 

 da/dt = - (7r/T2) U a2 sin (cj> 2 - <l> ) 



(16) 



in which a is the amplitude of the fictitious pendulum; 

 a2 is the amplitude of the middle pendulum; T is the 

 period of the fictitious pendulum; U is equal to (T2 -Ti), 

 that is, the deviation from isochronism in pendulums 1 

 and 2; a2 cos (0 2-0) is the component of the pendulum- 

 vector of the second pendulum in the direction of the fic- 

 titious pendulum -vector; and a2 sin (0 2 - '^) is the 



