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 different (resistance-) thermometers. 



4) dit = JT'X/) 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'^.— To) 

 by an amount 



A -f BAi 

 dt = dit + d.it + ^3/ + ^4^ = + C + W 



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

 temperatures is therefore 



Cj- Ci _ Ao-\- dt _ Ao 1 

 Co Ai Ai Ai 



'A + 5AA 



from which 



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

 family of straight lines of slope 



Co - ci B 



from which {co— Cij/co 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 T-i, 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 tepiperatures. 



The measurement of the changes in Ai= Ti— T'l, or A2= T'o— To, 

 by determining the difference Ri— R'l, or R'2— Ro, between a pair of 

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



