GEODESY AND PENDULUM EXPERIMENTS. 683 



invariable, the value of the acceleration due to the force of gravity, 

 is directly proportional to the square of the number of vibrations ; 

 or, which amounts to the same thing, the force of gravity is 

 directly proportional to the length of the second's Pendulum. If </ 

 be the acceleration at Greenwich, and o^ the acceleration at Port 



Bowen, then ^-l=.(^^^^V^V 001^6^5 , 

 g \86159-434/ 



4. Experiments made by Dr. Hayes at Port Foulke in 



September and October 1860, to determine the Figure of the 

 Earth. 



A series of experiments on the time of vibration of a Pendulum 

 were compared with a series made with the same Pendulum at 

 Cambridge, Massachusetts, before the Expedition sailed. The 

 number of vibrations in 24 hours at Cambridge was 86421 * 14, and 

 the number of vibrations at Port Foulke was 86550 '72. 



These values would give a compression or flattening of the 



pole = 



^ 372 



This value is smaller than that derived from Parry's experi- 

 ments and by other methods. Baily's Pendulum experiments 



gave the ellipticity , but other smaller values have been 



285 



obtained. The value given by geodetic measurements is — -. 



The ratio of the value of the force of gravity at Port Foulke, 

 and at Cambridge, from these Pendulum experiments, is 1 • 003 very 

 nearly. 



5. Geodesy. (Die zweite deutsche Nordpolarfahrt, vol. ii., 



p. 761.) 



A base line was measured on the coast near Germania Harbour, 

 and connected by a system of triangulation with three points in 

 Sabine Island, at some distance from the harbour and from one 

 another. 



The sides of this triangle were then used as bases of other 

 systems of triangulation extending to other islands, and to various 

 points on the mainland, extending over nearly one degree of 

 latitude. 



The comparison of these measurements, with the astronomical 

 observations for the elevation of the Pole Star at the different 

 places, gives, by the usual formulae for the length of a degree of 

 latitude, 72751 -429 metres. The length of a degree of latitude as 

 deduced from theoretical considerations is 72937*627 metres, 

 the difference being about one four-hundredth part of the whole 

 distance. 



The heights of a great many points along the coast were also 

 determined by trigonometrical measurement, as well as by the 

 barometer. 



