1880.] ^ • [Chase. 



same times ; * and that if a iluid be composed of particles mutually repelling 

 each other, and if the density varies as the compression, the centrifugal 

 forces of the particles will be reciprocally proportional to the distances of 

 their centres,! as if indicating a reaction against a force which varies as the 

 distance from the centre. The centripetal force is partially illustrated by 

 the rotation of planetary bodies ; the centrifugal, by the varying pressure 

 of elastic atmospheres. 



6. Such centripetal force as is above supposed, requires, for its complete 

 manifestation, an omnipresence of activity, which is devoid of inertia, of 

 ponderability, and of all other ordinary tests of material nature ; an activity 

 which may, perhaps, properly be regarded as spiritual. 



7. Laplace found himself obliged to recognize an activity in gravitation, 

 which is propagated with at least 100,000,000 times the velocity of light. J 

 This activity, he says, may be properly regarded as instantaneous. If it is 

 spiritual, it may without difficulty be regarded as absolutely instantaneous 

 throughout the universe. If it is material, it is difficult to conceive of any 

 relation of elasticity to density which would be so great as 10,000,000,000,- 

 000,000 times that of the supposed luminiferous sether. Yet such are the 

 requirements of the Newtonian law, that "the velocities of pulses propa- 

 gated in an elastic fluid are in a ratio compounded of thesubduplicate ratio 

 of the elastic force directly, and the subduplicate ratio of the density in- 

 vei'sely." § The importance of this law has been shown by the investiga- 

 tions of Graham, by the inquiries of English and German physicists into the 

 relations between electromagnetic and luminous velocities, and by my own 

 correlations of the force of solar rotation with the forces of light, gravi- 

 tation and chemical attraction. 



8. In any elastic or quasi-elastic medium, "if the distances be taken in 

 harmonic [or arithmetical] progression, the densities of the medium at 

 those distances will be in a geometrical progression." 1| I use the term 

 "quasi-elastic," in order to meet the views of Faraday. Preston •;[ and 

 others, who prefer to treat all kinetic questions in accordance Avith lines of 

 force. 



9. The distances of projection, under uniform resistance, are proportion- 

 ed to the living forces of projection, and inversely as the density of the re- 

 sisting medium. 



*Principia,B. I, Prop. 47. 



t lb. B. II, Prop. 23. 



JMec. Cel., X, vii, 22. 



gPrincipia. B. II, P. 4S. 



II lb., B. II, P. 22. 



HP. Mag., June, Sept., 1S77. Preston does not give Maxwell's demonstration 



of the ratio -*.'—, and neither he nor Maxwell seems to have been aware that I 

 \ 9 



had used the same ratio of vis viva Ave years previously, iu discussing results of 



gaseous energy (Proc. Am. Phil. Soc. Feb. 16, 1872, vol. xii, p. 394, foot-note). I 



showed that in the explosion of gases, the secondary centre of oscillation, on 



/ 12 2 12 — 9 5 \ 

 the return towards the centre, is at I -r-r ir ^^ — Ta~ ~ ^ / °^ *^® extreme 



excursion. 



