PERISCOMG CAMERA AND MICROSCOPE. 2J) 



that in the camera obscura, a much larger portion of the lens ^^ m * 

 is required to conspire in giving a distinct image of any one 

 object; so that the conformation best adapted for lateral ob- 

 jects would not be consistent with distinctness at the centre ; 

 and hence arises a limit to the application of the principle. On 

 the common construction, the whole lens is so formed, as to 

 give brilliancy and distinctness at the centre alone, without 

 regard to lateral objects. In adopting such a deviation from 

 the customary form, as I propose, in favour of a more ex- 

 tended view, some diminution of the aperture is required in 

 order to preserve the desired distinctness at the centre. In 

 my endeavours to ascertain the most eligible form of meniscus Best construe 

 for this purpose, I have assumed sixty degrees to be the field j'°" ^i ^ 

 of view required. But when so large a field is not wanted, v i 6V y. 

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

 tion 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 D , 1 , a?r ^ n V >5 " 

 any required focal length may be given to a meniscus, I have which the 



contrived a diagram by which very much labour of computa- radii or lense* 



are settled. 

 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 lensF=-— gj3;; 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 corres- 

 ponding to the focal length desired, and drawing a line FR 

 through a point R indicating any supposed length of th© 

 greater radius, the corresponding length of the other radius 

 will be found where the line drawn intersects the middle line 

 in the diagram. 



Inlaying down these lines, the length and position of AF 

 and AR were assumed at pleasure j and they were divided into 

 any number of equal parts. But the position and length of 

 the middle line Ar was adapted with care to the refractive 

 power of plate glass in the following manner, Since m = 



» ' -,.,. . ■ g= 1,08, a line BC was drawn, from the point 10 in 



the 



