136 PRINCIPAL J. D. FORBES ON AN EXPERIMENTAL INQUIRY 



tions admit of in other respects ; and I am particularly anxious to throw aside 

 every pretence of over-refinement. Now, this area is proportional to the difference 

 of the flow of heat across the section of the bar at x and that at x'. We have, there- 

 fore, by taking any number of areas, the differences 

 of such fluxes, or by approximating to the whole 

 areas ^x^ (which, I think, might quite well be 

 done), we have numbers proportional to the fluxes 

 themselves at x, x', x, kc. If these numbers are 



proportional to -^ in Table II., the Newtonian law is ^ ^~^ J 



correct ; if otherwise, the deviation will appear, and also the law, or at least num- 

 bers giving an empirical law. As I fancy this method to be new and important, 

 pray preserve this letter, and let me know at the same time whether you see 

 any flaw in the argument. You will probably not like the mechanical quadra- 

 tures ; but what else are our experiments but mechanical quadratures in many 

 cases ? And this is an experiment on paper capable, I apprehend, of being better 

 measured than an experiment to measure heat with a thermometer. 



8. " IV. It would be a most interesting verification to repeat the whole, with 

 the same bar having a mm surface given to it, which would radiate twelve or 

 fifteen times faster, which I believe might be done." 



9. My correspondent having expressed some doubt as to the accuracy with 

 which the quadratures could be performed, I thus wrote from Phoesdo, on the 

 11th October 1850: " The mechanical integration I spoke of could be got rid 

 of thus : — Treating a small part of the curve ah (in my former letter) as a 



logarithmic, calculate from it ^-y for each point ; these numbers should be pro- 

 portional to the corresponding ordinates of the curve a/5. Nevertheless, I suspect 

 that in practice the method formerly proposed would be more exact." It will be 

 seen presently, that the quadrature of the areas proved to be practicable and 

 accurate, and that it was the method adopted. 



10. In a letter, a few weeks later, the conclusions are carried further. 



"■Jo Professor Kelland. 



" Edinburgh, 11th Novemler 1850. 



" In my letter of the 26th September, I explained a form of experiment, by 

 which I proposed to test the fundamental assumption of the Mathematical Theory 

 of Heat. I shall now show that the same experiment performed on bars of 

 different metals, will give at once and directly, the constant of conducting power 

 for each metal, which, so far as I know, has never been done by experiments on 

 bars only, such experiments having given hitherto merely relative results. Fourier 



