46 



Colorado College Studies. 



dimensional. In this case it is necessary to consider only a 

 section, such as AC (Fiji;. 6). 



FIG. 6. 



Suppose under certain conditions a certain motion exists 

 at B. If the fluid is perfect a certain amount will flow into 

 the parallelogram J. C across the line ^£', due to the accelera- 

 tion of the velocity u. ED represents the whole increase 

 of inflow at E over that at A. 



But 



ED=AB-DC. 



= — , II beiner the velocity across 



DC u ^ 



AB, and u^ that across DC 



AB-DC n'-u 



±>y composition = 



AB u^ 



which reiDresents the distance of inflow at E when a unit 

 length of AB is considered. The time of inflow is di, hence 



AB—DC _ u'—u 

 ABclt ~ u\lt 



gives the rate of displacement in the direction of .v. 



iL/^^~"\=l/^l_ii\= ^ 



at 



di 



u + du 



dt\ ?r 



1 Ti /, dii , <lii^ du^ , d?t* , \n 

 =—1—1 1 -H etc. 



dtV. \ u n' 11^ u* ;J 



1 /du dn'^ , du^ dii* 



— 1 1- etc 



dt\ u u^ it'' it* 



Since this series converges very rapidly, unless the in- 



