and Microscope. i^7 



pose, I have assumed sixty degrees to be the field of view- 

 required. But when so large a field is not wanted, then 

 a lens that is less curved will be preferable; and the pro- 

 portion 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 

 computation may be saved, as a very near residt may be 

 obtained by mere inspection. This contrivance is founded 

 on the well known formula for the focal length of any 



lens F = -^^. : m being a certain multiple obtained by- 

 dividing the sine of refraction by the difference of the sines 

 of incidence and refraction. Hence, in applying this for- 

 mula to the meniscus, F : R : : mr : R— r. In fig. 3, lines 

 expressive of these quantities are so arranged, that by as- 

 suming any point F corresponding to the local length de- 

 sired, and drawing a line FR through a point R indicating 

 any supposed length of the greater radius, the correspond- 

 ing 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 di- 

 vided into any number of equal parts. But the position 

 and length of the middle hne Ax was adapted with care to 

 the refractive power of plate glass in the follo-A'ing manner. 



Since m — • = 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 di- 

 vided into ten equal parts, with their subdivisions, afibrdcd 

 the means of continuing the sanie scale to any desired 

 length. Since the first hne BC was laid down parallel to 

 AF, and equal to mr, any other lines drawi> through cor- 

 responding nr.nibers 7 and 7? 8 and 8, Sec. will be also 

 parallel, and, by preserving due proportion, will correctly 

 represent mr. llencc, in all positions of the line FR, the 

 same similarity of triangles obtains, and the same pro- 

 portion of F : R : : mr : l\—r; and consequently the focal 

 length, corresponding to airy assumed radiij is truly ascer- 

 tained. 



For the purpose of duly proportioning the curvatures 

 of flint-glass, a second line Ay might be laid down in a 



mode 



