962 Transactions of the Society. 



remain accommodated for it during rather a long time. This 

 distance has been chosen as 10 in, (25 cm.), and it is generally 

 called the ' distance of distinct vision.' This term often gives rise 

 to erroneous notions, and was not chosen very happily ; for at every 

 distance, for which an eye can accommodate, it sees equally dis- 

 tinctly. The term may, therefore, be regarded as an abbreviation 

 for the sJiortest distance {suitable for the discrimination of minute 

 details) for which a normal eye can accommodate for a consider- 

 able length of time, and wliich has been chosen arbitrarily for 

 the comparison of amplification. But what distance must then be 

 given to the virtual image formed by the optical system ? From 



B . . 

 the formula A = 1 — -- it is clear that if d> is small in comparison 



with yS, A may be taken as proportional to ^. When the virtual 

 image enlarges in the same ratio as the distance at which it is 

 formed, then the image on the retina of the eye, by which it is re- 

 garded, may be considered as remaining the same. Therefore 

 what distance is given to the virtual image might be quite in- 

 different. It is only from a practical point of view that it is also 

 placed at 10 in. from the eye, for then the number representing 

 the value of the linear amplification is not only represented 

 by the ratio of the two retinal images, but also by the ratio 

 of the virtual image and of the object itself, which is of great 

 importance in the practical determination. That this is really 

 the case may be easily deduced from fig. 222. C is the cornea, 



E the retina, A ^ a the axis of the observing eye j A B represents 

 the dimensions of the object, AB' the dimensions of the virtual 

 image when this lies in A, Kh being supposed to be the 

 distance of distinct vision; ah indicates the dimensions of the 

 retinal image of the object, when seen by the eye only, a h' when 

 seen through the optical instrument which forms the virtual image 

 A B'. If we now unite B and h, B' and h', it may be shown 

 that these two lines cross the axis at very nearly the same point, 



7 A ^ V ^^' AB' „* 



sav K. And now we have — r- = -— tt- • 

 •' ao A a 



* In the last part the translation slightly differs from the original, which was 

 necessary on account of the fact that the original made use of laws which were 

 explained in a previous chapter. 



