The following is from _Pictet's experiment: The apparent radiation and reflection of cold_ by James Evans and Brian Popp (1985). (google search for full pdf paper)
I think Evan's and Popp's criticism of Rumford's theory in the last paragraph below is mistaken. It is only the relative difference in frequency that determines whether a ray will be cooling (frigorific) or warming (calorific) rather than a relative difference in amplitude. An increase or decrease in amplitude will only affect the rate at which cooling or warming occurs so Rumford's theory is not plagued by internal inconsistencies as they argued. Another interesting part of Rumford's theory is that a body only cools or warms by the rays it receives rather than by the rays it emits. --Begin quote-- Rumford's own explanation of the radiation and reflection of cold was thoroughly undulationist in nature. As suggested at the beginning of this article, Rumford regard-ed radiant heat as an undulation analogous to sound, and seems to have viewed Pictet's experiment more or less as a case of a driven oscillator: "The cold body in one focusCompels the warm body the thermounctcr, in the ciber to-cus to change its note." This was the explanation he ven-tured to offer his companions at Edinburgh in 1800. Later,u lis eper of 1804, he gave a more or less complete sketch of his view of radiant heat. To begin, imagine a bell, or any other body perfectly elastic, placed in a perfectly elastic fluid medium and sur-rounded by other perfectly elastic bodies. When the bell is struck and made to vibrate, its vibrations are gradually communicated, by means of the undulations or pulsationsthey occasion in the elastic fluid medium, to the other sur-rounding bodies. If these bodies should happen already to be vibrating at the same frequency with which the bell vi-brates, the undulations occasioned in the elastic medium by the bell would neither increase nor diminish the fre-quency of the vibration of the surrounding bodies; nor would the undulations caused by the vibrations of these bodies tend to accelerate or retard the vibrations of the bell.But if the vibrations of the bell were more frequent than those of the surrounding bodies, the undulations produced by the bell in the elastic fluid would tend to accelerate the vibrations of the surrounding bodies. On the other hand,the slower vibrations of the surrounding bodies would re-tard the vibrations of the bell. The bell and the surrounding bodies would continue to affect one another until, by the vibrations of the latter being gradually increased and those of the former diminished, they would be reduced to the same tone. Now, if heat is assumed to be nothing more than the vibrations of the constituent particles of a body, the cooling of a hot object by radiation will entail a series of actions and reactions similar to those just described for the case of the bell. The rapid undulations produced in the surrounding ethereal fluid will act as calorific rays on the neighboring bodies, and the slower undulations produced by the vibra-tions of these colder bodies will act as frigorific rays on the hot body. These reciprocal actions will continue until the hot body and the colder bodies around it have acquired the same temperature, i.e., until their vibrations have becomeisochronous.It follows that cold and heat are relative terms. The rays from one particular object will be either frigorific or calo-rific, according as they impinge on other objects either warmer or colder than itself. Imagine three identical bo-dies, A, B, and C. Let A be at the temperature of freezing water, B at the temperature of 72 °F, and C at 112 °F. The Rays emitted by B will be calorific with respect to the colderbody A, but frigorific with respect to C. Moreover, they will be just as efficacious in heating the former as in cooling the latter. "According to this hypothesis, cold can with no more propriety be considered as the absence of heat than a low orgrave sound can be considered as the absence of a higheror more acute pitch; and the admission of rays which generate cold involves no absurdity and creates no con-fusion of ideas." 48 The application of Pictet's experiment is immediate and obvious. The rapid vibrations of the particles of the ther-mometer produce rapid undulations in the surrounding elastic fluid. These undulations arrive, after two reflec-tions, at the cold body, where they act to raise its tempera-ture. Simultaneously, the slower vibrations of the coldbody give rise to slower undulations in the elastic medium which proceed, again by means of two reflections, to the thermometer. The accumulation of these frigorific rays in the thermometer causes its temperature to fall. And, con-cludes Rumford, "...this is what actually happened in the celebrated experiment of my ingenious friend, ProfessorPictet, of Geneva.”:49 Rumford thus explains the experiment solely in terms of frequencies of vibration. That is, he assumes that the "dif-ference of temperature depends solely on the difference of the times of the vibrations of the component particles of bodies.” This assumption, however, was made only for the purpose of simplifying the discussion. Rumford remarks that it is possible, even likely, that the temperature differ-ence depends on the velocities of the particles. This modification of the theory was required to explain the obvious fact that the intensity of the radiation from a hot body falls off with distance. The pulsations produced in an elastic fluid by the vibrations of a body immersed in it are everywhere isochronous, but the mean speed of any individual particle of fluid diminishes with the distance from the cen-ter of the disturbance. Thus, remarks Rumford, in the case of sound, the frequency of the pulsations determines the note; but it is the velocity of the particles of the air, or the amplitude of the wave, that determines the strength or force of the sound. So too with light, it is likely that color depends on the frequency of the pulsations that constitute light, and that the heat produced by them is in proportion to their force. 50 Thus it was clear to Rumford himself that the elegant analysis based on frequencies alone could not stand. Yet,the introduction of amplitudes or velocities leads to other contradictions that Rumford did not perceive. Assume That the undulations in the elastic fluid are calorific in effectif their amplitude, or perhaps their mean speed, is greater than that of the particles of the body on which they im-pinge. As a hot body is moved to greater and greater dis-tances, the oscillations that it produces at a given fixed point in the fluid diminish in amplitude and velocity. Thus,if the body were removed to a great enough distance, it's undulations would apparently change over from calorific to frigorific in effect--something quite without foundation in experience. The essential difficulty with Rumford's ver-sion of the undulationist theory was that he wished to asso-ciate the change in temperature experienced by an object solely with the radiation absorbed by it, and denied the temperature changing effect of the emitted radiation. As a result, Rumford's system suffered from internal inconsis-tencies that did not trouble Prevost's.51 -- end quote --
