June 18, 1S75.] ^^* ' [Ohase. 



FURTHER RELATIONS OF MAGNETIC, GRAVITATING, AND 

 LUMINOUS FORCE. 

 By Pliny Earle Chase, 

 Professor of Mathematics in Haverpord College. 

 (Bead before the American Philosopliical Society, June 18, 1875.) 

 Ohm's law is a particular case of the general principle that an impul- 

 sive force may be measured by the product of resistance overcome, by 

 velocity communicated. Illustrations of this principle may be found 



In General Physics, Mass X Velocity = Momentum ; 



In Electricity, Resistance X Current = Electromotive force : 



In Chemistry, Atomic weight X Specific heat = Chemical cocstant ; 



In Cosmogony, Inertia-resistance X Gravitating impulse^ Centripetal constant 



Since all these expressions refer to actions from or towards given cer - 

 tres, they are governed by the same mathematical relations, and the diff- 

 erent names by which the activities are designated, do not necessarily 

 imply any differences in the nature of the forces themselves. 



Clerk Maxwell asks,* " Is it possible that the attraction of [tlie Sun and 

 Moon], by causing strains in the interior of the earth, produces changes 

 in the magnetism of the Earth, and so by a kind of tidal action causes the 

 semidiurnal variations?" Eleven years ago, in the paper which received 

 the Magellanic gold medal, and in other communications, f I anticipated 

 the question, and gave reasons for answering it in the affirmative. 



If the primary disturbance is of a tidal character, it does not involve 

 the entire force of \_M], but merely the differential force [i¥Z"^]. If we 



1 1 _3 



regard the electric \_M^'\ as really representing \_M-L "'\, each of the 

 mass-factors in Maxwell's table of electrostatic and electromagnetic 



_3 



dimensions should be multiplied by [L ^]. This multiplication produces 

 Zj precise correspo7i(?e7ice between the electrical and gravitating fields, both 

 in extent, and in many suggestive details. 



In my communication on the "Velocity of Primitive Undulations,":): I 

 showed that the present numei'ical value of the velocity-i-atio, It , at its 

 upper limit, or the limit between total solar dissociation and incipiect 

 aggregation, is the velocity of light, and that the planetary ratios are 

 also in close accordance with the ratio between the radius of gyration of 

 the solar system when nebulously diffused, and Sun's radius of gyration 

 about the centre of gravity of the system. If we wish to extend our 

 comparisons to the lower limit, or the limit between total aggregation 

 and commencing dissociation, the directions of «/ and Vn should be taken 

 tangentially instead of i-adially. Designating the symbols for the lower 



limit by enclosures we have («y) = -y^ -f- i/2 ; (»//) =„ Vn; (It ) = 



/n a 



V * -1 -1 



(»/ -^ v,i) ^=- -^ U ; (vg) = (v/) X, (It ) = «o -=- -. Therefore the maxi- 



* " Treatise on Electricity and Magnetism," ii, 127. 

 fProc. Amer. Philos. Soc, ix, 356, 397, 427, 487, &c. 

 I Proc. Amer. Assoc. Adv. Sci., xsiii, 99. 



