272 Prof. "R. Clausius oh the. Determination of the 

 and consequently 



Putting now, in equation (20), for -r-^-, the expression 



here found, whose last term gives in the integration, we 

 obtain 



In the two expressions (19) and (21) of Hi and n 2 the first 

 term arising on the resolution of the brackets agrees with the 

 expression of IT given under (14); hence we can write : 



n - n -4^W + ^->'> ^ 



If we now form, corresponding with equations (13), the 

 equations 



*>^-& (24) 



B rfF 



and if ; in these, for II x and n 2 we employ the previously given 

 expressions, in which the terms added to II do not contain the 



velocity-components -=-, -^ , and ~, and hence give on dif- 

 ferentiation with respect to these quantities, we obtain for 3t\ 

 and 3E 2 the expressions given under (11) and (12). 



For abbreviation, simple symbols may be brought in for 



those additional terms independent of -A -y-> and y , by put- 

 ting dt dt dt 



