Chase.] 14:t» [April 17, 



light, aucl the only mode of viewing gravitating action, under an inva- 

 riable relation to a uniform velocity, being the one which I have pointed 

 out in Theses 23 and 24, there seems to be an a 'priori probability that v 

 may be represented by some simple function of the constant velocity 

 gi", and that gravitating motion, as vs^ell as light motion, may be undu- 

 latory. Since gravitating fall acts, in orbital motion, until the sum of 

 successive gravitating impulses has communicated a tangential velocity 

 equal to \ gr, thus renewing the orbital velocity, it seems natural enough 

 to suppose that the same fall may also act, in rotary motion, until the 

 sum of successive impulses has communicated a centripetal velocity 



= -y' = « , thus renewing the velocity of primary impulsion. If the 

 gravitating thrusts or pulls are supiaosed to be all efficient, it is not only 

 right, but it is even our duty, as earnest truth-seekers, to try to trace 

 their efficiency as far as possible. 



In the oscillation described in Thesis 22, each equatorial particle is al- 

 ternately approaching to, and receding from, the orbital centre of gravity, 

 during intervals of a half rotation. The integral of gravitating im- 

 pulses, at the centre of our system, during each wave rise or fall, is, 

 perhaps, as closely identified with the velocity of light, as is the integral 

 of gravitating impulses, during the orbital description of radius, with 



the orbital velocity. For, from the equation ^ =: «' =: «''', we deduce^ 



for the time of solar rotation, t" = ^^g^ygg-^ X (sH^SG j'" ^^'^ 



value differs, by less than | of one per cent., from the estimate of 

 Bianchi, Laugier, and Herschel, and by less than 3^ per cent, from that 

 of Sporer, which is the lowest estimate hitherto published. From the 



constant solar equation, "i— ^ v\ we i-eadily obtain, by introducing the 



variable r, the general equation for planetary velocity, ygr = /^^'^ ' 



\ t" 



The following references are to the published volumes of the Pi'oceed- 

 ings of the American Philosophical Society, except when otherwise 

 specified. The Arabic numerals, prefixed to each set of I'eferences, 

 denote the Thesis which they verify or exemplify. 



2. ix. 371, April 15, 1864 ; ix. 427, 432, Oct. 21, 1864 ; x. 98, April 21, 

 1865 ; xii. 392, Feb. 16, 1873 ; xii. 411, July 19, 1872 ; Trans. Amer. 

 Philos. Soc, xiii. Art. VI. 



3. xi. 103, April 2, 1869 ; xiii.. 140, 142, Feb. 7, 1873. 



4. xiii. 345, May 16, 1873. 



6. xii. 518-22, Sept. 30, 1873 ; xiii. 193, 244, April 4, May 16, 1873. 

 9. xiii. 146, March 7, 1873 ; xiii. 343, 245, May 16, 1873. 

 12. xiii. 193, April 4, 1873. 



