THE 

 LONDON, EDINBURGH and DUBLIN 



PHILOSOPHICAL MAGAZINE 



AND 



JOURNAL OF SCIENCE. 





[SIXTH SERIES.] 



JUL Y 1914. 



I. Notes on Hydrodynamics. 

 By Professor A. Gray, F.R.S* 



I. Equations of Motion for any Axes. Theorems of Cir- 

 culation. Proof of Constancy of Moment of Vortex- 

 Filament. 



1. 4 T time t the equation of motion along a stream-line 

 JTJL in a perfect fluid is 



oq t 07 , dV 1 op n /1X 



Ot OS OS p OS 



where p is a function of p. 



For the first two terms are the acceleration along the stream- 

 line at the point considered, P say, and the third and fourth, 

 with their signs changed, make up the force per unit volume 

 due to the field of force for which the potential at P is V, 

 and to the gradient of pressure op/os. 



Integrating along the stream-line from a chosen initial 

 point P to P as a final point, we obtain 



Ru+i(</-</)+v-v + r^=o. . . (2) 

 jjt p p„ p p„ j p p 



* Communicated by the Author. These Notes are founded on a paper 

 published in the Trans. R. S.E. 1908, but the subject is presented in an 

 improved manner, and much of the matter is entirely new. 



Phil. Mag. S. 6. Vol. 28. No. 163. July 1914. B 



