Notes. 561 



nomenclature must be used. Any such system required that the valur 

 of the focal length should be known. In a single thin convex lens the 

 distance of the solar focus or burning point from the edge of the lens gav< 

 this important measurement ; but in compound instruments, although the 

 focal point could often be found, that portion of the instrument from which 

 it should be measured in order to obtain the true focal length was more 

 difficult to determine. 



Early English writers attempted to express this position by such terms 

 as " optical centre," or " perspective centre," but without a true understanding 

 of the correct principle, and they preferred to deal with an instrument as a 

 series of component parts, rather than as a whole. 



Fifty years previously it was thoroughly understood on the Continent 

 that there is no one position in an optical system from which the optical 

 measurements should be made, but two " equivalent planes," one for inci- 

 dent light measurements, the other for emergent Light measurements. 



Mr. Beck then showed, with the aid of a diagram provided with a 

 movable slide, that the most complex instruments can for most purposes be 

 represented by a thin lens of a certain focal length, if we imagine it to be 

 placed first, in the first equivalent plane to receive the light, and then shifted 

 to the second equivalent plane to discharge the Light. The focus of such a 

 lens is the equivalent or true focus of the compound instrument, and the 

 position of the equivalent planes becomes of prime importance. 



The author then explained diagrammatically how the separation of two 

 single convex lenses profoundly altered their position. Starting from two 

 lenses close to one another, he explained how the equivalent planes move 

 away from each other, and cross as the two lenses are separated, going to 

 infinity when the lenses are situated at a distance apart equal to the sum 

 of their focal lengths, reappearing on the other side of the lenses on further 

 separation. The argument was then applied to combinations of positive and 

 negative lenses with similar results. 



He then proceeded to illustrate the various types of instruments: the 

 photographic, or projection lens, the Telescope and the Microscope, by means 

 of the same pair of lenses separated by different amounts ; showing how the 

 telephoto lens, and especially the compound Microscope obtained their dis- 

 tinctive advantages by the position in which their equivalent planes were 

 placed. I 



A Microscope of the highest power considered as a whole, has an equiva- 

 lent focal length of only a few thousandths of an inch, the object being 

 placed approximately at the focal point. The earliest Microscopes were 

 constructed like our pocket magnifiers of single lenses of various curvature. 

 Such lenses could only be made of comparatively small magnifying power, 

 and even then the object had to be placed very close to the lens. If we 

 could conceive of a single lens with a magnifying power of 2000, the 

 focal distance would only be ^Vo or 2U0 incn > and the ob J ect would be so 

 close that it could not even be protected by a thin cover-glass. It is, how- 

 ever, interesting to note that lenses of different shapes, although they are 

 single lenses, are suitable to a greater or less extent for increasing this 

 so-called working distance, owing to the different position of their equivalent 



planes. 



For obtaining high magnifications, single lenses cannot be made with 

 sufficiently strong curvature, and the first idea that suggests itself is to place 

 three or four powerful lenses close together. Such an arrangement, however, 

 is even more unsuitable, because the equivalent planes are generally some- 

 where between the lenses, and the actual distance of the focus from the 

 front lens is reduced still further than in the case of a single lens. 



So it was, that without knowing the exact reason, the plan of using 

 lenses separated by large intervals was adopted in Microscopes as far back 

 as the year 1650. The equivalent planes are so placed that one of them is 



