824 
ME. W. HOPKINS’S EXPEEIMENTAL EESEAECKES 
arrived at by M. Walferdin respecting the rate of increase in the Chalk throughout a 
large portion of Northern France. Each of these results must be considered as the 
mean rate of increase in the particular well or shaft in which it has been obtained. 
In most cases the exact temperatm-es at different depths have not been observed at the 
only time when they can be obtained vdth accm’acy, i. e. during the sinking of the 
shaft or well. It will be remarked, however, that there are great UTegularities in 
the rate of increase in the ‘ Puits de Grenelle,’ and obsei'^ation appears to indicate 
similar variations in other localities ; but it is easily conceivable that such variations 
may be due to local and superficial causes, and that they may disappear at sufficient 
depths beneath the surface. Assuming this to be the case, and neglecting the effects 
of local causes, the preceding results of observation would lead to the conclusion that 
the rate of increase of temperature in descending beneath the earth’s suifface is nearlv 
uniform in each locality, and nearly the same in different localities. At the same time, 
many observations indicate material deviations from this equality of the rate of increase 
in different places, and to these I shall again refer ; but the general conclusion which 
has usually been deduced from observations on terrestrial temperature is that above 
enunciated. 
Now if an enormous sphere, like the earth, were originally heated to any degree, and 
were then left to cool by radiation into surrounding space, for a sufficient length of time ; 
and supposing, moreover, the conductive power of the mass, or at least of its more super- 
ficial portion, to be uniform — then the law of temperature above enunciated as deduced 
from observation, would be the actual law in the case now supposed, at points not 
remote from the surface of the sphere. This presumed coincidence between the results 
of theory and observation has natui’ally led to a very general adoption of the theory 
which assigns the existing terrestrial temperature entirely to a primitive heat, of which 
the remains, though producing a comparatively feeble effect udthin the range of those 
depths to which we can penetrate, may yet produce an enormous temperatm-e in the 
more central portions of the globe. The investigations on this subject, however, have 
hitherto been very imperfect with respect to the determination qf the law of increase of 
temperature in that stratified envelope of the earth which consists of so many layers of 
substances possessing, as I have now shown, such different conductive powers. I shall 
endeavour to supply this deficiency ; and for this purpose we must first solve the follow- 
ing problem : — - 
13. If any number of strata, bounded by parallel smffaces of indefinite extent, be 
superimposed on each other, the conductive power (^) for each stratum, and the trans- 
mitting power (^) for each discontinuity, being different, to find the law of temperature 
in the mass, the lowest surface being maintained at the constant temperatui'e ti , and the 
temperature of the atmosphere being r. 
Eecurring to the equations (/3.) (art. 8), we shall have, gmng to A’ and ^ theh different 
values, k^ k^ and q^ q^ respectively. 
