Dr. G-. J. Stoney on Microscopic Vision. 431 



The process that has been here followed might in fact have 

 been employed to prove Lagrange's Theorem ; but it is here 

 used for the purpose of showing that the ratio € 2 /e 1 is inde- 

 pendent of the values of a, and a! : in other words, that all the 

 rulings of which image C is formed are reproduced on a 

 larger scale in image D, and that the scale of the enlargement 

 is the same for them all. 



We thus learn that image D is formed of exactly the same 

 rulings as image C, only magnified and somewhat distorted — 

 distorted laterally by the convex form of the beams, and lon- 

 gitudinally owing to the decreased inclination of the beams 

 to one another. Image D accordingly contains every feature 

 which is present in image C, only somewhat distorted laterally, 

 and still more distorted longitudinally. 



Hence the great task we have to set before ourselves is to 

 find out what image C, standard image No. 2, contains. This 

 conclusion is not disturbed by pursuing the course of events 

 farther. 



26. From D to E, and from E to F. — The subsequent 

 stages need not detain us long. If, as before, we select two 

 of the beams of plane waves emitted by standard image No. 2, 

 and if we follow the course of the axial rays of these two 

 beams, we find that these rays intersect the optic axis where 

 tins axis pierces images C, D, and F (see the figure on p. 433), 

 and that if the portions of them which lie between the eye- 

 piece and the eye were produced backwards they would also 

 intersect the optic axis where that axis pierces the image E, 

 which is a virtual image. This last is the Visual Image, i. e. 

 the image which seems to the observer to be presented to 

 him. 



Let aoJ, /3/3 ; , 77', and 88 f be the angles at which the axial 

 rays of the two beams intersect the axis at C, D, E, and F. 

 At each of these images the two beams give rise to a ruling, 

 and if the spacings of these rulings in the successive images 

 be designated by e 1? e 2 , e 3 , e 4 , we have, by proceeding as in 

 §25, 



e 2 =Me 1? e 3 = M / 6 1 , e^M'^ . . (6) 



where M, M', and M x/ are the number of times that images D, 

 E, and F respectively are larger than the microscopic object ; 

 and where also, by equation (1), 



M =n sin a/sin /3, and is also = n sin a! j sin /3' 



W =n sin a/sin 7, and is also =n sin a'/sin «/ £- , (7) 



Jf /; = n sin a/n ; sin 8, and is also = n sin 



*7sin£' ") 

 a'/sin y' > 

 a' /n' sin 8') 



