^;^j^ RECENT PROGRESS IN PHYSICS. 417 



•The quantity 4.5, according to the table, sustains a weight of 4 

 grains Avhen only 1 jar is used, while the same quantity 4.5, divided 

 between two jars, sustains only 1 grain ; thus the eifect, the quantity 

 being the same, is inversely proportional to tlie square of the surface, 

 since with a double surface the effect is one fourth. 



Let us consider the experimental series with 2 jars. The quantity 

 4.5 sustains 1 grain double this quantity, 9.00 sustains a weight four 

 tinies as great or 4 grains ; hence, the surface being the same, the 

 weiglit sustained, or the force of repulsion, is proportional to the 

 square of the quantity. 



We conclude from the above data that the repulsion of the balls is 

 directly as the square of the quantity of electricity, and inversely as 

 the square of the surface, so that, 



or the repulsion of the balls is proportional to the square of the den- 

 sity of the E, J- indicating this density. 



6 



Having deduced this law from observations selected at random, we 

 have now to show how closely the rest of the observations agree with 

 it. 



According to the law, a double quantity of electricity produces, 

 with the same number of jars, a quadruple effect; each value of q, 

 therefore, on the lowest horizontal line, must be double the value of 

 q at the top of the same vertical column. This, however, is rigidly 

 true only for the series under the head of 2 ; the quotients 



4.5 13.3 1Y.7 24 



— = 2.25; =1.90; =2.03; —=2.40 



2 7 8.7 10 



vary more or less from 2. Taking the mean of all the five quotients, 



9.0 

 (that of — =.2 included,) we get the number 2.11, which in fact is 



4.5 

 very nearly equal 2. 



The quotients, obtained by dividing the values of the second line 

 by the value of q in the upper horizontal row, should, according to 

 the law^ be equal to ^2 = 1.41. The mean of the five quotients is 

 1.48. 



If the numbers of the first and third lines be compared in the same 

 manner, the mean of the five quotients will be the value 1.82, 

 while, according to the law, it should be equal to V3=il.^3. 



The repulsion being proportional to the square of the density, 

 according to the above law, with like effects, or equal values of^, the 

 quantity of electricity must increase in proportion to the number of 

 jars ; hence the numbers of the column headed with 2 must be twice 

 as great as those on the same line under 1 ; or in other words the 



4.5 6.0 1.1 9.0 

 quotients — , — , — , — , should all equal 2. Computing these 

 2 3.5 4.6 4.5 



27 s 



