METHODS AND APPARATUS. 29 



The body-temperature would then be expressed by the formula : 



Tu=T -BF 

 in which 



Tu = unknown temperature 

 To = oven-temperature 

 B = potentiometer balance 



F = factor showing relation between potentiometer balance and 

 temperature difference. 



Assume in an average case: T = 40 C, B = 32, and F =0.094. This 

 will give for Tu a value of 40-0.094 X 32 = 37 C. 



The precision of the various factors is determined as follows: T is the oven 

 temperature as read during the course of an experiment, and has been shown 

 in a previous paragraph to be expressed by the formula : 



T = A+KR . 

 where 



A = zero point of thermometer, which has been determined to at 



least 0.01 C. 

 K = 1.01 = constant 

 R = reading, taken to the nearest 0.01 C. 



B, the potentiometer balance, is determined in the last place by deflection, 

 which is read to the nearest half-division. The sensitiveness of the galva- 

 nometer in this case is such that a deflection of 1 division corresponds to a 

 change in B of 0.072 ohm. Hence the average deviation in B is 0.036 ohm. 



F is obtained by calibration. In calibrating, the following data are ob- 

 tained: To i, the oven temperature, which may be taken as 40 C; Tf h the 

 temperature in the calibrating flask, for instance, 37 C; and B h the potenti- 

 ometer balance, 32. From these the quantity F= (ToiTfo) -i-Bi is com- 

 puted. In calibrating, the temperatures are taken more precisely than in an 

 experiment, and this involves not only a closer reading, but a better deter- 

 mination of the zero point of the thermometers. As a matter of fact the 

 reading is taken to 0.002 C; and the zero known to 0.003 C. Therefore we 

 may say, similarly to the above, To^ =A'+ K'R' and Tf, =A" +K"R", where 

 A' and A" are known to 0.003C; K' and K" are constants; and R/ and R" 

 are known to 0.002C. B h like B, is known to 0.036. 



The complete expression for the unknown temperature is then as follows: 



Tu = A+K R -B {A ' +K ' R ' ) - (A " + K " R " ) 



B\ 



The average deviations of the variables are : 



A, a.d. = 0.01; R, a.d. = 0.01; B, a.d.= 0.036; A', a.d. = 0.003; 

 R', a.d.= 0.002; A", a.d. = 0.003; R", a.d. =0.002; B h a.d. =0.036. 



The constants K, K', and K" each have the value 1.01. 



