144 Mr. B. Stewart on certain Laws of Chromatic Dispersion, 



the other hand, the quantity a: is peculiar to each wave, the 

 medium and temperature remaining the same. 



Adopting, therefore, the above equation, and applying it to 

 the seven lines B, C, D, E, F, G, H, we obtain, in Mr. Ponton's 

 notation, the following seven equations : — 



e(b + a±b*)=B, 



e{c + a±c x )=C, 



&c. &c. &c. 



e(A+a±k) = H. 



In these, b y c, &c, B, C, &c. are supposed to be determined 

 by observation. We have thus remaining as unknown quanti- 

 ties e, 0, b X) c Xi &c. (nine in all), which require to be determined. 



In order to accomplish this, it is necessary to make two addi- 

 tional assumptions. These assumptions are quite arbitrary, and 

 have no relation to physical science. 



The first of these is made by Mr. Ponton in page 167, where 

 he assumes as true the following equation : 



(SB + 2C + D)-(F + 2G + 3H) _ 

 (3*+2c+rf) - (f+2g + M) ~ 6 ' 



An inspection of the seven equations given above will show 

 that this assumption implies that the following equality subsists : 



± 3k ± 2c x ± 4= ± 3k ± %g* ±U 



This equation, which is the immediate consequence of Mr. 

 Ponton's first assumption, he seems to regard as the general 

 expression for a law of nature, which he denominates the semel- 

 bis-ter law (see page ] 72). The second assumption is also made 

 in page 167. 



Calling B + C+D + E+F + G + H = S, 



b+ c +d+e +f+c/+ h=s } 

 it is assumed that 



S-€S = 



7e 



An inspection of the same seven equations will show that this 

 assumption implies that 



b x + c x + d x + e x +f x +g x +h x =0. 



This consequence of his second assumption appears also to be 

 recognized by Mr. Ponton as a law of nature in page 168, where 

 it is said, " In every case the motive energy gained by the one 

 set of waves is exactly balanced by the loss sustained by the 

 others ; so that the sums of the positive and negative extrusions 

 being each denoted by X, these two quantities are always equal. 



