182 Dr. Young's Hydraulic Investigations. 
of the surface of the margin of the wave is indifferent to 
the calculation, and it is most convenient to suppose its in- 
clination equal to half a right angle, so that the accelerating 
force, acting on any thin transverse vertical lamina, may be 
equal to its weight : then the velocity y must be such, that 
while the inclined margin of the wave passes by each lamina, 
the lamina may acquire the velocity v by a force equal to its 
own weight ; consequently the time of its passage must be 
equal to that in which a body acquires the velocity v, in fal- 
ling through a height b, corresponding to that velocity : 
and this time is expressed by ^ ; but the space described by 
the margin of the wave is not exactly z, because the lamina 
in question has moved horizontally during its acceleration, 
through a space which must be equal to b ; the distance ac- 
tually described will therefore be z ± b, and we have 
z + b = av ± by — bv — ip 2 by, y + % vy — a — 
~~ T> {y + * v ) 2 — ^ + 76’ but, m being the proper coeffi- 
cient, v = m v' b, and v* = m'b, ~ -{- jj= m' y = 
m ^ r 6 j±i v > and y+ v - m V (f+ rs) +£?• But when 
v is small, we may take y X v nearly m </ -, and % = ~„ x/ u 
J J V 2 rn^{\a) 
— v/ [sab), and x = a ±\/ (gab), while the height of a fluid, 
in which the velocity would be y t is nearly a + | y' (2 ab ) : 
consequently, when the velocity v is at all considerable^ must 
be somewhat greater than the velocity of a wave moving on 
the surface of the elevated fluid ; and probably the surface 
of the elevated portion will not in this case be perfectly hori- 
