i8 6 
Dr. Young’s Hydraulic Investigations . 
in a horizontal direction will be to its weight as b to c ; and 
the space d, through which it moves horizontally, while 
half the wave passes it, will be such that (c — d). (a -f- ■§■ b) = 
ac, when c e d — ~~ry But the final velocity in this space 
is the same as is due to a height equal to the space, reduced 
in the ratio of the force to the weight, that is, to the height 
2 ~ b y b , and half this velocity is \ m \/ (- y q J, which is the 
mean velocity of the lamina . In the mean time the wave de- 
scribes the space c -f~ d, and its velocity is greater than that 
of the lamina in the ratio of ~ -J- 1 to 1 , that i(j *£±6 + t 
?n 
a + b 
or r -j- 2 to i, becoming™ (£ + i) v (2 „ + t, - ■» v(jg+t) , 
which, when b vanishes, becomes m \/ as in Lagrange’s 
theorem, and, when b is small, m 1 1 / - 4- ~ -/•;- • b — if) , or 
m ; ^ ut if a were small, it would approach to m b, 
the velocity due to the whole height of the wave. 
