Prof. H. L. Callendar on Platinum Thermometry. 213 



As an illustration of the method of reduction by the differ- 

 ence-formula, it may be of interest to reproduce a table 

 exhibiting in detail the complete calculation of such a table of 

 reduction for the standard wire employed by Dewar and 

 Fleming. We select for this purpose the following corrected 

 data, taken from their paper in the Phil. Mag., July 1895, 

 p. 100. 



Thermometer in Melting Ice, B,° = 34059, t = Q°Q. 



„ Steam at 760 mm., R / = 4'2034, £ = 100° C. 



Liquid Oxygen, . R" = 0'9473, t- -182°'5C. 

 From these data we deduce : — 



Fundamental Interval, R' -P° = 1-0975. 

 Fundamental Coefficient, (R'-B, o )/100R° = -003533. 

 Fundamental Zero, y=l/c=283°'00. 

 In Liquid Oxygen, 



p t=-W6°'7, f=-182°-5, B = t-pt = U°'2. 

 Difference-Coefficient, d = I>/p(t) = U'2/5'lQ = 2'75. 

 Difference-Formula, D = *-/?* = 2"75(*/100-l)*/100. 

 To find the difference-formula in terms of pt, we have 

 similarly, 



Difference-Coefficient, d' = D/p(pt) = 14'2/5'84 = 2'43. 

 Pt Difference-Formula, D' = *'-7rt = 2-43(p*/100- 1)^/100. 



As a verification we may take the observation in solid C0 2 

 and ether, assuming Regnault's value t= — 78 0, 2 for the true 

 temperature. 



Difference-Formula (D) gives, t-pt=2'75 x 1-39 = 3°-82. 

 „ „ (D ; ) „ /'-^ = 2-43xl-49 = 3°-62. 



The observed value of ptis given as — 81 0, 9. Thus the 

 two formulae give, (D) f=s-78°-l, and (D') ^=-78°'3, re- 

 spectively. 



The following Table shows the comparison of the formulae 

 for every ten degrees throughout the range. The first three 

 columns contain the whole work of the calculation for formula 

 (D') . The second column contains the values of D' calculated 

 by the aid of a small slide-rule. These when added to the 

 values of pt in the first column, give the values of t shown in 

 the third column. The fourth column contains the correspond- 

 ing-values of the difference in t for 1° pt, obtained by differen- 

 tiating the difference-formula. These are written down by 

 the method of differences. The fifth column contains the 

 difference t — t' between the values of / deduced by the two 

 formulae. The sixth contains the values of t by formula (D) ; 

 and the seventh is added for comparison with the table given 

 by Dickson (Phil. Mag., June 1898, p. 527). 



Phil. Mag. S. 5. Vol. 47. No. 285. Feb. 1899. Q 



