The President's Address. By E. M. Nelson. 
131 
Suppose we wish to construct a plano-convex doublet whose contact 
curves are similar, and in which the positive lens shall be an equi- 
convex, what glasses must we employ ? Going hack to the fundamental 
equation for achromatism — > + - 7—7 = 0 , we have vf = — v J\ 
V J ?J 
Let r and s be the radii of the equi-convex lens whose focus is /, and 
r' that of the plano-concave whose focus is /', then putting the radii 
in place of the foci in the equation, we have, neglecting the sign,’ 
but r' = s ; therefore 
v r' vs 
= 2 0* - 1 ) ; 
0* - i) = v. 
Next let us choose a flint likely to suit our purpose ; if we want flattish 
curves we know that v must be small, therefore let us take the last 
glass in Table I., this has v — 32*0 and y! — 1*6734. 
Then 
And 95 (y — 1) = v. 
Now by means of an ordinary slide-rule we can try the glasses in 
the catalogue, and in a few minutes see if there is one in the list that 
will, when combined with the flint which we have chosen, suit our 
purpose. The method of search is as follows : — Set 95 as a multiplier, 
and the y — 1 of any glass to be tried as a multiplicand, then if the 
product, as shown by the slide-rule, is equal to the v belonging to 
that glass, as printed in the list, we have found what we wanted, but 
if it is not equal we must try again. For example, let us try the 
borate flint, the last but two in Table I. ; here the multiplicand y — 1 
= *5736, the slide rule gives 54*5 as the product, but Table I. says 
that v = 50*8, therefore this glass will not do ; moreover it shows 
that we have too large a quantity for our multiplicand. Looking now 
in the list for a smaller value of y — 1 , we can try the next glass 
above it in Table I., and put 5368 for the multiplicand, the slide rule 
shows the product to be 51 *2, which is the same value as they given 
in the Table, and this denotes that we have found the glass we require. 
Consequently, by this very simple method we have found in a minute 
or two a pair of glasses that fulfil the given conditions. You will 
observe that the formula has been framed in such a manner that only 
one “ set ” of the slide-rule is required, and the various products can 
be read off one after another in less time than it would take to write 
them down. 
The glasses in Case 2 , Example 4 (fig. 15), in my former Address 
were selected in this manner. A triple constructed of these two glasses, 
having two equi-convex lenses enclosing a double concave (fig. 17), 
