^{page 409 note *} A periodic variation of external temperature of one million years' period would give variations of temperature within the earth sensible to one thousand times greater depths than a similar variation of one year's period. Now the ordinary annual variation is reduced to of its superficial amount at a depth of 25 French feet, and is scarcely sensible at a depth of 50 French feet (being there reduced, in such rock as that of Calton Hill, to ). Hence, at a depth of 50,000 French feet, or about ten English miles, a variation having one million years for its period would be reduced to . If the period were ten thousand million years, the variation would similarly be reduced to at 1000 miles' depth, and would be to some appreciable extent affected by the spherical figure of the whole earth, although to only a very small extent, since there would be comparatively but very little change of temperature (less than of the superficial amount) beyond the first layer of 500 miles' thickness.

^{page 410 note *} For the mathematical demonstration of this solution, see Note appended to Professor Everett's paper, which follows the present article in the Transactions.

^{page 410 note †} That is to say, the quantity of heat conducted per unit of time across a unit area of a plate of unit thickness, with its two surfaces permanently maintained at temperatures differing by unity.

^{page 411 note *} Account of Some Experiments on the Temperature of the Earth at Different Depths and in Different Soils near Edinburgh; Transactions R.S.E., Vol. XVI. Part II. Edinburgh, 1846.Google Scholar

^{page 414 note *} The operations here described, involving, as may be conceived, no small amount of labour, were performed by Mr D. M'Farlane my laboratory assistant, and Mr J. D. Everett, now Professor of Mathematics and Natural Philosophy in King's College, Windsor N.S.

^{page 418 note *} The ‘conducting power’ of a solid plate is an expression of great convenience, which I define as the quantity of heat which it conducts per unit of time, when its two surfaces are permanently maintained at temperatures differing by unity. In terms of this definition, the specific conductivity of a substance may be defined as the conducting power per unit area of a plate of unit thickness The conducting power of a plate is calculated by multiplying the number which measures the specific conductivity of its substance by its area, and dividing by its thickness.

The thermal capacity of a body may be defined as the quantity of heat required to raise its mass by a unit (or one degree) of temperature. The specific heat of a substance is the thermal capacity of a unit quantity of it, which may be either a unit of weight or a unit of bulk.

^{page 422 note *} Professor Forbes on the Temperature of the Earth, Trans. R.S.E., 1846, p. 194.

^{page 426 note *} Because the absolute amount of heat flowing through the plate across equal areas will be inversely as the thickness of the plate; and the effect of equal quantities of heat in raising the temperature of equal areas of the water will be inversely as the depth of the water. The same thing may be perhaps more easily seen by referring to the elementary definition of thermal conductivity (footnote to § 11, above). The absolute quantity of heat conducted across unit area of a plate of unit thickness, with its two sides maintained at temperatures differing by always the same amount, will be directly as the areas, and inversely as the thickness, and therefore simply as the absolute length chosen for unity. But the thermal unit in which these quantities are measured, being the capacity of a unit bulk of water, is directly as the cube of the unit length, and therefore the numbers expressing the quantities of heat compared will be inversely as the cubes of the lengths chosen for unity, and directly as these simple lengths: that is to say, finally, they will be inversely as the squares of these lengths.