THK YOUNG SCIENTIST. 
131 
that even first-class mathematicians have 
hitherto shrimli from the attempt. 
Diagrams, however, are surprisingly 
accurate in their capability of indicating- 
causes and results in the microscope and 
object-glass ; for these lenses are minute, 
with deep curves and abrupt refractions ; 
so that if the projection is worked out 
some fifty times tlie size of the original, 
small errors can be detected. The work 
should be commenced at the back from a 
long conjugate focus, which not being a 
constant distance, may be taken as very 
near to parallelism. The high powers all 
have the means of correction within this 
distance, and perform better with a long 
posterior focus than with a very short one. 
The relative indices for the two or more 
rays should be marked on a large pair of 
proportional compasses, the long limb 
representing the sine of the angle of inci- 
dence, and the short one that of refrac- 
tion. Both the sines ought to be set off 
in a diagram behind, and neither of them 
in front of the ray in couse of projection ; 
this leaves the way clear, with the least 
confusion of lines. 
At the same time a second or counter- 
part diagram should be at hand, to which 
the rays only are transferred as soon as 
their direction is ascertained ; with these 
precautions a mistake is scarcely possi- 
ble. 
Now it is hoped that some improve- 
ments may be effected by this investiga- 
tion, on account of the simplicity attained 
in the combination, in which we have two 
single lenses of crown, whose foci bear a 
definite proportion to each other; w^hile 
all the corrections are performed by one 
concave of dense flint, the acting condi- 
tion of which is not altered by the in- 
fluence of any other concaves acting in 
the combination, and hitherto taking a 
share of the duty. This one flint is now 
to l)e considered singly as the heart and 
centre of the system in reference to the 
correction of the rays entering and leav- 
ing. 
This memoir is of necessity incomplete, 
for want of definite information concern- 
ing the optical properties of various kinds 
of glass. Nothing of importance has been 
published since Fraunhofer's Table con- 
taining the refractive indices for each of 
the seven primary color-lines of the spec- 
trum for ten kinds of glass. Great ad- 
vance has been effected since that date in 
the manufacture of optical glass, a most 
complete collection of which, of every 
variety, has been made by the Messrs. 
Ross, up to the present date. Selected 
specimens from this will be worked into 
prisms, and the relative spectra mapped 
out by the Fraunhofer lines, leading, it 
is hoped, to the discovery of a combina- 
tion of crown and flint glass which shall 
be free from secondary spectrum or abso- 
lutely achromatic (" Proc. Royal Soc," 
No. 141, 1873). 
