RKPORT ON HYDRAULICS. — PART 11. 459 



ever, have been contested by several engineers, and by M. Mi- 

 nard in his Observations sur un Systeme a jtetites Chutes. 



A fourth memoir*, published in the year 1826, examines the 

 question of the relative advantages and disadvantages which 

 belong to the conjoined or separate systems of locks. In this 

 memoir, M. Girard examines, under the different circumstances 

 of evaporation and filtration, the quantity of water necessary to 

 maintain a navigation of any given extent, the conditions of 

 which cannot always be fulfilled. 



M. Girard refers the failure of all the schemes, hitherto pro- 

 jected, for the purpose of replacing the defects of the common 

 lock, to the impossibility of resolving the problem completely, 

 without an unnecessary expenditure of mechanical force, and 

 therefore reduces the maximum efl'ect of the common lock to 

 questions of the comparative time and economy required by 

 boats for passing insulated or conjoint systems of locks. The 

 expression for the latter case is singularly modified in favour of 

 small rises of locks, when the boats pass in succession, and is 

 in favour of the conjoint system with regard to time. 



In the formulaf. number 4, 1 = -r + — -f=— j-, the 



time employed by the boat in passing through a number w, of 

 simple or isolated locks, distributed over the total inclination o. 

 The author does not take into consideration the stoppage of the 

 boat, and consequent loss of time occasioned by the repeated 

 changes in the force of trackage i-equired by the isolated system. 

 The value of the water lost can only be contrasted with the value 

 of time under certain circumstances ; the question had already 

 been discussed, by Gauthey and others, with reference to the 

 locks of the canals of Briarie and Languedoc. An abstract of 

 M. Girard's other hydraulic researches has already been given 



• Qualrieme Memoire sur les Canaux de Navigation consideres sous le rapport 

 de la Chute, et de la Distribution de leurs Ecluses. Par M. Girard. 

 f The following are the formulae : 



r a:=^ the total height to overcome. 



» a/ o /» — 1 + V 2 ^ s = the surface of the gate. 



o ^ the orifice or sluice for filling 

 ■^ the lock. 



1. 



/• ?? — 1 + V 2 \ 

 \ ^ n ^ 



o V g \ ^ n 



» ^~a / » — 2 + 



Vr /»-2+N(l+y2)\ I 5^ = gravity. 



._ y^ j^ — J I n n = number oi locks. 



L N = number of boats together. 



4. / = section of canal. 

 = space passed ov 

 in a second of 

 = length of the lock. 



V K m' + 2 ' ^^ space passed over the platform 



3. N = — -z — I j^= in a second of lime. 



1 + v/2 



