in a mass of Liquid in a state of Steady Motion. 109 



where z is the elevation of Q above some given datum level, 

 and w is the weight of a cubic foot of water. Differentiating, 



w g 



for the head at P, where Bz, being the elevation of P above Q, 

 is given by 



&z = PQ. cos<£, 



where <j> is the angle PQ makes with the vertical. 



But if we imagine a small cylinder described round P Q as 

 an axis and consider its equilibrium, it is clear that 



2 



8p .ot = — ".. — a. PQ — iv . a. PQ . COS d>, 

 9 P 

 where a is the sectional area of the cylinder, and p the radius 

 of curvature of the lines of motion at P Q. Combining this 

 with the former equation, we get 



9P 9 ^ ip fQJ 



Now it is already known that, if through a given particle A 



lines be drawn through B and C, two particles very near to A, 



such that A B and B C are at right angles to each other at the 



instant considered, then the mean angular velocity of these 



lines is the same in whatever direction they be drawn through 



A, and is equal to the angular velocity with which a small 



cylindrical element described round A would rotate if supposed 



suddenly solidified, which mean angular velocity may hence 



conveniently be called the molecular rotation. In the present 



v 

 case - is the angular velocity of the tangent, that is, of a line 



