84 The American Geologist. Feb. isao 
this direction was contributed by the writer to the pages of 
The American Geologist in June and July, 1888. The present 
paper does not record any new advance, but is merely intended 
to present the matter in a slightly different aspect, and without 
entering into much detail, to show to a non-mathematical reader 
the position taken by the mathematicians. Only the two princi- 
pal data will therefore here be introduced. These are (1) the 
amount of contraction suffered by each cooling shell of the 
Earth, and (2) the diminution of the space occupied by each 
in descending to a lower level. The whole problem is merely 
the investigation of the relation which these bear to each 
other. 
The Earth being a cooling globe, every layer of it from the 
center outward is gradually falling in temperature. But evi- 
dently at the surface and at the center the chilling process 
is reduced almost to zero, because in the one case the surface 
is already cold and in the other the center is so deeply cov- 
ered that the escape of heat is inappreciable. Physicists tell 
us that at so slight a depth as four hundred miles the cooling 
is infinitesimally small, and may be neglected. All the inves- 
tigations, therefore, may be confined to a superficial shell four 
hundred miles in thickness. Below this is a nucleus or core 
practically unchanging in temperature and size from century 
to century. 
Between these two zero limits is contained at present the 
cooling shell of the Earth. In this layer there must obviouslj'' 
be a level where the cooling reaches maximum. A moment's 
thought will render this clear to everyone. It is a consequence 
of the elementary laws of heat, and is as true of an iron 
cannon ball as of a planet. This layer of greatest cooling is 
placed by the physicists, at the present time, at between 
seventy and eighty miles deep, or at about one-fifth of the 
thickness of the cooling shell. 
Obviously this layer of maximum cooling must nearly, if 
not exactly, coincide with that of greatest contraction. Every 
cooling shell shrinks in three dimensions. It becomes shorter 
in circumference along two great circles at right angles to each 
other and it becomes thinner. The shell of greatest cooling 
will therefore show most diminution in thickness, and at the 
same time will tend to crack and leave open spaces in conse- 
quence of its shortening along the two great circles. 
