872 Mr. S. D. Wicksell on 



And finallv we get 



+ (14</> 4 -21^ 2 -6^ + 26 4 ) t z/ 4 + . . . . ]. . (3) 

 For the ideal gas we have 



and we see that the series 1-f </>z/+ .... can, according to 

 the nature of the constants, have no value equal to zero. 

 Accordingly, we have a right to invert the series, and thus 

 we get 



-(^) 4 (5^-10^ 2 -4^ 3 + 6 4 )P'----l • (4) 



The following numerical examples will illustrate the 

 magnitude of the different terms. 

 For carbon-dioxide we take at 0° C, 



o=0'011 



b^0'003. 



(All values are, when nothing else is stated, taken from 

 the work Die Zustandsgleichung by Prof. Dr. Kuenen.) 

 Then (4) becomes 



P V = 1-0-008P-0-00005P 2 -0'000003P 3 . 



For ethylene we take at 20° C. 



a = 0-00786 

 6=0*0024, 

 and get 



P v = l-073-0-0050P-0-000017p 2 -0-00000011P 3 . 



The results are given by the following table : — 



P. P 00050. P 2 0-000017. P 3 0-00000011. Py. Pi;, from (1). 

 31-9 0-16 0-02 0-003 0-89 0-89 



45-8 0-22 0-04 0-01 0*80 0-78 



It is seen that at 30 atmospheres we need not go farther 

 than to the second power of P in order to obtain a value ot 

 Pv with two decimals. It is furthermore seen that for 

 relatively low pressures, generally as high as 5 atm v the 

 second power of P can be neglected, if we want Vv given 

 with three decimals. 



