Penny Blood: Serial Sensation and Working-Class Entertainment — page 172: what you’re looking at

Machine-transcribed from the original scan — historical spelling and the odd misread are preserved.

CH. XII.] . THE THERMOMETER. 155 equal horizontal distances along the tunnel would bring us to the freezing-point within the rock supposing it extended to a sufficient height, and draw a curve through these points, which will touch the summit of the mountain. This curve will define what may be called the effective profile of the mountain, that is to say, the form of outer surface, which would give the same temperatures within the mountain as actually exist, were the temperature of the surface uniform. It will be seen that the contour so obtained is very considerably less convex than the actual contour. This shows that the real effect of the convexity of the surface upon the internal temperatures cannot be so great as at first sight it might appear likely to be. The isogeotherms within the mountain will evidently con- sist of a family of surfaces corresponding to the external effective profile, but decreasing in convexity with increasing depth. Eventually a plane horizontal isogeotherm will be reached. But it does not follow that the isogeotherms will continue to be planes beneath it. ‘Let 8 be the area of one of these surfaces, through which the same heat passes in a given interval of time as that which crosses the area A of the plane isogeotherm in the same interval. Let » be measured along the normal drawn to a point in the surface S, v being the temperature at that point, and « the con- ductivity. Then the flow of heat across the elementary area dS will be | dy Properly speaking S* will vary from point to point of the iso- geotherm. But if we consider it to be the average rate along the normal at every point of a given isogeotherm, then the flow across the whole of that surface will be dv But the same flow of heat crosses the plane area A, where let us call x’ the average rate of increase of temperature in descending ; wherefore the whole flow there will be «r’A. GONG oOo SS (CO)