Manchesier Memoirs, Vol. Iv. (191 1), No. %\. 11 



We have compared the results for the power and focal 

 length of a double convex lens of symmetrical form of 

 about 15 D. by calculation from the usual optical bank 

 formulse with the dioptriemeter value. In each case the 

 rays of light are considered to pass through the lens at a 

 distance of one cm. from its centre. 



Let fx be the distance from the centre of the lens to 

 the principal focus, that is, to the point of convergence of 

 rays originally parallel to the axis of the lens, and one cm. 

 from the axis. 



Let f., be \ of the distance between a small object and 

 its real image, when these are equidistant from the centre 

 of the lens and of equal size. 



Let /. be the reciprocal of the power as given by an 

 accurate reading on the dioptriemeter. 



The thickness of the lens was 5 mm. at one cm. from its 

 centre, and it was assumed that (ju— i)(2/R)= 15, where 

 ju = refractive index and R = radius of curvature of each 

 face in metres. The result of the calculations, the errors 

 referred to being corrected to a first degree of approxima- 

 tion, give : — 



yj = o"o685m. Dj = i4'6o. 



/., = o"o68t m. D,= i4'67. 



^ = o'o6Si m. D^= i4'68. 



A similar comparison between /i and f.. was made in 

 the case of a double concave lens of about — 10 D., the 

 thickness at i cm. from the centre being 2 mm. Here, 

 assuming (^— i)(2y''R)= 10, it was calculated that i//i = 

 lO'Oi, and i//3= 1007. 



There is usually no difficulty for a normal eye to see 

 the scale distinctly with any power of lens that can be 

 used, but if this should not be the case, a suitable focussing 

 lens can be placed in the lens holder just under the 



