( 195 ) 



^=aT -f hlog T+ c, 



where 1 represents the absolute temperature, [)roved absolutely 

 useless. 



cl. We have tried to obtain a better agreement with the observa- 

 tions by means of a formula of five terms with respect to powers 

 of /. To this end we have tried two forms : 



'^='w, + \m) ^Inoj +\m) +\w,) ■ • • <^) 



and 



^="100 + ^1100; +IÏÓ0J +lïööj +\m)- ■ ■ <^^ 



First the constants of the two equations are determined so that 

 the equations satisfy the temperatures — 59°, — 140°, — 159°, — 183° 

 and — 213°. (^1) indicated at — 253° a deviation of 113.1 micro- 

 volts, (B) a deviation of 91.8 microvolts. We have preferred the 

 equation (B) and then have sought au equation [BIY) which would 

 represent as well as possible the temperature I'ange from 0° to —217°, 

 two equations (^1 and ^III) which would moreover show a not too 

 large deviation at — 253°, for one of which (Bill) a large deviation 

 was allowed at — 217°, while for the other (Bl) the deviations are 

 distributed more equally over all temperatures, and lastly an equation 

 (i^II) which, besides —253°, would also include —259°. 



§ 12. Calculation of the coefficients in the formula of five 

 terms. The coefficients have first been derived from 5 temperatures 

 distributed as equally as possible over the range of temperatures, 

 and then corrected with respect to all the others without a rigorous 

 application, however, of the method of least squares. 



In order to facilitate this adjustment we have made use of a 

 method indicated by Dr. E. F. van de Sande Bakhuyzen in which 

 instead of the 5 unknown coefficients 5 other unknown values are 

 introduced which depend linearly on the former ^). For these are 

 chosen the exact values of E for the five observations used originally, 

 or rather the differences between these values and their values found 

 to the first approximation. 



Five auxiliaiy calculations reveal to us the influence of small 

 variations of the new unknown value on the representation of the 

 other observations and by means of these an approximate adjustment 



') Also when we rigorously apply the method of least squares this substitution 

 will probably facilitate the calculation. 



