JM. Girard on Navigable Canals. 118 
_ But these opposite dynamical effects, although successive, 
Operate in equal times, and according to the same laws ; for 
they are effected while the lock is filled or emptied ; and 
this filling and emptying takes place exactly in the same 
length of time, as may be immediately deduced from the 
formule = aiesiaiin those of spouting fluids in contigu- 
ous rated by vertical diaphragms, whence it fol- 
lows that a duheeenen of these dynamical effects is the rig- 
orous expression of the active force lost in producing them. 
This loss is therefore 
« (o—(t" —t'))+t’ae—t r=a a. 
2dly, When the expenditure of water y, is null, it is evi- 
dent that the dynamical effect downward is reduced to t” z; 
the: product of the mass sf the Hons multiplied by she fall of 
the. ock. .¢ 
The Syacmical effect apieeis, as in the piecing ddse, 
13 represen sented by b 
Consequently the eevee of these dyunmival effects, or 
the loss of active force is 
x (t'"—f)=a2; 
because when y = 0, we have always diane Barts 
3dly, When the expenditure y of water is negative, or, 
which is the same tings: hen. by the passage of the boats, 
ascending and descendi certain volume 
The —Ses dowowatd”1 remains equal to the 
product of the boat aye 3 by the height of the fall, and 
the —s action upward beco ual to the produ 
of e height natdacpail by the apne me masses of 
the boat rand the water raised, o 
so A sor w=): i fyi 
The loss of active force ig therefope sf 52 td 8 ag 
Vou. IV.....No. 3 
