348 NEWTON S PRINCIPIA. 



Hence, by D Alembert s principle, and the formula for hy 

 drostatical equilibrium, 



Let V be the velocity of the fluid, then since 



dt 



h 



d t* &quot; ds dt 

 = y^4 JlL 



T | I 7 , 



d s d s d t 

 Hence, substituting and integrating, 



an equation that will be necessary to us further on. 



This integral is obtained by summing all the elements 

 along any one curve, and C is therefore constant only 

 along one curve, and may vary from curve to curve. To 

 determine its variations we must have data given whereby 

 we can know its value for all points along some surface 

 cutting all the curves. Further it is manifest that these 

 curves may change with the time ; C is then a function of t, 



The motion is said to be steady when the motion is al 

 ways the same at the same point. Hence in this case 

 neither &amp;lt;p nor C are functions of t. And the equation be 

 comes 



The equation of continuity may also be greatly mo 

 dified by the introduction of &amp;lt;p. If the fluid be incompres 

 sible, we have 



