308 M, P. S. Girard on Navigable Canals. 



tion of society by the extension and distribution of public 

 riches.* 



It will not be proper to carry the consequences of the 

 theoretical principles which I have developed farther than 

 I have done ; they rest on an analogy easy to comprehend, 

 and which it is only necessary to remark, to circumscribe with- 

 in just bounds every case to which those principles are ap- 

 plicable. 



In whatever manner a certain volume of water descends 

 from a given height, it may always be made to raise, to the 

 same height, by means of a machine, a certain mass of wa- 

 ter smaller than itself. 



The product of the difference of these two masses of wa- 

 ter multiplied by the vertical ascent or descent is the meas- 

 ure of the active force absorbed by the machine, and the 

 machine is so much the more perfect as the loss of active 

 force is smaller. 



* What we here say of navigable canals, applies, without restriction, t«) 

 every thing that can tend to render the communications between remote 

 places, more convenient and less expensive ; it also applies to all kinds of 

 constructions, and enterprises (exploitations.) In reflecting on the different 

 branches of industry that may be improved by the application of Mathemat- 

 ical analysis, we are again led to render homage (o the truly philosophical 

 views which presided at the foundation of a celebrated school where analy- 

 sis is intended to serve as the basis of the instruction there received. 



Nevertheless, among those who have been called to enjoy the advantages 

 of that institution, and who might have applied very usetully the knowl- 

 edge they there acquired, they do not all appear to have attached an equal 

 degree of importance to the improvement of the professions they exercise. 



Mathematical analysis is a language which we forget when we cease to 

 speak or to write it ; and as research after truth always requires a certafin 

 exercise of the mind, it sometimes happens that we had rather blindly admit 

 received opinions, though erroneous, than substitute new trutbs in their 

 place, especially when a knowledge of these new truths can only be acquir- 

 ed at the price of labour ; besides we do not wound the vani'.y or self-love 

 of any one by repeating what every body says; we thus secure ourselves 

 from contradiction ; and men may even in certain situations, believe them- 

 selves interested in being considered as the champions of custom. This i? 

 not however, the conduct which we ought to expect from those whose 

 minds are exercised to the study of the exact sciences. We have too often 

 had occasion to admire the success obtained by graduates of the Polytech- 

 nic School, the exact sciences owe them too much progress, the arts too ma- 

 ny improvements, mostly obtained by the application of analysis, to leave 

 any room to apprehend that the example of those among them who negleot 

 the resources of this powerful instrument, will become contagious. 



These reflections which I deem it unnecessary to extend, are the only an- 

 swer I shall make to the observations that a younj,' engineer has published 

 en my first memoir. In submittin;; the matter which I have there treated to a 

 more profound examination, he cannot fail to recognize that all his reasaa- 

 ingSf however caustic his conclusions, are founded on a paradox. 



