Mr H'erschd on Achromatic ObjecUGlasses. 
glasses, may be of use to those who, without’ any large stock 
of mathematical knowledge, take a practical interest in ihe 
perfection of the telescope, I think I cannot do better than en- 
deavour to lay them before the public, through the medium of 
your valuable Journal, disencumbered of all algebraical sym- 
bols, and expressed in language which no artist can misunder- 
stand. I am well aware how formidable a barrier is raised 
against improvements suggested by theory, by expressing them 
in a manner unintelligible to the many ; and that, to the artist 
especially, the sight of an algebraic formula is apt to excite a 
degree of involuntary horror, a repugnance to come in contact 
with it, which no assurance of its correctness or utility on the 
part of its author is capable of overcoming. For this reason, I 
have been anxious in the paper itself to separate the investiga- 
tions from the results as mitch as possible, and to avoid the pe^ 
dantry of presenting the latter in the abbreviated symbolic form 
adapted only to the former. At the same time, I am aware that 
this cannot altogether be accomplished in a work destined almost 
entirely for scientific perusal, and I therefore the more readily 
embrace the opportunity you offer me. 
The first thing essentially requisite for an artist who would 
construct a refracting telescope by regular rules, by any certain 
process, independent of trials, is to know the materials he has to 
work upon. The refractive and dispersive powers of the glass 
employed, or at least the proportion of the latter, are indispen- 
sable data, and must be obtained before any calculation from 
theory can be made. The former is easily obtained, by grind- 
ing a small portion of the glass into a prism or lens, and ob- 
serving the deviation of the most luminous rays, or the best fo- 
cus of the lens ; but the latter, I am sorry to say, is an element 
whose determination presents great difficulties, at least when re- 
quired to a degree of exactness such as the purposes of the achro- 
matic telescope demand. In fact, the achromaticity of a double 
object-glass is itself so delicate a test of the adjustment of the 
dispersive powers of the lenses, that we cannot expect to succeed 
to the required degree of nicety in ascertaining their ratio in 
any instance, without employing a mode of observation at least 
as delicate. However, as this difficulty b^ars equally upon every 
construction of the telescope ever yet proposed, and as the best 
