386 Prof. R. Clausius on the Theoretic Determination of 

 written in the following order — 



fe iv K J 80 \iv + y W+y/ 



it changes, if for 27 7/ '80 and IT we put the values given under 

 (7) and (8) and then again reduce, into the following: — 



W __ (W-w)(2Ww + yW + yu) (Q , 



g w ~~ Vfw(W + w + 2j) W 



To this equation we will now apply the equation 



*=i° g J, (io) 



and the equation resulting from it, 



W=«*^ (11) 



by which we get 



A ~^ 1 V[a/( 6 + l) + 2 7 ] 5 

 or, differently written, 



X = q- g -M 2"> + 7(l + «- A ) . . t (12) 

 A ^ * ^tc(l + «- A ) + 27^' ^ ; 



This equation can easily be resolved with respect to w, and gives 



™=V X -2 + (\ + 2)e-* '> ( 13 > 



and from this, according to (11), it further results immedi- 

 ately that 



1 —2\p- K — e~ 2X 



If the quantities w and W are once calculated, equation (8) 

 can be employed for the calculation of the quantity II. But 

 if we wish to represent II as a function of X, we must put for 

 w and W in (8) the expressions given under (13) and (14); 

 we then get, after some reductions : — 



r ^_ 2 + ( x + 2)^].[(l-ry-^] 



y{l-e- k )(l-2\e- k -e~ 2k Y ' * K } 



For the determination of the last quantity, 0, it follows 

 from (7) that 



fl_27 7 W2fl(W + K> + 27) 



8 (W + 7)V + y) 2 ' ' * ' * V») 

 and if in this we insert for w and W their values from (13) 



