TRANSACTIONS OF THE SECTIONS. 



13 



have, in fact, the flux of heat passing from the hotter extremity of the body across 

 the particular section in question ; for the condition of permanence of the tempe- 

 rature of the bar arises from the equality of the heat supplied and dissipated. Hut 

 the whole heat dissipated in unit of time is the integral of the partial dissipations 

 represented by vertical ordinates of the last-named curve, taken between any as- 

 sumed point x and the furthest or cool end of the bar. This quantity, then, is F 

 or the flux across unit of section at the point x. 



V. We are now able to resolve the question whether or not the flux of heat is in 

 the given bar everywhere proportional to the rapidity with which the temperature 



decreases as x increases, or whether the equation holds, F= — Ay > the conducting- 



power k being supposed to be constant. 



The following Table shows that the constancy of k in the case of iron cannot be 

 assumed, — on the contrary, that the conductivity diminishes when the tempera- 

 ture increases. 



The author had pointed out so long ago as in 1833 the apparent coincidence of 

 the order of metals, taken with reference to their power of conducting heat and elec- 

 tricity. In 1852 he announced that the conductivity of iron for heat diminished 

 with the temperature. Since that time Dr. Matthiessen has clearly established the 

 same result for electricity, and finds, moreover, that the temperature- coefficient 

 varies most rapidly at lower temperatures — a law which may be observed also to hold 

 in the preceding Table for Heat. It would be premature to assert from these expe- 

 riments alone that the " percentage decrement " in the case of iron is the same for 

 heat and electricity, although it is not impossible that it may turn out to be so. 



On the Second Law of Thermodynamics*. 

 By W. J. Maccjuorx Rankixe, F.lt.S. 

 It has long been established that all the known relations between heat and me- 

 chanical energy are summed up in two laws, called respectively the first law and 

 the second law of thermodynamics, viz. : — First Law : Quantities of heat and of 

 mechanical energy are convertible, at the rate very nearly of 772 foot-pounds to 

 the British unit, or 424 kilogrammetres to the French unit of heat. Second Law : 

 The quantity of energy which is converted from one of those forms to the other 

 during a given change of dimensions and condition in a given body is the product 

 of the absolute temperature into a function of that change and of the kind and 

 arrangement of the matter of the body. By absolute temperature is here to be un- 

 derstood temperature measured according to a scale so gi-aduated that the tempe- 

 rature of a homogeneous body shall vary in the simple proportion of the quantity 

 of energy it possesses in the form of sensible or thermometric heat. The laws of 

 thermodynamics as here stated are simply the condensed expression of the facts of 

 experiment. But they are also capable of being viewed as the consequences of the 

 supposition that the condition of bodies which accompanies the phenomena of 

 sensible heat consists in some kind of motion amongst their particles. The first 



* Printed in full in the Philosophical Magazine for October 1865. 



