INTO THE LAWS OF THE CONDUCTION OF HEAT IN BARS, ETC. 137 



has shown (p. 406) [of the Theorie de la Chaleur] that when the thickness of bars 

 is small, though the temperature of equilibrium varies from the axis to the 

 surface, the temperature at any point is very approximately in a constant ratio to 

 the temperature of the central point of the section to which it belongs ; so 

 that the bar may be regarded as a bundle of parallel rods, in each of which 

 the temperature varies with the lengtli according to the same law. Now, the 

 experimental curve a/3 of my last letter represents the momentary loss of heat at 

 every point of the axis of the bar in thermometric degrees ; the area of the curved 

 space X a unit of transverse section near the axis, represents the number of 

 cubical units of volume of tlie material, raised 1° by the heat flowing through 

 [across] unit of section, near the axis of the bar at the point x. The specific heat 

 of the metal being known, we can convert this amount of heat or flux across x 



into absolute measure ; for the Flux is = - K j-, and ^ is known by Table I. of 



my former letter. Thus every experiment becomes an independent means of find- 

 ino" K, and that without reference to the state of the surface, which has always 

 been a difficulty in comparing different metals with unlike radiating surfaces." 



11. The preceding extracts sufficiently set forth the principles on which the 

 experiments were conducted, and I have preferred using the exact words in 

 which I first sketched them, because it serves to fix the date, and also because 

 they were in every point carried out in practice. 



12. The experiments referred to in the present paper were all made between 

 the 6th November 1850 and the I7th April 1851. They refer to the conductivity 

 of Wrought-Iron alone. I do not here intend to describe the experiments in 

 detail, nor to enter into the particulars of the reductions (which would require the 

 engraving of some elaborate curves) ; nor do I offer the final results as thoroughly 

 satisfactory to myself, though I hope, at a future time, to be able to lay before 

 the Society these details, and to carry out the reductions in a way which will 

 leave little to desire in the way of numerical precision. 



13. The causes of the delay in publishing the results were these : — The 

 thermometers, on whose exactness and comparability (especially at high tempera- 

 tures), the accuracy of the experiments materially depended,were furnished to 

 me by a Paris maker, who, at that time, enjoyed the highest reputation for trust- 

 worthiness and precision. I soon found, however, that some of the instruments 

 were unfit for my purpose, that one or two were disgracefully bad, and that others 

 were not entirely reliable at all points of their scales. The worst thermometers 

 were rejected, and the remainder were used with every possible precaution, and 

 were farther checked by other instruments in my possession. A severe illness in 

 November 1851, before I had resumed my experiments for the winter, brought 

 the series to an abrupt conclusion. Fortunately the data for wrought-iron were 



VOL. XXIII. PART I. 2 P 



