960 Transactions of the Society. 



XXII. — jRemarks on Prof. Ahhe's ' Note on the proper Definition 

 of the Amplifying Power of a Lens or Lens-system.^* 



By E. GiLTAY, Ph.D., Teacher of Botany at the State Agri- 

 cultural School at Wageningen (Netherlands). t 



{Read 11th November, 1885.) 



Before dealing with the more immediate subject of this paper, I 

 beg to reproduce in translation a portion of my recently issued book 

 'Introduction to the study of the Microscope,'! which deals with 

 the meaning to be attached to the expression " linear amplification," 

 and with the manner in which its value is to be ascertained. 



"If a person is seen working with a Microscope, the first 

 question asked him is, very often, ' How many times does that 

 instrument magnify ? ' However simple this question may appear, 

 it is not in fact so very easy to obtain a good idea of the meaning 

 to be attached to the answer that should be given. 



Let us simplify the matter by taking an object of very little 

 complexity, namely, a line at right angles to the axis of the optical 

 system. 



It is easily seen that if an image of this line is formed by a lens or 

 by a lens-system, it is impossible to say how many times the image 

 will be larger or smaller than the object, if no more he given. For, 

 according to well-known formulae, the proportion between image 

 and object is not only dependent upon the optical system, but also 

 upon the distance at which the object is placed or at which the 

 image is formed. But if the optical system is used as a Microscope, 

 are not then those distances determined ? Properly considered, no 

 more so than in the former case ; at the utmost they are limited, 

 for the image must of course fall at such a distance, that the eye 

 may be able to accommodate for it. But still in this case the 

 distances may be very different. Let us consider for instance an 

 emmetropic or normal-sighted eye with a normal power of accommo- 

 dation ; § here it might appear that to every lens-system any power 



B 

 might be attributed. For, using the equation A = 1 — - (A = 



*P 



amplification, /3 = distance of the image, ^ = focal distance of the 



system), it is at once clear that A will be arbitrarily large, if only 



^ /S is large enough, i. e. if only the observing eye accommodates for a 



long enough distance. Hence it might appear useful, when using a 



* See this Journal, iv. (1884) p. 348. 



t The original paper is written by Dr. Giltay in English. 



X ' Inleiding tot het gebruik van den Microscoop, door Dr. E. Giltay,' Leiden, 

 E. J. Brill, 1885, § 44, pp. 76-80. 



§ I. e. an eye which, when not accommodating, unites on its retina parallel 

 incident rays (and therefore can see at a long distance), and which, if strongly 

 accommodatinir, can see at a few inches distance. 



