430 Prof. F. Kohlrauseh on the Determination of 



The diagonal A B also represents the magnitude of the result- 



Fig. 2. 



I) E in F, and join A F. 

 is its diagonal, and AE 



ant of the forces P and Q at A. 



For if the diagonal A B does 

 not represent the resultant of 

 P and Q in magnitude, it must 

 either be greater or less than 

 this resultant. Let it be 

 greater, and take AG less 

 than A B to represent the re- 

 sultant in magnitude. Draw 

 D E parallel to B A. Produce 

 C A to meet D E in E. Draw 

 GF parallel to BD or C E meeting 

 Then AE F G is a parallelogram, A F 

 = AC, for both equal BD by construction. 



Apply a force E at A along A E equal and opposite to P, and 

 therefore represented in magnitude and direction by AE. 



Suppose the three forces P, Q, and R acting at A. We may 

 replace P and Q by their resultant A G. Hence the forces A G 

 and 11 acting at A must have a resultant acting in the direction 

 of AF. 



Therefore P and Q and E at A produce the same effect as a 

 resultant force acting along A F. Now if we remove P and R, 

 which we can do as they are equal and opposite, we have left Q 

 acting along A F as well as along AD, which is absurd. 



Hence the resultant cannot be less than A B. In the same 

 way it may be proved that it cannot be greater • and therefore 

 AF must coincide with AD, and the point G with the point B. 

 Therefore the diagonal A B represents the magnitude as well 

 as the direction of the resultant of P and Q. 



L. A Determination of the Specific Heat of Air under constant 

 Volume by means of the Metallic Barometer. By F. Kohl- 

 rauscii*. 



THE value universally assumed for the specific heat of air 

 under constant volume has been calculated from the velo- 

 city of sound. There has hitherto been no exact direct determi- 

 nation ; for the observations made by Clement and Desormes, 

 as well as by Gay-Lussac and Welter t, can only be regarded 

 as approximations by which the proof has been furnished that 



* From Poggendorff's Annalen, No. 4, 1869. 



f Clement and Desormes, Journal de Physique, &c., vol. lxxxix. pp. 321, 

 428 (1819) ; Gay-Lussac and Welter in Laplace's Mecanique Celeste, vol. v. 

 p. 125. In the first paper all details are wanting which would render pos- 

 sible an opinion as to the accuracy of the experiments. Only one experi- 

 ment is given in full ; of all the others only the mean of the results is given. 



