PHYSICAL SCIENCE. 



XIX 



So for as general principles are concerned, 

 mechanics were nearly brought to a state of per- 

 fection by Newton and the mathematicians of his 

 time. Perhaps the principle of the conservation 

 of living forces, introduced by John Bernoulli, 

 ought to be mentioned. 



To understand what is meant by this principle, 

 it may be requisite to observe, that to mere 

 pressure Leibnitz gave the name of vis mortua, 

 or dead force, and to the force of moving bodies 

 the name of vis viva, or living force. By the 

 conservation of living forces, Bernoulli meant 

 that permanence, through all the gradual changes 

 of any system of connected bodies, in the aggre- 

 gate of the products of their masses into the 

 square of their velocities. It abridges the solu- 

 tion of various problems, and was adopted by 

 Daniel Bernoulli, as the basis of his theory of 

 hydrodynamics, published in 1738. 



The task of composing a treatise on Dynamics, 

 full and original in every part, was taken up by 

 Euler. He bestowed upon it all the pains and all 

 the resources of his penetrating genius. It ap- 

 peared in 1736, in two quarto volumes, entitled 

 Mechanics, or the Science of Motion, and contain- 

 ed the most elaborate and complete body of 

 analytical investigation that had hitherto ap- 

 peared. 



D'Alembert published his Dynamics in 1743, 

 nnd founded the whole of his reasoning upon a 

 very simple general principle. In every system 

 of bodies acting mutually, their several move- 

 ments, at any instant of time, may be decom- 

 posed into two portions, one which is retained in 

 the next instant, and the other spent ; and since 

 an equilibrium must obtain among the lost 

 motions, an expression is thus obtained for the 

 motions which are preserved. The most intricate 

 questions in dynamics were thus reduced to mere 

 statical problems, and solved constantly in the 

 same easy and uniform way. Maclaurin's method 

 of expounding forces by co-ordinates, facilitated 

 still further the application of this principle, 

 which D'Alembert in 1744 and 1752 extended 

 also to hydrodynamics. 



Segner's theory of the motion of tops deserves 

 also to be mentioned. It was published in 1756. 

 He shows that every body having a determinate 

 figure, which after combined impulsions is 

 abandoned in free space, will, besides its pro- 

 gressive motion, perform simultaneously and 

 without the smallest interference, a constant and 

 uniform revolution about each of three principal 

 axes, mutually perpendicular and passing through 

 the centre of gravity. These axes of rotation 

 possess some curious properties, which were 

 afterwards investigated by Euler. 



In 1788, Lagrange,by combining the principle 

 of D'Alembert with that of virtual velocities, 



converted the whole into an absolutely analy. 

 tical science. He referred the efforts of every 

 particle of a moving system to three mutual 

 perpendiculars, and thence derived three several 

 differential equations, which, being integrated 

 would give the final solution of the problem. 

 But no general formula for integrating such 

 equations has been hitherto discovered. 



Such is a sketch of the gradual progress of the 

 mathematical investigation of mechanics. To 

 enumerate the application of these general prin- 

 ciples to the solution of particular problems to 

 point out the gradual improvements which have 

 been introduced into the construction of mechani- 

 cal engines, and the immense advantages which 

 have resulted from these improvements, especi- 

 ally in this country, where they have been car- 

 ried to the greatest extent, would require a 

 treatise of no ordinary length, and would be 

 quite incompatible with the limits within which 

 we are under the necessity of confining our- 

 selves. 



ASTRONOMY. 



THE ancients discovered the planets, and gave 

 them names, and noticed their motions, at a 

 very early period. The motions of the sun and 

 moon could not fail to attract their attention, 

 and the changes in the seasons which depended 

 upon these motions. The phenomena of the 

 eclipses of these luminaries, viewed with such 

 apprehension by the common people, necessarily 

 attracted the attention of the first observers of 

 the heavenly bodies : they soon observed a cer- 

 tain regularity in these phenomena, and became, 

 in consequence, capable of predicting them. 

 All these appearances could not be familiar to 

 /hem without some speculations about the motions 

 of the heavenly bodies. 



The stars appeared as so many luminous points 

 ixed in the heavenly sphere, having the earth 

 "or a centre, and revolving on an axis having 

 ;hat earth for a centre in the space of twenty- 

 bur hours. All the stars were found not to par- 

 .ake of this diurnal motion in the same degree ; 

 some were carried slowly to the east, and their 

 >aths, after a certain interval of time, returned 

 upon themselves. The astronomers of the 

 Alexandrian school set themselves to ascertain 

 he general laws of these motions. This could 

 not well be done without a hypothesis ; and the 

 implest was, that the planets move eastwards in 

 circles, and at a uniform rate. 



It was soon found, however, that the motion 



astward was not uniform. The planet began to 



more slower and slower, and, at last, became 



