44 A CONTINUOUS RECORD OF ATMOSPHERIC NUCLEATION. 



apertures would requii-e a temperatui-e excess of nearly 30°, which is out of the 

 question. 



7. Pressure decrement. — As none of the explanations are satisfactory, light 

 of a different character may be thrown upon the discrepancy by computing by 

 the approximate method of the earlier memoirs the density ratio, y', of the gas 

 after and before exhaustion, corresponding to the observed values, s\ Since if 

 n is the nucleation, z the order of the corona in a geometric series, b the co- 

 efficient of time loss, t the time intei"V"al between exhaustions, 



log n = z (i + bt) log y, 



the equation corresponding to a different exhaustion ratio would be 



log n' = z (i + bt) log y' 



if the same corona, z, and time interval, t, is implied. 



Hence log n/log w' = log y/\og y', while n={6ni/7ta^) 5' = As\ Therefore, 

 log y'/ log j'=(log A +3 log 50/ (l og A + 3 log s). 



The computed values s = a)^'nn/6'm are given and in the chart, figures 

 I and 2. From the latter for 5 = 5.0, 5' = 8.o to 9.0 cm. From the earlier 

 memoir,' the value computed for y was .819. Hence 



s' = %, y = .8o7, 



5' = 9, y = .8o4, 



whereas 3;=.8i9 was the value computed in my work on coroijas for the ex- 

 haustion 76-58 cm. 



Since, roughly, y= {p/poY^^, where ^ = 76 and ;/ = 1.4, the following 



values of 6p obtain : 



5 = 5.0 cm., Sp= 18.0 cm. 



s' = &.o 19. 1 



5' = 9.o 19.4 



Thus if the pressure decrement on exhaustion had been taken i cm. higher 

 than the observed value, the apertures comptited from successive exhaustions 

 in the former meinoir would agree with the average apertures directly measured 

 in the present paper. Observation ally this is out of the question, but it is 

 nevertheless difficult to know just what pressvu-e is effective in the adiabatically 

 cooled receiver (cf. Structure of the Nucleus pp. 35, 38), since neither the 

 isothermal nor the adiabatic conditions will rigorously suffice. The memoir 

 shows that isothermally y=.'j 64; adiabatically 3/ = .82 5; adiabatically with 

 allowance for condensed water ^=.819, as already specified. The aperture 

 data deinand ^ = .805, which is even nearer to the isothermal y than the value 

 taken. 



Incidentally one may note the precision with which y must be entered or 

 the pressure difference determined, if the observations are to be sufficiently 

 close to admit of a computation of d and n. In other words, it is probable that 

 the ratio y may be determined with greater accuracy from the successive aper- 



' Structure of the Nucleus, Chapters III and IV. 



