404 Biographical Account of (Duc. 
deal of esteem to him who renders more popular notions seemingly 
at first destined to be confined to philosophers. 
_ ‘The same advantage is evident in his method for the reversion of 
series. This subject has occupied the greatest mathematicians. It 
was afterwards treated in a more philosophical and more profound 
way ina fine memoir of Lagrange. But if the method ef Bossut 
has not the same generality, if it is not comprehended in a formula 
so singularly remarkable, it is distinguished by other advantages. 
It depends upon the most elementary theorem of differentiation ; 
it requires only ordinary and uniform cafeulations, though a little 
long ; it fixes itself in the memory, so that it is impossible to forget 
it; and the calculator who wishes to make use of it carries it always 
with him, and has no occasion to consult a book on the subject. 
Parent had formerly given, in order to estimate the effect of 
wheels moved by a fall of water, a very simple method, but v 
inaccurate. Bossut undertook to introduce into the calculation all 
the considerations neglected by Parent, and by all those who had 
adopted the rule of this mathematician with too much confidence. 
The problem in all its generality may be insoluble; but in the 
application of it we are at liberty to neglect the circumstances which 
do not occur in avy of the machines used, or which can only pro- 
duce insensible effects. By this means Bossut arrives at a formula 
which may be adapted to all possible cases, either by varying some 
terms, or by suppressing them altogether. He obtains in this 
manner, if not the rigid accuracy which belongs exclusively to pure 
analysis, that degree at least with which the arts may be satisfied. 
‘These particular memoirs, and various others which we have not 
room to-analyze, are to be found in the Encyclopedie Methodique, 
of which he was one of the editors, or in the Course of Mathe- 
matics which he composed for the use of the pupils whom he exa- 
mined, or in his Treatise of Hydrodynamics, a more recent work, 
in which he had introduced his different experiments on the motions 
of fluids. : 
“© It is only a mathematician,” said on that occasign Condorcet 
in the History of the Academy, “It is only a mathematician well 
skilled in the theory and practice who can give to experiments tlie 
form which they ought to have in order to be compared with the 
theory. It is only a mathematician who can know either what pre- - 
cision in the theory an experiment may produce, the accuracy of 
which is known, or with what precision experiments ought to be 
made in order to be employed in constructing or verifying a theory.” 
«« Experiments made by a mathematician like Bossut,” continues 
Condereet, ® oaght then to be very precious in the eyes of mathe- 
maticians who wish to understand the theory of fluids, and of meé- 
chanics who o¢eupy themselves with hydraulics.” 
In this first essay Bossut had considered the motion of fluids in 
general.. Four years afterwards Government charged him with a 
new set of experiments on the resistance of fluids in narrow and 
shallow canals. He made them the subject of a work published in 
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