SECT. IV.] PENETRABILITY AND PERMEABILITY. 463 



do not appear to us to be exact. Each of them, the first especially, 

 would rather express, according to all analogy, the faculty of being 

 conducted than that of conducting. 



Heat penetrates the surface of different substances with more 

 or less facility, whether it be to enter or to escape, and bodies are 

 unequally permeable to this element, that is to say, it is propagated 

 in them with more or less facility, in passing from one interior 

 molecule to another. We think these two distinct properties 

 might be denoted by the names penetrability and permeability 1 . 



Above all it must not be lost sight of that the penetrability of 

 a surface depends upon two different qualities : one relative to the 

 external medium, which expresses the facility of communication by 

 contact ; the other consists in the property of emitting or admit 

 ting radiant heat. With regard to the specific permeability, it is 

 proper to each substance and independent of the state of the 

 surface. For the rest, precise definitions are the true foundation 

 of theory, but names have not, in the matter of our subject, the 

 same degree of importance. 



431. The last remark cannot be applied to notations, which 

 contribute very much to the progress of the science of the Calculus. 

 These ought only to be proposed with reserve, and not admitted 

 but after long examination. That which we have employed re 

 duces itself to indicating the limits of the integral above and below 



the sign of integration I ; writing immediately after this sign the 

 differential of the quantity which varies between these limits. 



We have availed ourselves also of the sign S to express the 

 sum of an indefinite number of terms derived from one general 

 term in which the index i is made to vary. We attach this index 

 if necessary to the sign, and write the first value of i below, and 

 the last above. Habitual use of this notation convinces us of 



1 The coefficients of penetrability and permeability, or of exterior and interior 

 conduction (h, K], \vere determined in the first instance by Fourier, for the case 

 of cast iron, by experiments on the permanent temperatures of a ring and on the 



varying temperatures of a sphere. The value of by the method of Art. 110, 



and the value of h by that of Art. 297. Mem. de I Acad. d. Se. Tome v. pp. 

 165, 220, 228. [A. F.] 



