OF THE MOTIONS OF FLUIDS. 323 



-T-g* as well for the parts lying without the sides of a sup- 

 posed prismatic canal, as for the parts contained within it, 

 the inclination of the surface being the same without as 

 within those limits, and the fluxion of the height being in 

 the same proportion to that of the length a*, notwithstand- 

 ing that the pressure in one direction is derived, for the 

 extreme parts, from the surface of the collateral portion 

 of the wave : consequently the force, as referred to the sur- 

 face of the fluid, will still be expressed by —JLgy, It will, 



however, be modified by the depression attending a pro- 

 gressive motion, necessary for preserving the continuity of 

 the fluid, which must obviously be such that — 3^ may be to 



Sx, the progressive velocity, as y to x, and 5^ m "-^Sj ~ : and 



the accelerative force -/- a, considered with regard to its 

 da* ^ * 



efibct at the surface, will be modified in the same proper- 



d?/ 

 tion as the velocity, so that instead of -p^, it will become 



— ..^LadLzz. 4~9yy consequently the joint acceleration of 



the surface will be (-rr~i tAqV' ^ow -7-4 ^7r~, 



\dx^ xdxr-^ da2 2r* 



(194) which is the reciprocal of the diameter of the circle 



of curvature, and — |- is the reciprocal of x -r-, the height 

 xax ay 



of the intersection of the vertical line passing through the 



centre of divergence with the perpendicular to the surface 



of the wave, which will be very great in comparison with 



the diameter of curvature, when the distance from the centre 



Y 2 



