Hydraulic Invest' M0 



Sil w rSrJ fc w and ' callmg ^ + ^35 



* = ,/•— ^ / V) : anc * m tne samc manncr / 1S found, 



for the second case, equal to 77-;-^ — 7 4- — 7— . For ex- 

 1 cr (y ■+■ v) d 



ample, suppose the height a 2 feet, b — 1, c = 1, and con- 

 sequently e = 1, then d becomes \ y i» = 4, andy = 8; and 

 in the first case z = . 1, and in the second % = . 14. 



Iff, the velocity of the obstacle, were great in com- 

 parison with m \r 7 , the velocity of a wave, and the space c 

 z 



below (he obstacle were small, the. anterior part of the ele- 

 vation would advance with a velocity considerably greater 

 than the natural velocity of the wave : but if the space below 

 the obstacle bore a considerable proportion to the whoie 

 height, the elevation z would be very small, since a mode-, 

 rate pressure would cause the fluid to flow back, with a suf- 

 ficient velocity, to exhaust the greatest part of the accumu- 

 lation, which -would otherwise take place. Hence the ele-. 

 vation must always be less than that which is determined 

 by the equation m ^ zc == ev 3 and z is at most equal to 



(At*- \ = ~ b', but since the velocity of the anterior margin 



x 

 of the wave can never materially exceed m */ , especially 



*t 



x a 



when % is small, and ^ •- being in this case nearly ^/— -f- 



which, multiplied by z; shows the utmost quantity of the 

 fluid that can be supposed to be carried before the obstacle. 



Supposing I) — I a, this quantity becomes m A /-. ~ .-- ; 



and if - be, for example, -± €} it will be expressed by To '. 



an, while the whole quantity of the fluid left behind. 



A similar mode of reasoning may be applied to other cases 

 of tli e propagation of impulses, in particular to that of a ; 



contraction 

 1 



