268 DR. ROYSTON-PIGOTT. 



achromatism is obtained by the sacrifice of perfect apianatism. 

 When the spherical aberration is nearly destroyed, in all the 

 glasses I have been able to examine during the last ten 

 years, then the colour is increased or achromatism is de- 

 stroyed ; in a word, the most perfect definition of close points 

 is seen with colour ; the colour and their definition vanish 

 together. It is an exceedingly difficult task to demonstrate 

 this on paper without apparatus in operation. 



One other cause of imperfection in high-class objectives is, 

 the slight deviation of the centres of the various lenses from 

 the axial line. A brilliant point of light, imaged upon the 

 stage in the manner already described, and viewed by an 

 objective thus damaged by imperfect centering, displays an 

 immense quantity of intersecting circles, precisely resembling 

 the back of an engine-turned watch; and the greater the 

 number of the uncentered lenses the more complicated becomes 

 the pattern. 



{To be continued.) 



On the Differences between the Nominal and Solar 

 Focal Length of English Object-glasses. By Dr. 



RoYSTON-PlGOTT, M.A., &C., &C. 



Our English opticians have been somewhat hardly accused 

 of pretending, for trade purposes, that the focal length of 

 their object-glasses is misrepresented, and that they are really 

 of a much deeper character than the name they bear. 



Fortunately, with very little calculation, the honesty of 

 these nominal foci can be readily established. I have shown 

 (' Phil. Transactions,' p. 594, vol. ii, 1870) that if 



d be the distance between an object and its image formed 



by an equivalent lens, 

 m the number of times it is magnified, 

 / the focal length of the lens for parallel rays or solar focal 

 length; then 



d 



- j-; 



j» + 2 +— 

 m 



if m be very large, — is so small that it may be neglected, and 



then /. _ d 



m + 2 



But when m is small, ^ must be retained. For those 

 unacquainted with this kind of notation, it may be stated in 



