Penny Blood: Serial Sensation and Working-Class Entertainment — page 87: what you’re looking at

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

70 ELEVATIONS ON THE [cH. vr. tends to diminish the rate of increase of temperature in descend- ing, and to make the value of 2ke too large, by giving too great a thickness to the cooled crust. It is easily seen that, if we had taken our integrals from the surface to such a depth that the cooling represented by Pn becomes any given inappreciable fraction of the melting tem- perature, we need not have introduced the supplementary term which is multiplied by 0°:00468. If we suppose pa to be the depth in question, the corresponding value of Pn would be i ds) = Vf (Pp). This shows that the value of ~ which corresponds to any assumed fraction of V, does not involve any of the constants of the problem. But Pn will not altogether vanish until the integral becomes equal to £an/ 7, which, from a known definite integral, will not be until p 1s infinite. We have assumed p=2 for convenience of calculation, since even so small a value makes Pn small. But the relation } ke= I (ee [ay Pade) da can be made as exact as we please by taking p large enough. Had that been done we can see that the larger terms of the v(1- result would have been proportional to HVa’, since b= we 7 and the small terms of the bracket multiplied by = would have been proportional to E'Va’, a being equal to 2,/xt. We can therefore, by means of a proportion, deduce from the value of 2ke already found, its value corresponding to any other values of E, V,or«. For instance, if we introduce for V the temperature which Mr Mallet has determined for melting slag, viz. 4000° F., COMIC OOOKS.EO ~ . $$