M. H. Sainte-Claire Deville on Affinity and Heat. 365 



In the case where the points I, J lie on a conic of the series, 

 the consideration of this conic shows that the curve has a ninth 

 double point, the pole of the line IJ in regard to the conic in 

 question : in this case the sextic curve, as is known, breaks up 

 into two cubic curves. 



P.S. In general the curve Xv / A+^v / B + v\/C+7r\/D = 

 has (exclusively of multiple points at infinity) six double points ; 

 viz. these are situate at the intersections of the pairs of circles, 



(\\/A + ^\/B = 0, j/ v / C + 7r V / E'=.0), 



(Xv / A + v\/C = 0, fi</B + w\/D = 0), 



(Xv 7 A + 7r\/l> = 0, /x^B + 7T V / C = 0). 



In the case of the curve of foci, the first, second, and third pairs 

 of circles intersect respectively in the points (AB.CD), (AC.BD), 

 (AD.BC), which, as mentioned above, are double points on the 

 curve ; and they besides intersect in three other points, which 

 are the other three double points mentioned above. 



Professor Sylvester reminds me that he mentioned to me in 

 conversation that he had himself obtained the foregoing equa- 

 tion 2+ (B, C, D)v^A = 0, for the locus of the foci of the conies 

 which pass through the four points A, B, C, D. 



Cambridge, October 10, 1866. 



XLIX. Affinity and Heat. 

 By H. Sainte-Claire Deville*. 



ALL the labours, all the tendencies of modern science lead to 

 the identification of the forces which come into play in 

 the physical and chemical phenomena of nature ; all the nume- 

 rical determinations which have been obtained tend to establish 

 their equivalence in the most rigorous manner. Affinity and co- 

 hesion cannot escape this identification, and already the mecha- 

 nical theory encloses them within the circle of reasonings which 

 must soon dispel whatever vague and mysterious notions may 

 still be connected with them. 



It cannot be concealed that the study of primary causes, in the 

 phenomena which we observe and measure, presents in itself a 

 serious danger. In the absence of any precise and independent 

 definition of special facts, the consideration of primary causes 

 leads us, oftener than we suppose, into really begging the ques- 



* Translated from the first chapter of a series of Lectures on " Dissocia- 

 tion," published in the Legons de Chimie for 1864-65. 



