418 Dr. J. It. Mayer on Celestial Dynamics. 



values. The two extreme cases are, when x is considered in- 

 finitely small in comparison with T, and when x=T— # = i T. 

 These form the limits of all imaginable ratios of the parts T— x 

 and x, and will now be more closely examined. 



Terrestrial heights are of course excluded from the following 

 consideration. In the first place let x, in comparison with 

 T— x, be infinitely small. The final velocity with which x arrives 

 on the surface of the large mass, after having passed through 

 a great space in a straight line, or after previous central motion 

 round it, is, according to the laws developed in relation to the 

 sun in Chapter IV., confined within the limits of 7908 and 

 11,183 metres. The heat generated by this process may amount 

 to from 8685 x x to 17,370 x x units, according to the value of 

 the major axis of the orbit of x. This heat, however, vanishes 

 by its distribution through the greater mass, because x is, ac- 

 cording to supposition, infinitely small in comparison with T. 



The quantity of heat generated increases with x, and amounts 

 in the second case, when x = ^T, to from 6000 x T to 8685 x T 

 units. 



If we assume the earth to possess a very great capacity for 

 heat, equal in fact to that of its volume of water, which when 

 calculated for equal weights = 0-184, the above discussion leads 

 to the conclusion that the difference of temperature of the 

 constituent parts, and of the earth after their union, or, in 

 other words, the heat generated by the collision of these parts, 

 may range, according to their relative magnitude, from 0° to 

 32,000°, or even to 47,000° ! 



With the number of parts which thus mechanically combine, 

 the quantity of heat developed increases. Ear greater still 

 would have been the generation of heat if the constituent parts 

 had moved in separate orbits round the sun before their union, 

 and had accidentally approached and met each other. For va- 

 rious reasons, however, this latter supposition is not very pro- 

 bable. 



Several facts indicate that our earth was once a fiery liquid 

 mass, which has since cooled gradually, down to a comparatively 

 inconsiderable depth from the surface, to its present tempera- 

 ture. The first proof of this is the form of the earth. " The 

 form of the earth is its history." According to the most careful 

 measurements, the flattening at the poles is exactly such as a liquid 

 mass rotating on its axis with the velocity of the earth would 

 possess ; from this we may conclude that the earth at the time 

 it received its rotatory motion was in a liquid state ; and, after 

 much controversy, it may be considered as settled that this 

 liquid condition was not that of an aqueous solution, but of a 

 mass melted by a high temperature. 



