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III. — On Tube Length. 

 By Edward M. Nelson. 



{Read 20th February, 1901 ) 



The subject of tube length has been but imperfectly treated in 

 microscopical literature, and nearly twenty years have elapsed since 

 anything has appeared about it in our Journal, although promises 

 were at the time made that it would be dealt with more fully. The 

 object then of this paper is to lay before the Society a brief account 

 of the subject in such a way that it may be understood by any micro- 

 scopist, whether he has any previous knowledge of mathematical 

 optics or not. 



At the outset we may point out, that which nearly every rnicro- 

 scopist knows, that there are two tube lengths, viz. a mechanical 

 and an optical. The Mechanical Tube is measured from the end of 

 the nose-piece to the end of the draw-tube. The standard length 

 for the English tube is 8| in. (222 mm.), and for the Continental 

 160 mm. (6*3 in.). The mechanical tube does not in any way re- 

 present the distance by which the lenses of the eye-piece are separated 

 from those of the objective, as that obviously will depend upon the 

 manner in which those lenses are mounted, as well as upon the length 

 of the mechanical tube. In brief, the mechanical tube is the length 

 of the Microscope-body when in use. 



We now come to the Optical Tube. This in the nature of things 

 should be nearly as easy to describe as the mechanical tube, but, owing 

 to the fact that there are two optical tube lengths, a detailed explana- 

 tion of some length will be necessary. Most microscopists are aware 

 that every lens and every combination of lenses have what is called 

 an equivalent lens. This equivalent lens is a mathematical abstraction, 

 for it can neither be made nor always drawn ; its position on the axis 

 need not necessarily be coincident with that of the lens to which it is 

 equivalent, so that it may be found sometimes inside and sometimes 

 outside the actual lens. Now the bearing this has upon the matter 

 before us is very important, as will be realised when it is understood 

 that two lenses are in optical contact when their equivalent lenses 

 are in contact, and not necessarily when there is physical contact 

 between the actual lenses themselves. For the benefit of those 

 unacquainted with this subject, fig. 18 shows a plano-convex in 

 optical contact with a converging meniscus, and it will be noticed 

 that the actual lenses are not touching one another. The actual 

 lenses are represented by continuous, and the equivalent lenses by 

 dotted lines. When two lenses are separated from one another, the 

 optical distance of their separation is not the distance between the 



