330 | Review of the Principia of Newtons 
in great cities,are squandered up ts, would be muck 
better appropriated in this manuer, and when it is fully as- 
ined, th 
that balloons cannot be navigated by any practica- 
ble means, then let them remain as now, a brilliant and im- 
posing spectacle, auxiliary to amusement, war and philoso- 
phy, but the sport of the careering winds and tempests of 
heaven. Weconclude by wishiag Mr. Genet ample suceess- 
Failure will involve no disgrace, but success would add a- 
nother brilliant leaf to the book of discovery. 
Art. XXI.— Review of the Principia of Newton. 
(Continued from p. 35.) ‘ 
TuE action and laws of force in respect to particular 
neral prin- 
ciples of rectilineal and trajectory motion. The first and 
most simple cases comprehended in section 7, are those of 
bodies descending in a rectilinear direction to the centre of 
force, by virtue of any intensity, or law of force. ‘To shew 
the analogy between this kind of motion, and that of a body 
escending in a curve, according to the laws of force previ- 
ously investigated, it was only necessary to conceive the pro- 
jectile motion to be diminished sine limite ; the orbit then 
becomes a right line. The relations of space, time and velo- 
city, of a body urged only by a force to the centre, is but one 
case of the general problem of a body moving in an orbit, 
or trajectory. This method of deriving the circumstances 
of rectilinear motion by its analogy to, and connection with 
trajectory motion, though not the most general in the phys- 
ico-mathematical sciences, is certainly the best calculated to 
show harmony and connection of the general and philo- 
sophical principles ; the 7th section is therefore principally 
employed in developing that connection from principles es~ 
tablished in the preceding part of the work. These being 
necessary precognita for the due understanding of this part of 
the Principia, and not having been particularly referred to in 
te as being corollaries, or results of the more gene- 
Tac metples, it may be well to exhibit to the reader in this 
