ME. HOPEINS ON THE THEOET OF THE MOTION OF OLACIEES, 
687 
whole year might perhaps not much fall short of 31°(Fahr.)*. If the conductive power of 
ice were equal to that of the earth’s crust, the mean temperature would increase 1° (Fahr.) 
in descending some 60 or 70 feet; and therefore, on account of the smaller conductivity 
of ice, it would probably, in the case of a glacier, rise to 32° (Fahr.) at a depth of some 
30 or 40 feet. This would hold, it should be observed, on the supposition that the sub- 
stance below this depth should be capable, like the matter of the earth’s crust, of taking 
any temperature higher than 32° (Fahr.). This higher temperature would be acquired, 
as in the actual case of the earth, by the flow of heat from the earth’s interior. But in 
the case of a glacier this heat will be expended in melting the lower stratum of ice instead 
of communicating a higher temperature to the whole mass. Consequently, if the thick- 
ness of the glacier exceed some 30 or 40 feet (a depth at which, as above shown, the tem- 
perature will be invariable), the temperature of the lower surface will be constant and 
equal to 32° (Fahr.). 
The temperature at any proposed point (P) of the interior of a glacier, at a depth 
greater than that estimated above at some 30 or 40 feet, will always be constant and 
less than 32° (Fahr.), provided the mean annual temperature of the external surface of 
the glacier be so. To find this constant temperature at P, take for the temperature of 
the upper surface its mean annual temperature. Let it =T° (Fahr.). Also let «=thick- 
ness of the glacier, .r= distance, from the upper surface, of the proposed point, and t its 
required temperature. Then shall we have, according to the laws of conduction of heat, 
^-T° a; 
32°_T°“a’ 
the difierence of temperatures, as is well known, being approximately proportional to 
the distances from the upper surface. Hence 
^=T°-ff(32°-T°), 
which shows that t must always be greater than T°; it must also be less than 32° (Fahr.), 
and must therefore lie between those quantities. Consequently, since 32° — T° is small 
for the Alpine glaciers, their internal temperature must be nearly uniform, but always 
a httle below 32° (Fahr.), supposing it to depend only on the process of conduction. 
But the process of infiltration will tend to raise the internal temperature more nearly 
to 32° Fahr. ; for since the infiltrated water will have that temperature, it will constantly 
tend to heighten the temperature of the mass through which it passes till it rise to 
32° (Fahr.), and never to lower it. This water must thus bring to the glacier (a mass 
of lower temperature than itself) a continual accession of heat, which it can only lose 
again by conduction through the upper surface during the winter ; and this loss will be 
restricted to that small depth beyond which the annual variations of temperature cannot 
extend. For all points at greater depth infiltration must ultimately raise the tempera- 
ture to 32° (Fahr.). 
* M. Agassiz states that the temperature given by his experiment might possibly be somewhat too high. 
There is no probability, however, that the error would he s’xfficient to affect the reasoning in the text. 
5 B 2 
