MECHANICAL PRINCIPLES OF FLUIDS. 71 



We must allow that the assumptions by which 

 this result is obtained are somewhat arbitrary ; and 

 those which Newton introduces in attempting to 

 connect the problem of issuing fluids with that of 

 the resistance to a body moving in a fluid, are no 

 less so. But even up to the present time, mathe- 

 maticians have not been able to reduce problems 

 concerning the motions of fluids to mathematical 

 principles and calculations, without introducing 

 some steps of this arbitrary kind. And one of the 

 uses of experiments on this subject is, to suggest 

 those hypotheses which may enable us, in the man- 

 ner most consonant with the true state of things, 

 to reduce the motions of fluids to those general 

 laws of mechanics, to w r hich we know they must be 

 subject. 



Hence the science of the Motion of Fluids, un- 

 like all the other primary departments of Mechanics, 

 is a subject on which we still need experiments, 

 to point out the fundamental principles. Many 

 such experiments have been made, with a view 

 either to compare the results of deduction and ob- 

 servation, or, when this comparison failed, to obtain 

 purely empirical rules. In this way the resist- 

 ance of fluids, and the motion of water in pipes, 

 canals, and rivers, has been treated. Italy has 

 possessed, from early times, a large body of such 

 writers. The earlier works of this kind have been 

 collected in sixteen quarto volumes. Lecchi and 

 Michelotti about 1765, Bidone more recently, have 

 pursued these inquiries. Bossut, Buat, Hachette, 



