154? THE RADIATION OF HEAT ON THE PROPAGATION OF SOUND.
that, in the case of these experiments, the intensity would he diminished by a sort of reflexion at the bondings" of the tube, as well as by the friction of the air against the sides of the tube, and the internal friction of the air itself. That the cause last mentioned would produce a small but not utterly insensible effect in causing a diminution of intensity, I have shown in the course of a paper " On the Effect of the Internal Friction of Fluids on the Motion of Pendulums/' recently read before the Cambridge Philosophical Society*. If we suppose, at a venture, that a diminution of intensity in the ratio of 2 to 1 is the utmost which we can attribute to radiation in the case of M. Biot's experiments, putting N=2, and #=3120, the length of the tube in feet, we get from (20) y = 0*834 for a superior limit of q. If we suppose ^ = 0*834, we get for the ratio in which the temperature of a small portion of slightly heated air would be diminished in the course of one second, 1 to e"q, or 1 to 0'4343, or 7 to 3 nearly. It is curious that it should, theoretically speaking, he possible to assign a superior limit to the velocity of cooling of heated air by observations on sound ; but I imagine that the real value of q is a good deal smaller than any limit which it would be practically possible to assign in this way.
I have supposed, as was already observed, that radiant heat is capable of traversing great lengths of air before any considerable portion of it is absorbed. 'Phis is especially the case with heat of such high refnui^ibility as to place it within the, limits of the visible spectrum ; whereas heat- of low re fra nubility, such as that which would emanate from slightly healed air, is absorbed more rapidly. Should the distance to which radiant, heat can proceed in air before a i^'ivon fraction of it, such as one-li;ilf, is absorbed, not. be extremely «jreat compared with the length of a wave of sound, it may be seen after a little reflection that the general conclusions arrived at will be unchanged, though the numerical details would be .somewhat altered. 1 have not met with any experiments relating to the absorption of non-luminous heat by air which could be made a foundation for numerical calculation.