SPECIFIC HEAT OF AMMONIA. 343 



The initial value of the equalized temperature is known by the 

 intersection of the initial line with the time ordinate through the point 

 where the heater was switched on, and the above procedure gives the 

 final value; the difference of the two is the "observed temperature 

 change." It remains to correct this observed temperature change for 

 the heat transfer to the surroundings and for the heat due to stirring, 

 during the time of the heating period. Two assumptions are made: 



1. That the rate at which the mercury changes temperature due 

 to heat transfer to the surroundings is proportional to the tempera- 

 ture difference. (Newton's Law of Cooling.) This may be written 



ddr/dt = K (da - e) 



(Wr being a change of temperature due to heat transfer alone, K, the 

 modulus of thermal leakage, assumed constant for any one measure- 

 ment, da, the temperature of the surroundings, assumed constant for 

 any one measurement, and d, the actual temperature at any instant 

 of the mercury. 



2. That the rate of temperature change due to stirring is constant 

 throughout any one measurement. This may be expressed 



dds/dt = X = a constant. 



where dds is a change of temperature due to stirring alone. 



Since all temperature measurements are made in terms of resistance 

 instead of in degrees, it is convenient to rewTite these two ecjuations 

 in terms of R rather than 6. 



dRr/di = /.• {Ra - R) (7) 



dRs/dt = X, a constant. (8) 



R being the resistance corresponding to the temperature of the mer- 

 cury at any instant. The sum of these two rates, given by (7) and (8), 



■ — - -\ ), represents the rate at which the temperature is changing 



dt dt J 



due -to heat transfer and stirring alone. Calling this sum, (-7^), we 

 have 



^\ = (kRa + X) - kR (9) 



wliich is the differential equation of both the initial and final lines, and 

 moreover gives the "cooling rate" during the heating period. This 

 equation may be integrated to give the "cooling correction." To ob- 



