Determining the Mechanical Equivalent of Heat* 163 

 and let - per cent, be the maximum accuracy of result obtain- 



x 

 able under these conditions. 



Since 6=a:<d, 



and t = xT, 



and the ratio of heat lost to heat received is 



we have „ ® m 



M.x® = I00? 

 or 



100^' 



x 2 - 



2M 



lOOS.e.T' 



(1) 



We also know, say from preliminary experiments, that the 

 heat received in calories is about 0*24 time the energy in 

 watt-seconds. 



M«©=0-24W#T, 

 or 



M0 = O-24WT (2) 



In equations (1) and (2) M and x are the only unknown 

 quantities, for S is a function of M depending on the shape 

 of the vessel containing the water. Thus for a cylindrical 

 vessel of height equal to its diameter, 



S = 5-53M* ; 



while for a spherical vessel, 



S=4-84Mi 



We can therefore find both M and x from the equations, and 

 since 



= x&, 



and t = xT y 



6 and t are also determined. 



It may be observed here that as S varies as M 3 , and x 2 



M 



varies as -~, x is proportional to the 6th root of M or to the 



6 th root of W. Hence if the number of watts available is 

 doubled the accuracy of the experiments is by no means 

 doubled, but is only increased by about Jth. 



In the particular case for which the apparatus was designed 

 the number of watts available was about 300, the maximum 

 current being 30 amperes. This determined the resistance 

 of the coil or strip as \ of an ohm. 



M2 



