of Iron and German Silver. 495 



ference between the temperature of the middle of the rod and 

 that of the surrounding air was not perfectly constant, as it 

 should have been according to the theory, but that variations 

 occurred which might have for their consequence deviations of 

 half a degree from the mean value. It may be that the cause of 

 this is to be sought in the non-accordance of the bases of the 

 theory with what takes place in reality, or in the place where the 

 middle wires were soldered to the rod not coinciding exactly 

 with its centre. But in this case there would necessarily have 

 been a certain regularity in the variations, which, hov/ever, was 

 not observed. It is therefore probable that they were occasioned 

 by air-currents, which, notwithstanding all precautions, could 

 not be entirely avoided. 



Each series of observations consisted of an even number of 

 readings .^Jq, ^i, . . . s.2n_i, which were made in regular intervals of 

 time 8 = 15", the first of which fell on ^o = 45". In order from 

 these observations to calculate the value of jo according to equa- 

 tion (13), it appears the simplest to form the differences {sq—s^)j 

 (^i — ^2)^ (^a — '^3)? • • • ^^d to divide these by one another. A little 

 consideration, however, shows that herein the unavoidable 

 errors of observation must have a very important influence 

 on the result. The following treatment leads to more accurate 

 results. 



If we first form the differences 



we obtain a series of equations of the form 

 Sq-s^ =Q[e-P^^e-P^-), 

 Si-Sn+i = Q [e-P'o - e-P'n) e-P^, 

 ^2 - ^n+2 = Q [e-P^ - e-P^n) e'^ps, 



If we take the logarithms on both sides and denote log(5Q— ^„), 

 log [s^ — Sn+i), • • . by »?Q, nijf . . . and for abbreviation put 



log Q(e-^o _ e~P^n) — Xy log e'P^ = y, 



there result equations of the form 



m^ = x-\~2y, 



from which, by the method of least squares, x and y, and with 

 them p and Q, were found. With the aid of these values we 



