l6 Turner, Total Solar Eclipses. 



leave on one side the consideration of the absolute magni- 

 tude of these velocities, only remarking that a diminution 

 of the sun's attraction is for our purpose equivalent to a 

 diminution in the velocity of projection. We can substi- 

 tute one for the other and leave the path of the particle 

 practically unaltered ; so that we lose no generality by 

 asking how particles ejected with different velocities and 

 in different directions would be distributed, keeping their 

 size and the sun's attraction the same. For simplicity 

 let us restrict the problem further still and consider the 

 variation in magnitude and direction separately. Let us 

 first suppose a velocity given in magnitude but varying 

 in direction. Take, for instance, a velocity just sufficient 

 to project a particle vertically to the height of one radius 

 of the sun ; then the same velocity, with horizontal pro- 

 jection, would send the particle skimming round the sun 

 completely as a very close satellite ; while intermediate 

 directions would cause it to describe trajectories of 

 different heights ; all, however, less than one radius. If 

 particles be shot out from a point on the surface in all 

 directions with this velocity, there will certainly be more 

 of them at any moment near the surface than far away. 

 Beyond one radius there are none at all, and just within 

 that limit there are only the few projected nearly vertically. 

 Lower down we get a greater number from directions 

 more and more inclined to the vertical, and so as we 

 approach the sun the density increases. Close to the sun, 

 indeed, it becomes infinite ; for the particles which come 

 skimming along the surface occupy that region for a 

 finite time, whereas all other particles are at any particular 

 distance for an infinitesimal time only. Working out 

 the law of density mathematically, we find that it is not 

 unlike that required, excluding the little shell close to 

 the surface which may be regarded as part of the chromo- 



