The President's Address . By E. M. Nelson. 129 
the dispersion of a certain crown between the same limits. Now, 
if the dispersion of this flint between E and H is also double that 
of the crown between those limits, no secondary spectrum will be 
present. But no glasses as yet manufactured possess this quality ; 
for suppose the dispersion of a flint is 3 times that of a crown between 
the limits of B and E, it may be 4 times that of the crown between 
E and H. It is therefore to this want of proportionality in the 
dispersions of the two glasses that the irrationality of the spectrum 
is due. We shall best understand the value of the small figures if we 
take a silicate crown and flint from Table I. for the construction of 
an achromatic doublet, say for example the 3rd and 6th on the list ; 
then the focus of the positive lens will be 36*3 and that of the nega- 
tive 60*2, the dispersive ratio, or ri, being—, = 1*66. Now let us 
v 
examine the small figures below the dispersions, and see the state of 
the secondary spectrum by subtracting the values for the crow r n from 
those for the flint, thus : 
Flint 605 714 609 
643 703 566 n’ = 1*66. 
- 38 +11 +43 
Again, let us take the 4th and the 7th in Table I., we have foci 
of 32 * 0 and 51 • 2 respectively, the ratio being 1 • 6, and the secondary 
spectrum better than before, a very fair result considering the large 
value of ri. 
Flint 597 717 619 
Crown 628 708 582 n' = 1*6. 
- 31 +9 +37 
This might have been expected ; for as a general rule the amount 
of the secondary spectrum increases with the increase in the value of 
n\ for example : 
Flint 600 715 615 
Crown 651 701 559 »'=l-89. 
- 51 +14 +56 
Nevertheless a good deal may be done by a careful selection of 
suitable pairs, thus : 
Flint 606 713 607 
Crown 642 704 568 w' = l-55. 
-36 +9 +39 
