16 REPORT 1856. 



Thus, proceeding in all cases on the principle of vis viva, and that of the mecha- 

 nical equivalence of the incident, reflected, and refracted vibrations, — on the hypo- 

 thesis of equal densities, — of vibrations parallel to the plane of polarization, — and of 

 Maccullagh's law of equivalence, vie have Maccullagh's formulas (H) and (K). (A.) 



On the hypothesis of increased density, — of vibrations perpendicular to polariza- 

 tion, and Maccullagh's law of equivalence, we have Fresnel's formula (H), but a for- 

 mula (K) differing from Fresnel's in the signs. (B.) 



On the same hypotheses, but taking that form of the law of equivalence which 

 Fresnel adopted in one instance, we have (H) differing from Fresnel's in sign, and 

 (K) the same as Fresnel's. (C.) 



The theoretical principles seem as yet to furnish no guide to a choice between 

 these assumptions ; but the results of experiment must be appealed to. 



The only known experimental results which bear upon the question between these 

 several formula and the hypotheses on which they are deduced, are — 



I. Professor Stokes's result of the change of plane of vibration and polarization in 

 diffraction, which sets aside absolutely the hypothesis of vibrations parallel to the 

 plane of polarization, and by consequence Maccullagh's formulae (A), and the hypo- 

 thesis of equal densities on which they are founded. 



II. The result of Arago, Fresnel and Brewster, as to the change of plane of polari- 

 zation by reflexion ; the new plane being, at small incidences, on the opposite side of 

 the plane of incidence to that of original polarization ; while after passing the inci- 

 dence of complete polarization it comes to the same side. This requires formulas 

 which give h' and V of opposite signs at small incidences, and of the same sign after 

 the polarizing incidence, which is only the case with Fresnel's original formulas 

 (B, a.) and (C, /3), and excludes those on the other hypotheses, (R, /3), and (C, u). 



III. The result of Dr. Lloyd from his interference fringes, where at the extreme 

 oblique incidence the incident and reflected ray are in opposite phases ; this requires 

 both h' and h, as also Ic and V, to be of opposite signs at great incidences, which 

 agrees only with Fresnel's original formulas (B, a) and (C, /3). 



But these inferences assume the correctness of the reasoning on the symbols as 

 hitherto adopted, both by the original investigators referred to, and also in the ele- 

 mentary treatises of Mr. Airy and others. Some suggestions lateh^ made in order 

 to bring the other formulas into accordance with the facts, can only do so by setting 

 aside the validity of the entire reasoning just referred to. These suggestions turn 

 on the geometrical change in position which (in the case of vibrations parallel to the 

 plane of incidence) the directions of the vibrations undergo, with the change of posi- 

 tion of the ray, in passing from small to large incidences, so that if they accord in 

 the first instance they will (from this cause alone) be opposed in the second. 



On the other hand, the original formulas of Fresnel are still deficient in respect 

 to their direct deduction from any one of the above-mentioned hypotheses ; they will 

 only follow from partially adopting two of them, viz. (B, oi) and (C, /3). 



A suggestion for deducing them on another principle has been since made by the 

 author in the ' Philosophical Magazine,' October 1856. 



On a Modification of the Maynooth Cast Iron Battery. By W. Symons. 



A recent paper by Professor Callan in the ' Philosophical Magazine ' on a cast iron 

 batter)' which he states to be equal in power to Grove's nitric acid battery, will 

 probably induce many persons to adopt this very cheap but cumbrous metal. The 

 battery now exhibited is an improvement on one published by the author in the ' Phar- 

 maceutical Journal ' for February 1853, and its recommendations are compactness, as 

 it can be moved as one mass ; and simplicity and economy of construction, as one 

 wooden screw is sufficient for 10 or 12 pairs. The construction was minutely de- 

 scribed, and two arrangements of plates were shown, one adapted for a Wedgewood 

 trough with cast-iron plates on each side of each zinc plate, and the other fitted up 

 in a similar manner to a battery described by Martyn Roberts, in which he proposes to 

 use both sides of both plates : such an arrangement may perhaps be advantageous 

 where the resistance is very small, but from a few experiments with the battery shown, 

 it appears to be far from economical where the resistance is equal to that required for 

 the decomposition of water. Six pairs on each plan were fitted up with similar plates 



