466 MOSSOTTI ON THE FORCES WHICH KECULAXE 



— ax 



g V (q + zs) S V, (cr, + q,) (1 + a ty) e 



— {9 ~ y) ra' V S OTv v» — — =: o 



(A) ^ V (q + ot) S V, (ziT, + q,) (1 + a r,) e 

 — (r/ — y) CT V 2 t<r,v, ^-1^ — ^ = o 



fj V (q + ot) il V, (ar, + q,) (1 + a r,) e 



Zw — Z 





— (ff—y) ■^ V 2 S7, v» -^ = o, 



where tiie sums 2 are to be extended to all the members v, that is to 

 say, to all the molecules except tliat whose equilibrium we are con- 

 sidering. 



7. The equations which we have just found are those which must 

 take place in case of equiiibriimi, or in the natural state of a body com- 

 posed of spherical molecules, if Franklin's liypothesis respecting statical 

 electricity may be applied to the constitution of bodies also. The form 

 in which the equations present themselves shows that this cquiliijrium 

 takes place exactly as if there existed between each pair of molecules 

 a reciprocal action, in the direction of the straight li.ie which would 

 join their centres of gravity, and would be represented by 



(«) <7v(ot + q)v,(tzr, + q,) kL±J^lilf _ (^_ y) vct.v, ar, 1 



r,- Ti- 



Let us examine the nature of this action. We are able to distinguish 

 in its expression the products 5* v (rs + q). v, (ct, + q,), (^ — y^-urx. 

 cr, Vp the constant a and the variable r,. 



As the diffei'ence (g — y) between these two accelerative forces is 

 to be supposed very small relatively to g, the product of this force by 

 the masses v (to- -{■ q) v, (tsr, + q,) will, for a twofold reason, be 

 greater than the product of the difference 5' — y by the masses -ns v. ro-. 



The value a depends on that of /and k, that is to say on the repul- 

 sive force of the atoms of the aether, their mutual distances, their 

 masses, and their volumes, which are all unknown to us. The agree- 

 ment of the results of calculation with those of experiment requires 

 that a should be a very high number. 



On tlie conditic n that a is very great, the first term of the expression 



{fi) will decrease rapidly w'xih. r,, because of the multiplier e ' ; if 



