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TRANSACTIONS OF THE SECTIONS. 9 
referring to the ideal analogy of musical intervals. Yet Newton’s notion of the 
permanency of the proportions in the analysis of light might seem but the necessary 
consequence of the permanence of the synthetic result. And this main difficulty 
yet remains to be cleared up. 
The Abbé Moigno has also referred more particularly to this subject in his 
‘ Répertoire d’Optique Moderne’ (Paris, 1847, vol. i. p. 123-126). After giving 
M. Cauchy’s formula, he states that in my comparisons of observation and theory 
for a great number of media the differences never exceeded the probable errors of ob- 
servation., Unfortunately not only is this not the case, but I have expressly dwelt 
upon it, in reference to one or two most highly dispersive substances. He also ob- 
serves, that M. Cauchy (in his ‘ Nouveaux Exercices’) has re-calculated the results, 
and shown a perfect accordance. But this applies only to Fraunhofer’s ten media, 
and does not extend to the highly dispersive oils. He further states the deduction 
from M. Cauchy’s formula, that the differences of the squares of velocities of pro- 
pagation are very nearly as the reciprocals of the squares of the wave-lengths ; but 
adduces only one case of flint-glass in proof. It seems to be often overlooked, that 
though there is a close accordance for all moderately dispersive substances, yet a 
very few instances to the contrary in the higher part of the scale suffice to show that 
the formula stands in need of some essential modification to make it apply to them, 
while it shall still include the former. I have pointed out * that an empirical con- 
stant for each medium will rectify the discordance. Whether this can be justified by 
theory, is the point to which the attention of mathematicians ought I think now to 
be directed. 
Both M. Mossotti and M. Moigno admit the necessity of assuming (according 
to the number of terms taken) three or four experimental constants for the medium. 
I notice this, because it has been objected to in my investigations. But on distinct 
grounds it appears to me evident that from the nature of the problem we must suppose 
at least three constants to characterize each medium. In other words, the problem is 
a compound one, each medium having as it were three distinct properties :—1st, the 
absolute magnitude of its refraction, or deviation of the whole spectrum or of a mean 
ray; 2nd, the magnitude of dispersion, or expansion of the whole; 3rd, the cha- 
racter of the dispersion or relative expansion of the parts: conditions which are 
certainly independent of each other, and each of which would involve a separate 
constant. 
On Irradiation. By the Rev. Prof. PowEii, F.R.S. §e. 
The phenomenon known by the name of Irradiation is best exhibited by the me- 
thod of M, Plateau, which forms the basis of all the author’s experiments, and 
which consists of a card or lamina cut so that a long paral- 
lelogram has one half cut out and the other left, the por- 
tions at the sides being cut away. ‘Thus the effect is seen 
doubled either by transmitted or reflected light. [In the 
annexed sketch the shaded portions represent the parts cut 
away.] It is well established that the effect increases with 
the intensity of the light. It is also evident that it decreases 
rapidly towards the edge of the enlarged surface. 
The effect has been ascribed by most writers to a peculiar 
kind of physiological affection of the retina. But (allowing 
for the effects of dazzling, contrast, &c.) the author has shown that this is not the 
fase, since exactly the same effect is produced in an artificial eye, or camera obscura. 
The effect has also been tried photographically, in some cases especially in direct sun- 
light, with perfect success; in others without effect. But the most effective photo- 
graphic rays are not the most illuminating, and may therefore not be equally subject 
to this modification. 
These phenomena appear to be simply cases of the enlarged focal image of a lu- 
minous point, which is a well-known result, both of theory, as investigated by Mr. 
Airyt, and of observation, as seen in the discs of fixed stars under contracted aper- 
tures. 
f * Treatise on Dispersion, &c., p. 119. + Camb, Trans. v. 283. 
Wy 
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