Mr. Pratt's Demonstration of the Parallelogram of Forces. 39 



2nd, That the most trustworthy experiments on the spe- 

 cific heats of the gases, combined with the law of Dalton, 

 Dulong, and Neumann, lead to an opposite inference. 



3rd, That several examples of chemical combination are 

 inconsistent with the doctrine of numerical equalityof atoms 

 in equal spaces of the different gases. 



4th, That the original hypothesis of Dalton, which contem- 

 plates the self-repulsive gaseous molecule as identical with the 

 ultimate chemical atom, has in its favour the greatest amount 

 of probabilities. 



Manchester, June 7, 1834. 



V. A Demonstration of the Parallelogram of Forces. By 

 J. H. Pratt, Esq.* 



T ET P Q be two forces acting on a point, their directions 

 -*- i including an angle a ; and let R be their resultant, acting 

 in the same plane with P and Q, and making an angle 6 

 with P. 



Suppose P to be equivalent to two forces Pj P 2 , acting in 

 direction of 11, and perpendicular to this direction ; and let Q 

 be equivalent to Q x Q 2 , acting similarly; 



To find the relation between F x and P, we observe that 

 since the law of resolution must be independent of the magni- 

 tudes of P and Pj so long as their ratio is the same, P l must 

 be of the form P x = P./(0), 



where/* (0) is to be found. 



Now, when = X — , tt 1 rjcft 2ttj ... 



P 1 = P,0,-P, Q, Px 



and from these we see that if n be any integer 



/(*•?) =^(«-i) (2-) 



When has any value not comprised in the above formula, 

 the only conditions to be satisfied byf(Q) are, that the sum 

 of the resolved parts of Pj and P 2 in the direction of P shall 

 equal P, and perpendicular to this equal : 



.-. P-P 1 /(») + P g /(-|--»), 



* Communicated by the Author. 



