Physics. 321 
of the two “ee sate oe Pos their arithmetical mean: ¢, the 
time; x, the dis of any poi a4 rom the middle plane; v, the 
above solution shows that for all values of the time when 
=0,v=v,, so that the temperature at the medial plane is 
cmt 
Then differentiating v with regard to the time we have— 
& a 
oe . 
ah, area) # 
This expression is that required for the rate of are We now 
wish to find where it is a maximum. onsider ae Fanetion 
ze’; this is clearly a maximum when log z— 2 is imum, 
and by the ordinary rules this is a maximum when —= 22, or 
Zz 
dv : 
when z?=4. Hence it follows that — a has its maximum value 
where «?= 2kt, Now when the unit ei length is a foot and of 
time a year, k= 400; hence «= 4/800! 
_ This formula shows that the seat of bi maximum rate of cool- 
ing moves inward as the time increases. If the time which has 
elapsed from the initial state be two hundred million years, or 
t=2X108, we have x= 400,000 feet, or a little less than eighty 
nhiles 
Sir W. Thomson shows, in his paper on the igual CoOHng: of 
very 
nearly correct for the case of the earth, which is su ea a 
hot sphere cooling by radiation. It follows, therefore, ea the 
numerical result which is given above that the seat of the maxi- 
below the earth’s surface. It does not, of course, necessarily fol- 
low that the seat of the maximum rate of contraction of volume 
should be identical with that of the maximum rate of cooling; 
yet it seems probable that it would not be very far removed 
rom. it. 
e Rey. O. Fisher very justly remarks that the more rapid 
contraction of the interna! than the external strata would cause 
4 wrinkling of the surface, although he does not admit that this 
can i the sole cause of geological ig age The fact that the 
region of maximum rate of coolin so near to the surface 
wh ards a 
 Sheneibe that Mr. Fisher may have under-estimated the contracti- 
ility of rock in cooling, and that this is the sole cause of geologi- 
cal contortion ?— Nature, Feb. 6. 
