SOME PRINCIPLES AND RESULTS OF HARMONIC MOTION.* BY PLINY EARLE CHASE, LL.D.
" When two bodies, in relative motion, come into contact, pressure begins to act between them to prevent any parts of them from jointly occupying tile same space.
Any force in a constant direction acting in any circumstances, for any time great or small, may be reckoiled on the same principle; so that what we may call its whole amount during any time, or its 'time-integral,' will measure, or be measured by, the whole momentum which it generates in the time in question." (Thomson and Tait, Nat. Phil., i, sec. 294, 297.) No relative motions can be more important, and no contact more complete, than those which exist between the all-pervading luminiferous rather and the sun. In the conversion of tangential luminous waves into spherical vibrations, gravity is acting in a constant direction toward the sun's centre. The amount of its activity upon each eethereal particle,/~, or its time-integral during each cyclical period, t, is measured by/~gt. The study of the various correlations which flow from this integral involves the following considerations :
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The principle of Galileo, that the total effort is equivalent to tile effective sum of tile causes which are operating. This is illustrated at sun's surface, which is the region of greatest energy in our system, by the cyclic equation, .~-'g -~-gt ~ vs" 2. The equality of pressureslor resistances to opposing forces, in all equilibrating tendencies. In consequence of this equality, every interruptiou or prevention of the free action of any force may be measured as a rate of change of momentum in tile opposite sense.
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The invariability of the sum of kinetic and potential energies. 4. The maximum of kinetic energy in all cyclical motions~ at the point of the trajectory which is nearest to the centre of force, and the maximum of potential energy at the point which is most remote from This paper has been written, in part, to meet a desire which has been expressed by some members of the Royal Astronomical Society for an introduction to the article on "Harmonic Motion in Stellar Systems" (this Journal. Nov., 1884). The author will feel under obligation to any readers of the Journal who will inform him of other points which need further elucidation.