176 TENTH ANNUAL REPORT OF 



four, or any numher of impulses are applied. And the thought I 

 wish particularly to present is^ that these results of calculation are 

 just the same in all the movements of common life, in the operations 

 of every machine, and in the revolutions of the moons, planets, comets, 

 and suns of the universe. There is not one system of mechanics for 

 rolling marbles, playing ball, and pitching quoits; another for guid- 

 ing ships and railroad cars, and driving machinery ; and a third for 

 maintaining the revolutions of days and seasons on the planets, and 

 working out the grand harmonies of creation. Here, as in every de- 

 partment of Grod's works, we see infinite variety comprehended in a 

 simple unity. 



This identity in the laws of terrestrial mechanics and of "me- 

 chanics celestial" affords the highest satisfaction to the student of 

 astronomy. He feels that he is treading on safe ground ; he sees it 

 to be as preposterous to suppose the foundations of the present sys- 

 tem of astronomy subverted, and Newton's Principia and La Place's 

 Mechanique Celeste giving way to some new method of explaining 

 the movements of worlds, as to imagine that philosophers should 

 abandon the principles of projectiles, the laws which fix the relations 

 of wheels, levers, and screws in a machine, or the methods of calcu- 

 lating and applying the forces used in locomotion, and should substi- 

 tute in their place some new system of principles and laws. 



Perhaps I ought to state the exact meaning of two words which I 

 shall occasionally use — inertia and gravitation. Gravitation is the 

 tendency of all masses of matter in the universe towards each other, 

 which tendency varies directly as the quantity, and inversely as the 

 square of the distance. Inertia is a negative term, implying that 

 matter is unable to change its condition as to motion and rest. If a 

 body is at rest, it will never move, unless a force acts upon it ; if it is 

 in motion, it will forever move in the same straight line, and at the 

 same rate, if no external force causes a change. A mass of matter 

 can no more stop, or go faster or slower, or change its line of motion, 

 than it can begin to move from a state of rest. 



These two properties of matter explain not only the ordinary facts 

 of terrestrial mechanics, and those phenomena of astronomy which 

 were known in the days of Sir Isaac Newton, but a vast number of 

 other planetary movements and disturbances, some of them most del- 

 icate and intricate, which have since been detected. Not a new fact 

 as yet has come to light which conflicts with these simple first princi- 

 ples. No system but the true one could bear a test like this. 



In attempting to give experimental illustrations of astronomical 

 movements^ we meet with difiiculties which cannot be entirely re- 

 moved. The earth attracts ; the air obstructs : a revolving body 

 must be supported by pivots ; these retard by friction. The best con- 

 trived experiments, therefore, are only approximations to the phe- 

 nomena which they are intended to illustrate. 



A fundamental fact in rotation, whether on an axis or in an orbit, 

 and one, too, which is a direct consequence of inertia, is this : a re- 

 volving body tends to keep its plane of rotation always parallel to 

 itself. This fact is apparent in all the bodies of the solar system. 

 For example, the earth, though it travels over a journey of six hun- 

 dred millions of miles every year, maintains its equator parallel to 



