[3] This is, however, by no means the whole of the matter. The motion is not a simple circle nor has it a readily specifiable period. There are several disturbing causes. All that is given here is a first rough approximation. [4] The proof is easy, and ought to occur in books on solid geometry. By a "regular" solid is meant one with all its faces, edges, angles, &c., absolutely alike: it is of these perfectly symmetrical bodies that there are only five. Crystalline forms are practically infinite in number. [5] Best known to us by his Christian name, as so many others of that time are known, _e.g._ Raphael Sanzio, Dante Alighieri, Michael Angelo Buonarotti. The rule is not universal. Tasso and Ariosto are surnames. [6] It would seem that the fact that all bodies of every material tend to fall at the same rate is still not clearly known. Confusion is introduced by the resistance of the air. But a little thought should make it clear that the effect of the air is a mere disturbance, to be eliminated as far as possible, since the atmosphere has nothing to do with gravitation. The old fashioned "guinea and feather experiment" illustrates that in a vacuum things entirely different in specific gravity or surface drop at the same pace. [7] Karl von Gebler (Galileo), p. 13. [8] It is of course the "silver lining" of clouds that outside observers see. [9] L.U.K., _Life of Galileo_, p. 26. [10] _Note added September, 1892._ News from the Lick Observatory makes a very small fifth satellite not improbable. [11] They remained there till this century. In 1835 they were quietly dropped. [12] It was invented by van Helmont, a Belgian chemist, who died in 1644. He suggested two names _gas_ and _blas_, and the first has survived. Blas was, I suppose, from _blasen_, to blow, and gas seems to be an attempt to get at the Sanskrit root underlying all such words as _geist_. [13] Such as this, among many others:--The duration of a flame under different conditions is well worth determining. A spoonful of warm spirits of wine burnt 116 pulsations. The same spoonful of spirits of wine with addition of one-sixth saltpetre burnt 94 pulsations. With one-sixth common salt, 83; with one-sixth gunpowder, 110; a piece of wax in the middle of the spirit, 87; a piece of _Kieselstein_, 94; one-sixth water, 86; and with equal parts water, only 4 pulse-beats. This, says Liebig, is given as an example of a "_licht-bringende Versuch_." [14] Draper, _History of Civilization in Europe_, vol. ii. p. 259. [15] Professor Knight's series of Philosophical Classics. [16] To explain why the entire system, horse and cart together, move forward, the forces acting on the ground must be attended to. [17] The distance being proportional to the _square_ of the time, see p. 82.