STELLAR EVOLUTION JEANS. 163 



The sun and moon, as we know, raise tides on our earth the height 

 of which forms only an inappreciable fraction of the earth's radius. 

 If our earth were replaced by a mass of liquid or gas of low density 

 the fraction would be greater, varying inversely as the density of the 

 mass. If the sun and earth were placed much nearer to one another 

 than now the tides would be increased in the ratio of the inverse 

 cube of their distance apart. We can easily imagine conditions un- 

 der which the heights of the tides would be comparable with the 

 radius of the earth, and here the simple formulae which the mathe- 

 matician uses to calculate the heights of terrestrial tides become use- 

 less. The general investigation of the succession of shapes which 

 will be assumed by a gaseous or plastic mass as the tidal forces on 

 it continually increase presents a difficult but not altogether intract- 

 able problem for the mathematician. 



It is found that the tides will be of the general type with which 

 we are familiar on the earth until a certain critical height of tide is 

 reached. This criical height is comparable with half the radius 

 of the mass, being greater or smaller according as the mass is of 

 more or less uniform density. After this critical height has been 

 passed, there is no longer a configuration of equilibrium under 

 the tidal forces. Dynamical motion ensues, and the general nature 

 of this motion will consist in the ejection of two arms or jets of 

 matter, one towards the attracting mass and one, which may be 

 smaller, or may be absent altogether, in the exactly opposite direc- 

 tion. If the tide-generating forces should be suddenly removed at 

 this stage the jets would, of course, fall back into the mass from 

 which they emerged, and this would in time resume its spherical 

 form. But if the tidal forces persist, the jets will continue to be 

 thrown out, and it can be shown that a continuous distribution of 

 density in these jets would be unstable, just in the same way, and 

 for similar reasons, as in the case we previously discussed of the 

 jet thrown out from a rotating mass of gas. Condensations would 

 form in the jets, and ultimately the jet would break up into separate 

 detached masses. 



According to the tidal hypothesis of the origin of the olar system, 

 the sun was at some past time subjected to intense tidal forces from 

 a passing star, the sequence of processes we have just described took 

 place, and the emitted jet broke into fragments which are our pres- 

 ent system of planets. From the mathematical investigation on 

 which this hypothesis is based, it appears that the fragments would 

 each be comparable in mass with the original sun if the matter of 

 the sun had been of approximately uniform density, but would be 

 very small by comparison if the sun had been gaseous with high 

 central condensation. The smallness of the masses of the planets 

 in comparison with that of the sun must, therefore, be taken as in- 



