■■ 



58 Mr. J. J. Waterston on the Intensity of Gravity 



The following is computed for an ellipse with a same as our 



e 

 planet, but with - = '99, and U as above : 



a 



' [~] = + '° 0a21 ; 8t= ~ 28 dayS * 



This example shows that a periodic comet with small perihe- 

 lion distance and large excentricity is favourable for discovering 

 the absolute value of U. St, computed for one revolution of 

 Halley's comet with U as above, gives 70 days as the decrement 

 of period. 



The following is computed for Encke's comet : — 



'^1 ™^. fl e l __.nnnss. [V 



■P 

 6Y=-0 d -66. 



g] = -00037 ; g] = -000 3 8; g]- + «00. i 



It is admitted that the period of Encke's comet is shortened 

 half a day by some unknown cause; so if the finite value of 1*32 

 million miles is assigned to TJ, we have a sufficient cause for the 

 decrement. On the other hand, the excentricity of the earth's 

 orbit would diminish by this cause '0000008, which is double 

 the amount of decrement assigned to it by the secular variation : 

 also there would be a shortening of the period of Halley's comet 

 by 53 days. These, it may be presumed, are both inadmissible. 



It would be interesting if physical astronomers could assign a 

 limit ; for it cannot now be believed that the living force, which is 

 apparently generated and lost by means of gravitation, is abso- 

 lutely created and destroyed. That would be to make gravita- 

 tion an exception to the general rule of conservation. Besides, 

 it is demonstrated that space is filled with a material instrument 

 that is the carrier of living force outwards ; so may that or an- 

 other even more subtle and dominant be the source from which 

 descending matter acquires the vis viva that it carries centripe- 

 tally inwards. 



Appendix. 

 To prove w; = c.tan^. 



g-=. feet fallen through in one second at earth's surface. 



4g= feet square velocity acquired in falling through one 

 foot. 



r 9 q 2 = miles square velocity acquired in falling through 

 one foot. 



