The accuracy of' my approximation to the apparent semi-diameter of the Sun* is confirmed by the following kinetic considerations, some of which, though seemingly of great fundamental importance and character, have been generally overlooked.
- Matter ]ms been usually regarded as composed of discrete particles. This hypothesis enters even into the kinetic theory of gases. If it is true, all three must be transmitted from particle to particle, and time must, therefore, he required to overcome the inertia of lll~tsses.
Atmtetion and repulsion have been generally considered under
the influelme or' central fi)rces, varying inversely as the squares of the distances from the (.entres and, therefbre, 1)roducing nlotiollS with variable velocity.
-
Waves, ~wt)ital undulations, and other cyclical motions, are generally propagated with unifbrm ()r nearly uniform velocity, although they are often a(~eompanied by subordinate movements with varying ~'elocitv. V.wial)le veh)eities ave often converted into {mifornt or nearly unitl,rm velocities, as in the e~se of conical l)endulums, planetary rotations and orbital revolutions.
-
In all undulations, and in all cyclical motions through all undulating medium, there are tendencies to synchronism. The synchronism m:ff be complete, producing equal cyclical nmtions in equal cyclical times, or nodal, producing harmonic series of cyclical motions which are eompleted in equal times.
-
Newton showed that if' a centripetal force varies as the distance of a body fi'om the centre, all bodies, revolving in any planes whatsoever, will descrihe ellipses and complete their revolutions in equal times;? that bodies whi(.h move in right lines, running backwards and forwards alternately, will eoml)lete their several periods of going and returning in the same times ;t and that if a fluid be composed of" "~ Proceed. Am. l)h iL ,%e., x v i i i, :~Sq ~. + I'vi~ci'l)bt , B. 1, Prop. 47.