Mr. Hopkins on the Conductive Powers of various Substances. 315 



much as in the former case, whereas the depths corresponding to the 

 same increase of temperature are only as 65 to 60, instead of being 

 in the ratio of about 65 to 35, as they ought to be according to tlie 

 theory here considered. In all the other cases the conductive powers 

 of the masses penetrated are doubtless greater than that of the chalk 

 at Paris, though, for the most part, they present a more rapid increase 

 of temperature in descending, instead of a less rapid increase (as this 

 theory would prescribe) than the Puis de Grenelle. 



Within the region comprising the cases above cited, there are 

 many local variations as to the rate of increase of terrestrial tempe- 

 rature in descending below the earth's surface. The author conceives 

 that these phenomena cannot be accounted for according to this 

 theoiy without the introduction of arbitrary hypotheses. 



Upon the whole, he beheves that in the present state of our 

 knowledge of terrestrial temperature, it is impossible to account for 

 its phenomena by regarding them as the consequence simply of heat, 

 not generated in, but transmitted through the crust of the globe 

 from some deep-seated central source. 



The discrepancy between the actual terrestrial temperatures and 

 those which would be assigned by the theory here discussed, may be 

 illustrated perhaps by placing the subject in a rather different point 

 of view. It is assumed in the theoretical investigation, that the iso- 

 thermal surfaces at depths sufficiently great (as 50 or 100 miles for 

 example) are approximately concentric with the earth's external 

 surface, or, speaking with reference to areas not too large, parallel 

 to that surface, in which case it is proved that the isothermal sur- 

 faces at comparatively smnll depths (not much exceeding that of the 

 sedimentary beds) cannot be parallel to the external surface. For 

 example, the depth of an isothermal surface of given temperature 

 which should be some 3000 feet at the Puis de Grenelle, ought to be 

 nearly 6000 feet at the coal shaft at Duckenfield ; and at other places 

 it ought to be very nearly proportional to the conductive power of 

 the terrestrial mass lying above it. But the observations above cited 

 demonstrate that, independently of local irregularities, such an iso- 

 thermal surface is nearly at equal depths throughout the whole region 

 of Western Europe. 



No theory of terrestrial temperature, then, can meet the require- 

 ments of observation which does not account for isothermal surfaces 

 approximately parallel (with local variations) to the earth's external 

 surface at comparatively small depths beneath it. Moreover, it is 

 easily shown that the quantity of heat transmitted from such a surface 

 to the external sui J'lce, must'be proportional to the conductive power 

 of the sui)erincumbent mass through which the transmission takes 

 place (in the previous case the quantity of transmitted heat is 

 independent of that power). Consequently, whatever may be the 

 cause supplying the heat at depths not much exceeding the general 

 aggregate depth of the sedimentary l)eds, it must furnish a quantity 

 of heat projiortional to the vertical flow of heat, i. e. a quantity pro- 

 portional to the conductive power of the superincumbent mass. 

 Thus the energy of the producing cause must have distinct relations 



