But Thomson put forward a third argument in the paper on Geological Time, which has always been regarded as the most important. It is derived from the fact, established by abundant observations, that the temperature in the earth's crust increases from the surface inwards; and that therefore the earth must be continually losing heat by conduction from within. If the earth be supposed to have been of uniform temperature at some period of past time and in a molten state, and certain assumptions as to the conductive power and melting point of its material be made, the time of cooling until the gradient of temperature at the surface acquired its present value can be calculated. This was done by Thomson in a paper published in the _Transactions, R.S.E._, in 1862. We propose to give here a short sketch of his argument, which has excited much interest, and been the cause of some controversy. In order to understand this argument, the reader must bear in mind some fundamental facts of the flow of heat in a solid. Let him imagine a slab of any uniform material, say sandstone or marble, the two parallel faces of which are continually maintained at two different temperatures, uniform over each face. For example, steam may be continually blown against one face, while ice-cold water is made to flow over the other. Heat will flow across the slab from the hotter face to the colder. It will be found that the rate of flow of heat per unit area of face, that is per square centimetre, or per square inch, is proportional to the difference of the temperatures in the slab at the two faces, and inversely proportional to the thickness of the slab. In other words, it is proportional to the fall of temperature from one face to the other taken per unit of the thickness, that is, to the "gradient of temperature" from one face to the other. Moreover, comparing the flow in one substance with the flow in another, we find it different in different substances for the same gradient of temperature. Thus we get finally a flow of heat across unit area of the slab which is equal to the gradient of temperature multiplied by a number which depends on the material: that number is called the "conductivity" of the substance.