Steam of Maximum Density. 183 



It may also be shown from the general formula, on putting 

 AlogP^log^that 



i_!f 



i t> i — § — = t— =e fc* =10 =10 «+' nearly. 



logP^-logP^_! la? J 



By taking the ratios of two consecutive differentia] coefficients 

 of log P corresponding to the temperature t—^ and t + \, 

 we get 



d.togP^ \a + t-i) ' 

 but 



d.\o S V t+i _ A log P,+i- A log P, ,. 



rf.logP^ A log P,_ A log RTi y ^ 



consequently 



AlogP, _/ fl + * + i \-i 

 AlogP,_! V« + /-i/ ' 

 the last being a formula which gives the ratio to one another of 

 consecutive values of A log P^ with great accuracy. 



A log P* 



Equating the two values thus obtained of -^ — ~ — , we get, 



on taking common logarithms, 



1 1 , a+t+i 



= —7- com los: 



a + t k °a + t—± 



, i a+t+l 



If Q be taken to represent A log P, so that 



Qo=log£, Q! = l0g& Q, = l 0? ^i, 

 r r l *t 



we shall have, according to what has preceded, 



Q, _ log P <+1 -logP; _ in -^_/ fl + * + '5 \4 

 Q#-,"logP,-logP,_r- 1U \a~+7^) ' 



If, according to the former of the two equations, we take suc- 

 cessive values of -~~ differing from one another by intervals of 

 Ht-i 



a unit of temperature, we have 



By multiplying together the quantities on the same side of these 



