426 



RECENT PROGRESS IN PHYSICS. 



h indicates the depression in the thermometer expressed in lines, 

 q and s have their former signification. 



If we assume that the depressions are proportional to the temper- 

 ature of the wire used, and this will be proved further on, it appears, 

 from these experiments, that the temperature is directly proportional to 

 the square of the electrical densit}^, hut inversely to the magnitude of 

 the surface of the hatterv, or that 



s 

 which is easily deduced from the above table. 



The depression 7i being proportional to the square of the quantity 

 q, with an equal number of jars, the quantity 8 must produce four 

 times as great an effect as the quantity 4. We have for 3 jars (7 = 8, 



h = 17.5 ; q= 4,h=z 4.5 ; then HA rr 3.89, or 4 nearly. For 



4 jars, this quotient is IzlL = 4.4 ; for 5 jars, }1A= 3.77 ; for 6 jars, 



3.2 



= 3.57. The mean of these quotients is 3.9 or very nearly 4. 



9.3 

 3:9" 



Hence, the double quantity corresponds to the fourfold effect. 

 Comparing the effect which the quantity 3 produces with that of 9, 



we get for 4 jars the quotient- ^^-^ — 8.9 ; for 5 jars, l^=z 9.53 ; the 



2 1.5 



mean is 9.4. The triple quantity then produces a ninefold depression. 



Comparing in the same manner the other numbers of the table^ we 

 find that, with an equal number of jars on an average, h is pro- 

 portional to the square of ^. 



The table also shows that the value of q being constant, /< is in- 

 versely proportional to s ; hence, if the same quantity of electricity 

 be distributed over a double or triple surface, the depression is twice 

 or thrice as small. The table, in the mean, gives this almost exactly. 



For s =z 3, (7 riz 4, according to the above table, we have h = 4.5. 

 Substituting this value in the above equation : 



16 



4.5 =. n —5 



hence n = 0.843. 



If in like manner we compute the value of the constant n from all the 

 single observations, that is, from all the corresponding values of 7i, s, 

 and q, of the above table, n is found as a mean to be equal to 0.88. 



