142 PRINCIPAL J. D. FORBES ON AN EXPERIMENTAL INQUIRY 



25. The Statical and Dynamical forms of experiment on the relations of a 

 given bar to heat {both of which are required for the solution of our problem), 

 each present their peculiar difficulties. But there is one difficulty in connection 

 with the latter, which I think it right to mention, because I did not succeed in 

 wholly removing it when temperatures approaching 200" Cent. (392^ Fahr.) are 

 to be employed. The object of the Dynamical experiment (as already explained), 

 is to find the rate at which any point of the bar in the Statical experiment 

 is, in point of fact, parting with its heat by the surface, ascertained in terms of 

 the temperature shown by the thermometer sunk into it at that point. But 

 when a bar has been uniformly heated in all its parts by immersion in the metal- 

 bath, the distribution of heat over any transverse section is not at first the same 

 as when the bar in the statical experiment has attained a permanent temperature ; 

 nor the same as when the bar under experiment has cooled to a certain extent. 

 In fact, Fourier's analysis shows, that in the early stages of cooling of a body at 

 first heated uniformly, the temperature includes in its expression certain circular 

 functions, which, by and by (and in good conductors very rapidl}^), become in- 

 sensible. Such oscillations affecting the rate of cooling (or - ->|- j are perceptible 

 in the experiments which I have made, and influence the determination of this 

 important quantity in the highest part of the scale. The general tendency of the 

 effect is manifestly to make the rate of cooling of the thermometer, sunk to the 

 axis of the bar, at first too small. For the bar being uniforml}' heated from centre to 

 surface when it is withdrawn from the metal-bath, it is only as the superficial parts 

 cool that the central parts begin to lose heat, which they supply to the surface. 

 Next, the rate of superficial cooling will be relatively somewhat accelerated, and 

 a fresh demand upon the interior will occur. These gushes of heat will gradually 

 disappear, and, as I have said, are in good conductors only at first perceptible.* 



26. The initial irregularities at temperatures approaching 200° Cent, are the 

 greatest difficulties which met me in this inquiry, and I fear that they have been 

 but partially overcome. We are precluded from obviating them by the natural 

 expedient of heating the bar initially to a much higher temperature, and allow- 

 ing it to cool spontaneously down to that at wdiich the observations commence. 

 For even polished iron changes the condition of its radiating surface at tempera- 

 tures which considerably exceed 200° Cent., so that this plan is inadmissible. In 

 fact, the heat was pushed in these experiments quite to the limit.f I have fully 

 stated this difficulty, in order that future experimenters may be prepared to con- 

 tend with it. Electroplating might possibly succeed, though I fear not. 



* This interpretation of the physical origin of the periodic functions in the cooling of bodies was 

 given in the Encyclopcedia Britannica, Sixth Dissertation, Art. (674). When the circular functions 

 have exhausted themselves, the exponential portion of the expression for the temperature alone 

 remains. See Fourier, Theorie Analytique de la Chaleur. 



f When coated with paper, the paper begins to singe at a temperature slightly above that of 

 melting tin, or 442° Fahr, 



