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MATHEMATICS AND NATURAL PHILOSOPHY. 
Agr. VIII. dn Analysis of the Principles of Natural Philosophy. By M. Youné, 
THE heads of a course of lectures are 
contained in this work, which will be use- 
ful only to tutors who are engaged inva 
similar employment, or those who hav- 
ing gone through a course of natural 
philosophy, wishto refres}: their memory, 
by reviewing frequently the objects of 
their studies. Demonstrations are very 
seldom given to any article; but where 
they are given, it is done with great taste 
and judgment. Mechanics,- hydrosta- 
tics, aerostatics, hydraulics, pneumatics, 
acoustics, optics, electricity, magnetism, 
are analysed in the order specified. The 
work would have been rendered much 
more valuable by references to the works 
where a demonstration might be found 
of each article: this'is done sometimes, 
but much too sparingly ; and we cannot 
say that the author is always very suc- 
cessful in his definitions. Thus we are 
told that space is the order of things 
which co-exist, and time is the order of 
things which exist in succession; whence 
few persons, we apprehend, will find any 
assistance in forming to themselves an 
idea of the things defined. 
In demonstrations we have observed 
that the author is more successful, and 
we will insert one on the greatest velocity 
cominunicated through an elastic ball to 
another at rest. 
*« Let A and C be two given bodies, be- 
tween which is inserted the body X of inter- 
mediate magnitude ; if the velocity of A be 
called a, the velocity of C = ak rane 
4Aa 
— 
= AC 
: ih RS X+C, amaximum; but the 
gumerator is given, therefore this quantity 
will be greatest, when the denominator is 
least, that is, when AE + X is least, 
because A and.C are constant ;_ now the rec- 
tangle AC X X is a given quantity, being 
x AC 
equal to AC; therefore the sum of x 
and X is least when they are equal, that is, 
8vo. 
AC 
when ———~ 
<= X, and A C = X?;_ that is; 
4 
when X is a mean proportional between A 
and C.” 
The difficulties attending the problem 
of Huygens on the ultimate velocities 
of bodies descending in fluids are well 
known. ‘The demonstration of this au- 
thor is-well adapted to the subject. 
«« Mathematically speaking, bodies des 
scending in fluids will not acquire their tlti-” 
mate and uniform velocity in any finite time 
whatever. ' 
«< The absolute force with which the 
body descends is’ the difference between its 
weight and the weight of am-equal bulk of 
the fluid ; and this difference divided, by the 
weight of the body will be the accelerating 
force, which let us suppose equal to d; now 
the resisting force increases as the square of 
the velocity 7, and therefore will be equal to 
some constant quantity multiplied into v?; 
let this antcitiey be e, therefore the absolute 
accelerating force, upon the whole, will be 
d—ev?. Let the constant force d be repres 
sented by the given line AC, and, let the de- 
crement of this force by the resistance, be AK, 
and consequently the absolute accelerating 
force = KC; also let the absolute velocity 
AP of the body be a mean proportional be- 
tween AC and AK, and therefore in the sub- 
duplicate ratio of AK. Let the increment of 
the resisting foree be KL, and the contempo- 
raneous increment of the velocity be PO; with. 
the centre C, and the rectangular asyunptotes 
AG, CH, let the hyperbola BNS be describ- 
ed, meeting the ordinates AB, KN, LO, 
Because AK :: AP?, the moment of the for- 
mer KL will be as the increment 2 APQ of — 
the latter; that is, as AP % KC, for the in- — 
crement PQ of the velocity is as the absolute 
accelerating force KC; therefore KL x KN 
2: AP X KC x KN:: AP, because KC X¥ 
KN is constant. Therefore the indefiuitely 
little hyperbolic area KNOL: AP. And 
the hyperbolic area ABOLis composed of the 
particles KNOL always praparsiopal to the 
space described with that velocity, the par- 
ticle of time in which KL is generated being 
given. Consequently, when KC the absolute 
accelerating force vanishes, that is, when the 
motion of the body beeomes uniform, the 
space described ABSHCA, and therefore the 
time; will be infinite.” 
Art. IX. A Practical Treatise of Perspective, on the Principles of Dr. Brook Tayler 
By E. Eowarns, Associate and Teacher of Perspective in the Royal Acad. 4to.. pp. 350. » 
TECHNICAL and scientific men are 
t 
principle of the art by which he makes 
constantly at variance. The technical his fortune, produces 4a work whose exe- 
Taan, without understanding a single 
cution the scientific man neither can nor 
