374 
Dr. Wollaston on a 
then a lens that is less curved will be preferable ; and the 
proportion of the radii must be varied according to the angular 
extent intended to be included. 
For the purpose of estimating by what combination of radii 
any required focal length may be given to a meniscus, I have 
contrived a diagram by which very much labour of computa- 
tion may be saved, as a very near result may be obtained by 
mere inspection. This contrivance is founded on the well 
known formula for the focal length of any lens F = ~ R ^ . : 
m being a certain multiple obtained by dividing the sine of 
refraction by the difference of the sines of incidence and re- 
fraction. Hence, in applying this formula to the meniscus, 
F : R : : mr : R — r. In fig. 3, lines expressive of these quan- 
tities are so arranged, that by assuming any point F corre- 
sponding to the focal length desired, and drawing a line FR 
through a point R indicating any supposed length of the 
greater radius, the corresponding length of the other radius 
will be found where the line drawn intersects the middle line 
in the diagram. 
In laying down these lines, the length and position of AF 
and AR were assumed at pleasure ; and they were divided into 
any number of equal parts. But the position and length of 
the middle line Ax was adapted with care to the refractive 
power of plate glass in the following manner. Since m = 
- ■ 5o * _ i = 1,98, a line BC was drawn from the point 10 in 
the line AR, parallel to AF, and equal to 19,8 divisions of the 
primary lines ; so that if r be = 10, then the line BC = mr. 
The distance AC being then divided into ten equal parts, 
with their subdivisions, afforded the means of continuing the 
