16 REPORT — 1859. 



From these two constants, a second series of refracted wave-lengths may be calcu- 

 li C 

 lated, thus : — - cc = b 2 , — — a = c 2 &c, which will represent what the refracted wave- 

 lengths would be, were the medium free from irrationality. This series is presented 

 in Table III. ; and from it, compared with the series found by observation, as ex- 

 hibited in Table II., the values of x, or the extrusions for the different media, are 

 deduced, as exhibited in Table IV. 



In the larger proportion of the media which have been examined, these quantities 

 x are governed by certain determinate laws. The departures from these laws, pre- 

 sented by several media, are shown to be traceable to errors of observation ; and 

 they wholly disappear when the numbers are brought under the dominion of the 

 more general law, subsequently determined. Then only two exceptions remain — 

 the solution of muriate of zinc, and the oil of cassia. The discrepancy, in the for- 

 mer case, it is suggested, is probably due to errors which the observer himself 

 (Powell) suspects to exist in his determinations, — the discrepancy in the case of the 

 oil of cassia being probably traceable to a similar cause. 



The extrusive force, on which the irrationality depends, exhibits itself in the form 



of a transfer of motive energy, from the terminal to the central parts of the spectrum. 



The undulations, corresponding to the lines D, E, and F, are a little less retarded 



than they would otherwise be, and their wave-lengths within the medium are accord- 



. U 

 ingly a little less shortened. Hence for D, E, and F the formula is — — »-\-u x =u. 



The undulations, corresponding to B, C, G, and H, are a little more retarded than 



they would otherwise be, and their wave-lengths within the medium more shortened; 



. U 

 so that for these four the formula is — —« — ««=«, the positive and negative values 



€ 



of x balancing each other. Hence twice their sum, or 2X, is reckoned the measure 

 of the extrusive power of the medium. 



Every medium accordingly presents two nodes where the extrusion is nil and 

 passes from positive to negative. The upper node lies between C and D, and pro- 

 bably occupies the position of the mean wave ; the lower lies between F and G, and 

 near G. The only permanent exception is the oil of cassia, in which the lower node 

 falls a little below G. 



All regular media present the following relation : (3b., + 2c x — d x ) = (3h x -\-2g x —fx). 

 It is proposed to call this "the Semel-bis-ter law." Hence, if K = (B + C + G+H) 

 — (D + E+F) and Q = (b-\-c+g-\-h) — (d+e+f), the extrusive power may be ex- 



pressed thus: (Q+a+2X)=0. 



If the extrusions be taken in pairs, equidistant from the centre e x , and if the dif- 

 ference between b x and h. v be denoted by S, that between c x and g x by 8 2 , and that 

 between d x and/? by 8 3 , then the differences between each pair of these three quan- 

 tities o\, §,, and S 3 constitute a progression of the form f, 2<f, 3£, the quantity £ vary- 

 ing with the medium and temperature. It is proposed to call this " the law of the 

 equicentral common difference." 



The series of refracted wave-lengths b 2 , c„, d 2 , &c. having been calculated, as in 

 Table III., the refractive indices corresponding to them may be found from the 



R P 



formula - =f*fi, — =/s*j C, &c. This series of indices /*., B, fc. 2 C, &c. is what the 

 o 2 c 2 



medium would present, had it no extrusive power ; and the differences between these 

 and the observed indices show what portion of the latter is due to that property. 

 These two sets of indices present nodes, corresponding to those of the extrusions ; 

 and it is shown to be a general law, that the refractive indices, corresponding to the 

 nodes of the extrusions, coincide with the nodes of the two sets of refractive indices. 

 It is proposed to call this " the law of coincident nodes." 



The apparent exceptions to these laws are then pointed out, and the probability 

 of their being all due to errors of observation is discussed. 



The product of the two constants, or ess, deducted from each of the normal wave- 

 lengths, shows how much each normal is shortened in passing through the medium, 



