386 Dr. Gerlaeh on the Mechanical Theory 



2. A body a, which strikes ivith the velocity v a body at rest, 



(IV 



imparts to it the velocity j- What velocity would be pro- 



duced by another body whose vis viva was x times as great as that 

 of a? 



2 



ccav 

 The vis viva of this body would be — — ; yet the factor x may 



be connected in the most varied manner with a and v. The 

 most general form of the combination is attained by putting 

 x=mn } and making the velocity n times as great; thus 



ma . N2 

 2 — (nv) 2 

 x av z n 



2g 2g 



ma 

 We have then — for the mass, mav the quantity of motion, and 



we obtain for the velocity c which is imparted to the body b the 



equation 



mav mnav 



c= = . 



m 7 ma-\-nb 



~ a + b 



n 



If w==i ; then 

 and if ?n~\, 



ax + b' 



xav 



a -j- xb 



These results express, as regards their form, the intensity of 

 the current of a combination of mn elements, according as they 

 are joined either to form a battery of m cells with n elements, or 

 a battery of mn cells with single elements, or a single cell with mn 

 pairs of plates. An increase in the size of the zinc plates corre- 

 sponds to a smaller mass (density) with increased velocity; a larger 

 number of cells to a greater mass, the velocity remaining un- 

 changed; the electromotive force corresponds to the quantity of 

 motion, the consumption of zinc without and with an interpolar 

 to the vis viva before and after the impact. 



As these fundamental examples, from a series of theorems 



belonging to one class, agree, the corresponding ones may be at 



once deduced by simple translation. In a battery we need only 



me m 



call the velocity, —/the density } me the quantity of motion 



7Yi j n 



n 



