620 hersey: derivatives of physical quantities 



Cut out a double faced templet to the curve e~ 'X = const., 

 i.e., to the curve 



F=log|+logX (11) 



in which K is chosen at pleasure. If n is the number of steps 

 needed for traversing the curve 



y =x> . (12) 



from Xi to x 2 with this templet, . 





X2 



e- xi dx = nK (13) 



The device therefore is not limited to problems involving empiri- 

 cal curves to start with. It is applicable also to cases in which 

 the integrand is given analytically. It will be practically useful 

 in such cases, whenever F(x) is sufficiently complicated to 

 warrant the trouble of dealing separately with the two functions 

 4>(x) and /(?/). 



PHYSICS. — Note on a relation connecting the derivatives of physi- 

 cal quantities. 1 M. D. Hersey, Bureau of Standards. 

 (Communicated by E. Buckingham.) 



Statement of the problem,. Given the fact that some relation 

 of unknown form 



Qo = / (Qi, Q„ • . . . Qn-i) (1) 



subsists between N physical quantities Q , Qi, Q2, . • • Qn-u 

 no others being involved, it is required to deduce a relation of 

 known form 



0Q1 XoQo / 



(2) 



such that at any point whose generalized coordinates, Q , Qi, 

 Q 2 , etc., are given, the value of any one of the N-l partial deriva- 

 tives of Q can be computed from any other. Thus, it is required 

 to calculate one of the component slopes of the generalized sur- 



1 This work was done at the Jefferson Physical Laboratory, Harvard Uni- 

 versity. 



