OPTICAL INSTRUMENTS. 



The dimensions in the table are com- 

 puted on the supposition of the focal 

 length of the object-glass being 1 ; and 

 to adjust them to any other assigned 

 focal length, all that is required is to 

 increase or diminish the radii here set 

 down on the proportion of the assigned 

 focal length (in inches, feet, or parts of 

 any given scale) to ten parts of the 

 same scale. 



When the refractive powers of the 

 two media are exactly 1.524 and 1.585 

 (which are nearly their average values) 

 respectively, and the dispersive ratio is 

 any one of the numbers in the first 

 column, this table gives at once the 

 exact values of the radii required ; but 

 when this is not the case, we must 

 proceed as follows :' Suppose (for ex- 

 ample's sake) we would find the proper 

 radii for the surface of an object-glass 

 of 30 inches focal length : the refractive 

 index of the crown lens being 1.519, 

 and that of the flint 1.589, the disper- 

 sive power of the former being to that 



of the latter 'as 0.567.1 or 0.567 being 

 the dispersive ratio. 



The computation must first be made 

 as for an object-glass of 1 inches focus, 

 and first, we must determine the focal 

 length of the separate lenses, to this end. 



1. Subtract the decimal (0.567) re- 

 presenting the dispersive ratio from 

 1.000, and the remainder multiplied by 

 1 0, is the focal length of the crown lens 

 (in this case 10 x 0,433, or 4,330.) 



2. Divide unity by the decimal above 

 mentioned (0.567,) subtract 1,000 from 

 the quotient and multiply the remainder 

 by 10, and we get the focal length of 

 the flint lens. In this case before us 



g-^- = 1.7635 and 0.7635x10= 7.635 



is the focal length required. We must 

 next determine by the tables the radii 

 of the 1 st and 4th surfaces for the dis- 

 persive ratios their set down, (0.55 and 

 0.60), next less and next greater than 

 the given one. For this purpose we 

 have 



Refractive powers given 1.519 

 Ditto ditto in the table 1.524 

 Differences 



The given refraction of the crown 

 being less and the flint greater, than 

 their average value on which the table 

 is founded. Looking out now opposite 



- 0.005 and + 0.005 



to 0,55 in the first column for the varia- 

 tions in the two radii corresponding to 

 a charge of + 0,010 in each of the two 

 refractions, we find as follows : 



For a charge = + 

 Ditto ditto = + 



1st surface 4th surface. 



0.010 in crown -f 0.0740 + 1.0080 

 0.010 in flint 0.0011 0.5033 



But the actual variation in the crown 

 instead of + 0.010, being + 0.004, we 

 must take the proportional parts of 



these, changing the sign in the case of 

 the crown : Thus we find the variations 

 of the first and last radii to be : 



For 0,005 variation in crown 

 For + 0.004 ditto in flint - 



1st surface. 

 0.0370 

 0.3004 



4th surface. 

 0.5040 

 0.2010 



Total variation from both causes 0.3374 and 0.7053 

 But the radii given in the table are + 6.7184 and + 14.5353 

 Hence the radii interpolated are, 6.6810 and 13.8300 



If we interpolate (by a process exactly similar) the same two radii for a "dis- 

 persive ratio 0.60, we shall find respectively: 



1st surface. 4th sxirface. 



For 0.005 variation in crown 0.0338 and 0.5524 



For + 0.004 ditto in flint + 0.0015 3.2264 



Total variation 0.0323 and - 0.7788 



Radii in the table 6.7069 14.2937 



Interpolated radii 6.6746 and 13.5149 



