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XV. Rules and principles for determining the dispersive ratio of' 
glass; and for computing the radii of curvature for achromatic 
object-glasses, submitted to the test of experiment. By Peter 
Barlow, Esq. F. R. S. Mem. Imp. Ac. Petrop. &c. 
Read May 3, 1827. 
1. It is very remarkable, since the achromatic telescope is 
altogether of English origin, that in no one of our separate 
optical treatises are to be found specific rules for its con¬ 
struction, fitted for the use of practical opticians. Some 
essays of this kind have indeed been attempted ; the first of 
which is found in Martin’s “ New Elements of Optics,” 
published in 1751 ; but the principle there adopted is erro¬ 
neous, and of course the deductions, although possessing a 
great appearance of simplicity, are wholly useless. Under 
the article Telescope, in the Encyclopaedia Britannica, is 
another essay of this kind, which is correct in principle, but 
far from possessing the degree of simplicity which is desira¬ 
ble for practical purposes. 
Under the like article in Rees’s Cyclopaedia is a treatise 
on the same subject, which may be considered wholly prac¬ 
tical ; it is founded however upon Martin’s method, but 
corrected by an empyrical multiplier, which answers remark¬ 
ably well in many instances, but is erroneous in ail extraor¬ 
dinary cases. 
Lastly, an elaborate and highly scientific investigation re¬ 
lative to these constructions was published by Mr. Herschel, 
