108 



Mil. F. E. SMITH ON THE CONSTRUCTION OF 



divided into centimetres and millimetres, 1 centim. being equivalent to about 0'6 C. 

 Both before and after the observations, the thermometer was calibrated and tested under 

 the direction of Dr. J. A. HARKER, the greatest difference between the mean and the 

 observed values being 0'01 C. All recorded temperatures are on the hydrogen 

 scale, the resistance being expressed in the same units as before. In the tables, 

 those measurements marked with an asterisk were taken when descending the scale 

 of temperature. 



The results are as follows : 



TABLE XL Mercury Standard U, Jena Glass 16 



in 



It should be noted that observations at approximately the same temperature 

 represent, in general, an interval of several hours. Thus at 1771 C. five observa- 

 tions are recorded, but 5 hours elapsed between the first and last of these. The 

 results give thirty-five equations connecting resistance and temperature. Assuming 

 the resistance to be such a function of the temperature that it is expressible in the 

 form Rr = R (l + T + T 2 ), the equations enable a and to be found. 



In evaluating these quantities, twice the weight has been given to the four 

 observations at the ice-point. The three normal equations resulting by the method 

 of least squares are 



(A) 39x + 436-47a -f 7207'9363/j = 0'381818, 



(B) 436-47x -f 7207'9363a -f 133386'3226 = 6'3182355, 



(C) 7207-9363a; + 133386'322a +2670818736 =117122-320, 



where x = R - 0'973576, a = 0'973576a, and 6 = 0'973576& and finally 



