416 Scientific Intelligence. 
suppose that the chromatic aberration is at least partially corrected. 
One result of the calculations into which 1] have entered (which were 
first in part undertaken at my request, by Mr. James Clerk Maxwell, 
stated in two lines. If we calculate the effect upon the final focal 
distance of the whole refracting system of the eye (q’), of a varia- 
tion in the refractive index of each of its th 
M2, us, ua). e find this equation when the incident rays are parallel, 
or reach the eye from a very distant object :— 
: 0q" = 1-579 du2 + 1-150 dus — 2-788 dus. 
Let the coéfficients du2, dus, dua denote the dispersion or differences 
of the indices of refraction for extreme rays, corresponding to the three 
media, then it is evident, from the negative sign of the third term on 
the right hand, that they may be so chosen as.to annihilate the second 
side of the equation, or make the variation of focal distances nothing, 
for the differently refrangible rays. ' 
If the rays proceed from a point 10 inches distant from the eye, the 
e 
equation for the variation of the focus will 
0q’= 1873 Ou2+-1-402 dus —3:298 dus 
and the condition which makes this equal to zero, or the focus inde- 
ndent of small variation of the refrangibilily of the ray may be 
satisfied, at the same time that the former equation is satisfied also ; 
sequently, with three media, as in the eye, we may have perfect 
achromatism for any lwo distances; which would also be sensibly per- 
fect for the intervening ones. Of course by perfect achromatism, we 
here mean a union of the extreme red and violet rays, the irrationality 
of dispersion does not concern this question. 
II. Mrineratoey. 
1. Allanite from West Point; by Dr. C. Bercemann, (from Pog- 
gendorff’s Annalen, Ixxxiv, p. 485, and communicated to this Journal 
by W. G. Letrsom.)—From Mr. Saemann the mineralogist I received 
for examination a substance resembling Allanite from the gneiss at West 
Point, N. Y., which he procured while in the United States, It resem- 
bles most the. allanite of Jotunfjeld, except that at West Point crystals 
of considerable size are met with, as well as pure compact masses of 
the mineral. : 
Although of late years allanite has been examined more than once, 
I thought it as well nevertheless to analyse the mineral derived from 
was not observable in the fragments at my disposal. — 
all but deprived of its solubility in acids by exposure to a red heat. 
