For the same reasons, although the directions of gravity in the different points of the projectile's flight, are lines converging nearly to the centre of the earth, we may con sider them as all parallel, because none of our projectiles fly four miles, which produces a convergency of nearly four minutes, a deviation from parallelism which needs not be regarded.
In general, therefore, we may consider all such projec tiles as under the influence of equal gravity, acting in lines parallel to the vertical or plum-line drawn through the place of projection. This reduces the theory of projectiles to a great degree of simplicity.
Accordingly, this is the first department of mechanical philosophy which first received improvement by the appli cation of mathematical knowledge. We are indebted for this fortunate introduction of mathematics into the doc trines of motion, to the celebrated Florentine, Galileo Galilei. This excellent philosopher read his discourses on local motion about the beginning of the 17th century. Those lectures contain the whole of this doctrine, nearly in the state in which it continued till about the middle of last century. There is no branch of natural philosophy that has met with so much assistance and encouragement, it having been considered in all nations as the foundation of the art of gunnery ; an art unfortunately too much con nected with the security of every nation. It has therefore been patronised by princes and magistrates—most costly establishments have been made for its cultivation ; the ma thematicians have occupied themselves with its problems, and more numerous and expensive volumes have been published on this than on any other part of mechanical philosophy. Yet there is none in which so little improve ment has been made. Galileo's lessons contain every thing that has been clone in a scientific way, till M. Robins, in 1742, gave it a form altogether new.
We shall first consider the perpendicular ascents and descents of heavy bodies; and in the next place, their cur vilineal motion, when projected in directions deviating from the vertical.
The motion of a falling body is uniformly accelerated, and that of a body thrown straight upward is uniformly re arded.
For the accelerating or retarding force is constant, and therefore the motions are such as were considered in DYNAMICS.
All the characteristic phenomena of these motions hav ing already been sufficiently considered, all that is wanting for the application to this class of mechanical phenomena, is merely one experimental determination of the accele rative power of gravity, that is, the velocity, or increment of velocity, which gravity will generate in a body by acting on it uniformly during some given time. Galileo, who first demonstrated that an invariable gravity most produce a uni formly accelerated motion, was also among the first who appealed to experiment in all inquiries. We now think lightly of this, and wonder that a man shall think of ano ther argument who has this in his power. But when Galileo began to communicate his knowledge to the world, this was the last support that a philosopher would think of. 'Clic), had received a parcel of topics from their roaster, which had been handed down in the schools during many ages; and from these was every thing accounted for or explained. Aristotle, or his immediate pupils, had said that the velocities or falling bodies increased with their weights; Galilco's doctrine was incompatible with this, and he thought himself obliged to use arguments in his support. He said, that if Aristotle's doctrine be true, two crown pieces must fall faster when sticking together than when unconnected, which, said he, is contrary to common experience. Not doubting that he had convinced his audi ence, he described the experiments which he was to ex hibit next day, shelving that in a double time a body would fall four times as far, &c. The experiments were performed in the dome of the great church, before a vast concourse of people, and succeeded most perfectly. Yet so little were the philosophers moved by this kind of argument, that they represented Galileo as a dangerous person, un friendly to the state; and he was obliged to leave his native city in a few days, and take shelter in Padua. It is very remarkable that Baliani, one of the first geometers and mathematicians of that age, and who perfectly understood Galileo's speculations on this subject, should teach ano ther doctrine, reviving or supporting an old scholastic as sertion, that the velocity of a falling body might be as the space fallen through, calling this motion also a uniformly accelerated motion.