a Cloud farmed by Expansion of Moist Air. 191 



In conjunction with the size of a single drop, as found from 

 the rate of fall of the cloud, it gives the number of drops in 

 unit volume and so the number of the ions which form the 

 nuclei of the drops. In making the calculation Prof. Thomson, 

 following C. T. R.Wilson, makes the assumption that the air 

 is cooled down to the full extent by the adiabatic expansion 

 before the drops begin to form. Then condensation proceeds 

 and the latent heat liberated warms the air until the density 

 of the remaining vapour is such as to saturate the air at the 

 increased temperature. This process is, of course, irreversible. 

 There is no reason to doubt that it represents closely the 

 actual experimental conditions ; but with a view to estimate 

 the amount of error which would be introduced by a small 

 departure from the assumed process, it seems of some interest 

 to calculate, for comparison, the result of the other extreme 

 assumption, viz., that the expansion and condensation exactly 

 keep pace with each other, the density of vapour at each stage 

 being the saturation-density .corresponding to the instan- 

 taneous value of the temperature. In this case the process 

 would be reversible, and we can equate the initial and final 

 values of the entropy of the combined mass of air and water- 

 substance. Since an irreversible change is accompanied by 

 an increase of entropy, it is easy to see that on the new 

 assumption we shall arrive at a lower value for the density of 

 the remaining vapour and higher value for the mass of water 

 in the cloud. 



In both cases the solution is most easily obtained by a 

 graphical method. We plot a curve connecting the vapour 

 density p and temperature t at any stage of the condensation, 

 and find where it intersects the curve representing the 

 maximum density of saturated vapour at different tem- 

 peratures. In the irreversible case the former curve is the 

 straight line. 



P = 



P--™(t-UV; 



where (using the notation of the authors quoted) p 1 is the 

 initial saturation density, <v the expansion ratio, t 2 the calcu- 

 lated temperature after adiabatic expansion, M the mass of 

 unit volume of air after expansion, C specific heat of air at 

 constant volume, L latent heat of the vapour. The heat- 

 capacity of the drops is neglected in comparison with that of 

 the air. For the reversible case the equation of constant 



* Equation (2), loc. vit. 



