132 



Prot. H. L. Callendar and Mr. H. T. Barnes. 



The full curve in fig. 2 represents this difference-term on a scale of 

 2\ cm. to 1 millivolt. The crosses represent the results of actual 

 observation at the different points. The mean difference of the 

 observations from the curve, if we except those at 30° C, is only 

 three-hundredths of a millivolt. The observations at 30° C. differ by 

 more than one-tenth of a millivolt, and those at 40° C. by a whole 

 millivolt from the simple parabolic curve. These differences cannot, 

 we think, be explained as being due to errors of observation. This is 

 proved by the accuracy with which the cells returned to their 

 original values at 15° C, and also by the agreement of the twenty or 

 thirty different readings at each point. Moreover, the observations 

 have been repeatedly verified by others, not shown on the curve, 

 with celLs of different types, to within one or two-hundredths of a 

 millivolt. We conclude that no simple parabolic formula can be 

 made to fit the observations throughout the range 0° to 40° 0. Over 

 the range 0° to 28° C, however, the differences, even if real, are not 

 of great importance, and we may take the formula, 



E< = E 15 -0-001200 (£-15) -0-0000062 (*-15) 2 , (L) + (P) 



as representing the temperature-variation of the E.M.F. of these cells 

 within about one-twentieth of a millivolt between these limits. The 

 symmetry of the curve shows that we may take the very convenient 

 round number 1*200 millivolt, for the change of E.M.F. per 1° C. at 

 15° C. 



Taking formula (P), we find for the temperature-coefficient at t° C, 



d/dt (E,/E 16 ) = -0-000837-0-0000087 (i-15), 



and for the mean temperature- coefficient between t° and 15° C, 



(E,/E 15 -l)/(£-15) = -0-000837-0-00000-43 (t - 15). 



It is generally, however, more convenient to use the formula (L-fP). 

 Between the limits of 12° and 18° C. we may use the simple linear 

 formula (L), without risk of making an error greater than one- 

 twentieth of a millivolt. If, however, we were to use the temperature- 

 coefiicient 0"00076 (which is very commonly taken) over the same 

 range, the error might amount to nearly three-quarters of a millivolt. 



§ 16. Results of Previous Observers. 



The formula given above for the temperature- coefficient differs 

 from that of previous observers chiefly in the direction of making the 

 change of E.M.F. more nearly uniform. 



Lord Rayleigh* tested two cells under similar conditions of slow 

 temperature change. For one cell he found the temperature-coeffi- 

 cient^ at t given by the formula 0'00083 + 0-000018(£-15), which 

 * 'Phil. Trans.,' vol. 176 (18S5), p. 794. 



