u 



E. F. J. LOVE. 



The calculations required are very simple. Let^ x and g 2 be 

 the values of gravity at any two places, V x and V 2 the vibration 

 numbers of an invariable pendulum at the same places : then 



9, *V 



Pi" 



or g 1 = g 2 y-$ 



hence if V 1} V 2 , and g 2 be known, g x is determined. 



The values of gravity for the three places at which the absolute 

 determinations have been made are as follows : — 



For Greenwich : g = 981*05 cm. sec. 2 

 „ Melbourne: g = 979 961 „ „ 

 „ Kew: g = 981-197 „ „ 



From these we obtain the following table of values of g for 

 Sydney : 



TABLE III. 



Pendulum. 





Calculated from 





Greenwich. 



Melbourne. 



Kew. 



No. 4 



97955 L 



979*671 



979-606 



No. 6 



979-531 



979-686 



979593 



No. 11 



979521 



979678 



979-622 



Mean 



979534 



979-678 



979-607 



Mean 979-606 cm. sec.- 2 



The greatest difference from the mean is about 1 in 14,000; 

 while the mean itself differs by about 1 in 600,000 from the value 

 obtained by comparison with Kew, for which station — as already 

 mentioned — the value of g is known with very great exactness, 

 the determinations executed there with two entirely different 

 sets of apparatus agreeing within 1 part in 3,000,000. We are 

 therefore warranted in adopting 97 9 606 cm. sec.- 2 



— at any rate provisionally — as a very fair approximation to the 

 value of g at the sea-level in Sydney ; the possible alteration can 

 scarcely exceed a few units in the second decimal place. 



In English units, assuming 1 metre = 39*37000 inches — as 

 determined by the U.S. Coast and Geodetic Survey — this quantity 

 becomes 32-1392 ft. sec. 2 



