THE 73° CALORIE. 379 



3) dst = C{f, i) Due to differences in the temperature rise pro- 



duced by the thermometric measuring current 

 in the dift'erent (resistance-) thermometers. 



4) dit = ir(/) Due to the heat-equivalent of the work of 



forcing the water through the tubes. 



These errors will influence the quantity Ao= {Ti— T'l) — {T'2— T2) 

 by an amount 



A + BX 



dt = dif + 34 -I- ^3/ + ^4/ = -. + C + Tf' 



The true value of {co— Ci)/c2 in terms of the flow and the measured 

 temperatures is therefore 



C2- Ci _ X+ dt _ ^ 1 

 c-2 iAi Ai Ai 



from which 



'A + /iAA 



Ao= {-^-^ - - ) Ai- - - 6' - W 



If Ao and Ai be regarded as variables, this equation represents a 

 family of straight lines of slope 



Co — ci B 



from which (co— Ci)/c2 may be obtained by varying the parameter/. 

 If B is small, / need not be accurately known (in the work to be de- 

 scribed the B/f correction was of the order of .001). The ratio 

 (c2— Ci)/c2 has been assumed constant over the range of temperatures 

 employed. This assumption, not hazardous in the first place, is ex- 

 perimentally justified if the data for any one flow lie on a straight line. 

 That this was true within the limits of error of the data presented 

 below, appeared from the preliminary tests. 



The temperatures Ti and T2, which are not changed, have no in- 



' fluence on the changes in Ai or Ao, and are mere auxiliary temperatures. 



The thermometers at these temperatures serve only to balance the 



bridge, and to compensate automatically for any slight changes that 



might occur in the water supply temperatures. 



The measurement of the changes in Ai= Ti— T'l, or Ao= T'o— T2, 

 by determining the difference R\— R\, or R'2— R2 between a pair of 

 similar thermometers, to the required accuracy of one per cent, is not 



