Mayer — Electric Potential as measured by Work, 385 



repulsive force existing between it and the fixed sphere. The 

 end of the sliding rod during the motion of the sphere from 

 \ towards will have traced out the curve I) FOG, \vho>e 

 ordinates are as the inverse squares of their distance from < ). 



Thus we get a trace in a manner similar to that given by the 

 steam-engine indicator, or by one of the many instruments 

 which draw curves, showing the varying effects of pressures, 

 or of Btresfi 



The potential at any point readied in the progress of the 

 charged body towards O >= work done = resistance overcome 

 in pushing body from infinite distance to that point ; and this 

 work done is measured by the sum of the resistances at each 

 point of path X the length of path. But this product is equal 

 to the area included between the ordinate (say B) of path, the 

 axis of X and the curve, both indefinitely extended ; or, say 

 C B A D. 



If the body has been moved from infinite distance up to E, 

 a certain amount of work has been done; and it is to be 

 proved that if the body has been moved from infinite distance up 

 to B,=J distance OE, that twice the amount of work lias been 

 done. In other words, it is to be proved that area C B A D is 

 twice the area F E A D ; or, generally, that such areas will 

 vary inversely as the distance of the bounding ordinate (such 

 as F E or C B) from O, the origin of coordinates. 



The equation of the curve is 



a 



Area A B C D, indefinitely extended = 



f*. ydx =fl % dx = -HEE = 0+ l ■ ' • 



Or, area indefinitely extended, which represents the work, is 

 inversely as the distance of y (the bounding ordinate of area) 



from O, or, Y= — , but also, V= — , and as Y= — , r= C: r 



a r C 



being expressed in cms. 



I had supposed that the mode of presenting this problem 

 and the demonstration based on that conception, as given in 

 this paper, must have occurred to others before it did to me, 

 but Professor B. O. Peirce, of Harvard University, who is 

 better versed in the literature of the subject than I am wrote 

 me as follows : " My experience has taught me that students 

 who have not paid much attention to mathematics almost in- 

 variably find it difficult to get any true idea of the meaning of 

 the word "potential" and that they value highly anything 

 which helps to make this meaning clearer. 1 our graphical 



1 

 oc - 



X 



