I 



» 



I 



H. Helmholtz on the Interaction of Natural Forces. 211 



example, how Proteus-like the effects of a single cause, under 

 altered external conditions, may exhibit itself in nature. Be- 

 sides these, the earth experiences an action of anotberkind from 

 its central luminary, as well as from its satellite the moon, wbich 

 exhibits itself in. the remarkable phenomenon of the ebb and 

 flow of the tide. 



Each of these bodies excites, by its attraction upon the waters 

 of the sea, two gigantic waves, which flow in the same direction 

 round the world, as the attracting bodies themselves apparently 

 do. The two waves of the moon, on account of her greater 

 nearness, are about 3^ times as large as those excited by the 

 sun. One of the^e waves has its crest on the quarter of the 

 earth's surface which is turned towards the moon, the other is at 

 the opposite side. Both these quarters possess the flow of the 

 tide, while the regions which lie between have the ebb. Al- 

 though in the open sea the height of the tide amounts to only 

 about three feet, and only in certain narrow channels, where the 

 moving water is squeezed together, rises to thirty feet, the might 

 of the phenomena is nevertheless manifest from the calculation 

 of Bessel, according to which a quarter oi thQ earth covered by 

 the sea possesses, during the flow of the tide, about 25,000 cubic 

 miles of water more than during the ebb, and that therefore such 

 a mass of water must, in 6^ hours, fliow from one quarter of the 

 earth to the other. 



The phenomena of the ebb and flow, as already recognized by 

 Mayer, combined with the law of the conservation of force, 

 stands in remarkable connexion with the question of the stability 

 of our planetary system. The mechanical theor}^ of the plane- 

 tary motions discovered by Newton teaches, that if a solid body 

 in absolute vacuo^ attracted by the sun^ move around him in the 

 same manner as the planets, this motion will endure unchanged 

 through all eternity. 



Now we have actually not only one^ but several such planets, 

 which move around the sun, anci by their mutiial attraction cre- 

 ate little changes and disturbances in each other's paths. Nev- 

 ertheless Laplace, in his great work, the Mecanique Celeste, has 

 proved that in our planetary system all these disturbances in- 

 crease and diminish periodically, and can never exceed certain 

 limits, so that by this cause the eternal existence of the plan- 

 etary system is unendangered. 



But 'l have already named two assumptions which must be 

 made : first, that the celestial spaces must be absolutely empty ; 

 and secondly, that the sun and planets must be solid bodies. 

 The first is at least the case as far as astronomical observations 

 reach, for they have never been able to detect any retardation of 

 the planets, such as would occur if they moved in a resisting 

 niedmm. But on a body of less mass, the comet of Encke, 



I 



