The Energy of Segmentation 293 



Or, it is likewise for the same reason permissible to substitute in 

 place of 0, and A in equations [4] and [7] E as standing for any 

 and all energy quanta added to the system under reversible con- 

 ditions, thus getting 



,/r'= E y [9] 



which becomes, by substituting for E its value, found in [2], 



dW=W+ iU,- U,) ^^ [10] 



from which equation [8] is again obtained. 



Equation [8] is accordingly an epitomized expression of the First 

 and Second Laws, since they alone have been used in deducing it, 

 and therefore also, of the Third and Fourth to the extent, at least, 

 to which these last have been found, in the preceding section, to be 

 either further aspects or implications of the first two. The equa- 

 tion is, for these reasons, of the greatest importance. 



In this equation ^signifies the maximum external work produced 



by any reversible change taking place in any system at a constant 



intensity/; L'^. — f/i; is the accompanying change (increase) in the 



energy of the system itself; dfF-^ the increase in the quantity of 



work produced when the same change in the system takes place 



dfF . 

 at the intensity I + dl; —— is the potential coefficient, the extensity 



factor; /, the intensity; the resultant change in the energy of the 

 system equals the product of the two. 



Now, the above equation is worked out tor changes taking 

 place under reversible conditions; but since a change to be rever- 

 sible must take place under equilibrium conditions, and it is upon 

 these that the quantity of work produced is dependent, the above 

 equation makes it possible to determine the effect of temperature 

 or any other intensity on an equilibrium by calculating dWidI 

 when the other quantities fV and U^ — U^ are known. The equa- 

 tion will, then, have been applied to a concrete change, taking place 

 of course according to some specific law, when the values for W 

 and U; — U, have been found bv measurements and have been 



