That which has been learned by an ingenious analytic calculation, expressly perfected for this class of investigations,* p 173 regarding the motion of heat in homogeneous metallic spheroids, must be applied with much caution to the actual character of our planet, considering our present imperfect knowledge of the substances of which the Earth is composed, the difference in the capacity of heat and in the conducting power of different superimposed masses, and the chemical changes experienced by solid and liquid masses from any enormous compression. [footnote] *Here we must notice the admirable analytical labors of Fourier, Biot, Laplace, Poisson, Duhamel, and Lame. In his 'Theorie Mathematique de la Chaleur', 1835, p. 3, 428-430, 436, and 521-524 (see, also, De la Rive's abstract in the 'Bibliotheque Universelle de Geneve', Poisson has developed an hypothesis totally different from Fourier's view ('Theorie Analytique de la Chaleur'.) He denies the present fluid state of the Earth's center; he believes that "in cooling by radiation to the medium surrounding the Earth, the parts which were first solidified sunk, and that by a double descending and ascending current, the great inequality was lessened which would have taken place in a solid body cooling from the surface." It seems more probable to this great geometer that the solidification began in the parts lying nearest to the center: "the phenomenon of the increase of heat with the depth does not extend to the whole mass of the Earth, and is merely a consequence of the motion of our planetary system in space, of which some parts are of a very different temperature from others, in consequence of stellar heat (chaleur stellaire)." Thus, according to Poisson, the warmth of the water of our Artesian wells is merely that which has penetrated into the Earth from without; and the Earth itself "might be regarded as in the same circumstances as a mass of rock conveyed from the equator to the pole in so short a time as not to have entirely cooled. The increase of temperature in such a block would not extend to the central strata." The physical doubts which have reasonably been entertained against this extraordinary cosmical view (which attributes to the regions of space that which probably is more dependent on the first transition of matter condensing from the gaseo-fluid into the solid state) will be found collected in Poggendorf's 'Annalen', bd. xxxix., s 93-100.