5 
are in accordance with a corollary of Kepler's third law, 
viz., " that the masses of the planets vary as the square roots 
" of the distu.)iees."* If, therefore, the density of the earth 
can be proved to have been considerably greater, it follows 
that the earth's orbit must have been less, and have had a 
corresponding nearer proximity to the sun. 
The density of the rocky cmst of the earth is two-and-a- 
half times that of water, while the mean density of the whole 
earth, according to Maskelync, is five times the density of 
water ; and it is calculated that if gravitation exert itself 
uniformly towards the centre of the earth, water, at 362 
miles from the surface, would be as heavy as quicksilver ; 
air as heavy as water at 34 miles ; while, at the centre, the 
weight of marble would be increased 119 times ! 
Now it is certain that the pressure upon these central 
masses and their condensation has been, before the expan- 
sions and elevations of the crust of the earth, enormously 
greater than at the present time. In fact, to whatever 
amount, portions of the earth's crust have been raised, to the 
* History of Astronomy, p. 53. (Library of Useful Knowledge.) 
He (Kepler) supposed the sun to be a centre of attractive force which 
diminished as the distance from that body increased; again, the magnitude of 
the orbit increased as the distance. From these two causes combined, he 
concluded that the periodic time varied inversely as the square of the distances. 
But in the epitome of the Copernican system (Book iv, c. 4) he modified his 
theory by introducing the consideration of the mass and of the volume of the 
planet. His reasoning on this head is very curious. There are four causes 
on which the length of the periodic time depends : — 
1. Length of the path described. 
2. The mass of the body to be transported. 
3. The strength of the moving force. 
4. The volume under a given mass of the body to be moved. 
According to Kepler there is an exact compensation between these two 
last causes, so that the orbit depends really upon the first. Now he con- 
ceived that he had established a law showing that the masses of tlu planets 
varied as the square root of the distances, and the circular paths of the planets 
were certainly in the simple proportion of these distances. Compounding, 
then, these two ratios, he found " the squares of the periodic times to vary as 
the cube of the distances." 
