1904.] Cotton ~by Water and ly Water Vapour. 247 



was more than one determination. The curves for earlier series are 

 similar, as far as they go. The absorption occurs rapidly at first, and 

 proceeds with diminishing velocity, but the evidence does not point to 

 even practical finality being reached for many days, and there is no 

 theoretical limit to the process. Like the 6 curve, that for dm/dt 

 would evidently show an asymptotic approach to the t axis. For 

 comparison, the complete 9 curve for the 12-hour experiment of the 

 series is shown on the same plate (B) as the m curve (A). It is very 

 evident that the moment of maximum temperature marks bub a small 

 advance in the progress of absorption, and that the heating effect of 

 the latter must be continuous throughout, and would continuously raise 

 the temperature if not counteracted. 



Relation of the Temperature, I'ime, and Absorption Values, 



The net rate of gain or loss of heat by the covered thermometer at any 

 moment must depend upon both the rate at which it is receiving heat 

 from the vapour condensation, and the rate at which it is losing heat 

 by radiation, convection, and conduction. If it be assumed (1) that 

 the heat received is directly proportional to the weight of moisture 

 condensed, (2) that the rate of loss of heat due to the above causes 

 is directly proportional to the difference of temperature between the 

 thermometer and its environment (assumptions which the results will 

 justify later), it follows that 



dm/dt = cO + kdB/dt (IV), 



where m, t, and have the same significance as before; c is the 

 normal heat loss by the covered thermometer, due to radiation, etc., 

 per unit 6 per minute ; k is the heat capacity of the same, i.e., of the 

 cotton and that part of the thermometer which is directly affected ; 

 and the unit of heat adopted is that quantity which is rendered 

 available by the absorption of 1 milligramme (unit m) of moisture by 

 the cotton. 



tFrom Equation (IV) it follows by integration that m = c\ 6dt + kO, 

 for brevity, 

 m = cA + *0 (V), 



a result which is manifest when it is considered that the total heat 

 received by absorption from the beginning of any experiment up to 

 any stated time is represented in part by the total heat lost within that 

 time, and in part by the amount still retained by the covered ther- 

 mometer in excess of its original heat contents, and also that the total 

 heat lost is proportional to the average and the whole time, the 

 product of which is A. 



It is evident that, while c is a constant (by hypothesis) throughout 



