620 



KNOWLEDGE & SCIENTIFIC NEWS. 



[December, 1906. 



Cotuiucted by F. Shillington Scales, b.a., f.r.m.s. 



The Limits of Resolving Power. 



It is an accepted fact that there i.s a tht-oretical limit 

 to the resolving- power of all microscope objectives, this 

 limit being strictly proportional to the numerical aper- 

 ture of the objective, the numerical aperture itself be- 

 ing- a method of notation which takes into consideration 

 not only the angular aperture of an objective, but also 

 the medium with which it is designed to be used, gener- 

 ally air, water, or oil, thus bringing dry and immersion 

 lenses into one common and universal system of nota- 

 tion. It is on account of this theoretical limit of 

 resolution that mere magnifying power, as such, offers 

 us no real advantage, as we are unable to increase the 

 amount of detail shown unless we can increase the 

 aperture of our objectives. It is advisable to call at- 

 tention to this limit of resolution, because there is some 

 misunderstanding as to the advantages to be gained by 

 increased magnification, more especially with regard to 

 improvements in the image when highly magnified. To 

 put it in another way, we may say that the power of a 

 lens to show detail depends on its aperture, and on the 

 refractive index of the medium with which it is used. 

 This resolving power may be modified, however, to a 

 certain extent by the wave-length of the light used, by 

 the refractive index of the mounting medium, and even 

 in certain cases by the obliquity of the cone of illumina- 

 tion, but the aperture of the lens and its medium are 

 the two important factors. Given such resolution, we 

 must have a certain magnification before we can see 

 what the lens can show us, and an immersion lens of 

 1.4 N.-A.. (which is our present practical limit for 

 ordinary work) requires quite a moderate magnification 

 to show us all that it is capable of showing. There- 

 fore, we hear nothing now of lenses like the 1/40'' and 

 1/50" of former days, and high eye-piecing is likewise 

 unnecessary. High eye-piecing has the further draw- 

 back of giving us, for various technical reasons, an 

 increasingly imperfect image, and though ingenious 

 methods have been devised to improve such a highlv 

 magnified image, it really shows us no more than is 

 shown by the more moderate magnification, and does 

 not, unfortunately, open out to us the new worlds of 

 microscopic vision which some uninformed readers of 

 the microscopic literature of the day seem to anticipate. 

 With regard to this theoretical limit, however, a 

 paper by Mr. E. M. Nelson, in a recent issue of the 

 Journal of the Royal Microscopical Society, though for 

 the most part technical, contains suggestions which are 

 of interest to workers with the microscope who are 

 engaged in research of various kinds. In the first place 

 Mr. Nelson reminds us that the actual theoretical limit 

 of resolution is not fully determined, the physical nature 

 of the image at the focal point not being yet fully 

 understood, and, consequently, the mathematical de- 

 ductions not agreeing with the practical results. It 

 follows that estimates of measurement of structure 

 based upon hitherto accepted mathematical tables re- 

 quire modification. Of course, this does not mean 

 that we can see more than we are at present seeing, 

 but that we may be to some extent in error as to our 



measurements of what we see, when based upon exist- 

 ing tables. .Such tables are published by the Royal 

 .Microscopical Society, and reproduced in certain text- 

 l)ooks on the microscope, and they may require modify- 

 ing accordingly. But Mr. Nelson's second practical 

 suggestion is that these tables are based on the assump- 

 tion that the worker uses a nearly full cone of illumina- 

 tion, which few workers do, as few lenses will stand 

 such a cone, whilst, perhaps, fewer workers know how 

 to obtain and utilise it, and, in fact, with the un- 

 corrected .Vbbe condenser so commonly used it would 

 l)e impossible. Mr. Nelson gives the specific instance 

 of a biologist who has discovered .some minute struc- 

 ture, and announces it as having been made with a 

 1/12" oil-immersion lens of 1.3 N..\., comp. ocular 12, 

 X 1,500, and Gifford screen. A reference to the pub- 

 lished tables would lead one to suppose that the capacity 

 of resolution of this new discoverer's apparatus was 

 135,800 lines to the inch, and that the structure is 

 smaller than it really is, because he has omitted to in- 

 form us that his condenser either would not give a full 

 cone, or was stopped down say to a J-cone, with a con- 

 sequent limit to I N..-\., and a limit of resolution of 

 70,000 lines to an inch. Mr. Nelson proposes to 

 obviate all this by the suggestion that the observer 

 should, without disturbing either his illumination or 

 any of his adjustments, place a Grayson's band-plate on 

 his stage, and see which band was resolved, so that 

 in the above case he would add to his published data 

 the words "Grayson band, 60, coo," and so do away 

 with ;dl ambiguity, and make it apparent that either a 

 small cone of illumination was employed, or that his 

 objective, apparatus, or eyesight must have been de- 

 fective. 



Royal Microscopical Society. 



October 17. — .\n old portable microscope made by 

 DoUond, presented to the Society by Major F. R- 

 Winn Sampson, was exhibited. This microscope, like 

 others of the same period, was a modification of Cuff's 

 " Newly-Constructed Double Microscope." Instead of 

 a box-foot it was hinged on a bracket in the bottom of 

 the case, which latter thus formed the base of the 

 instrument and admitted of either a horizontal or up- 

 right position. One end of the case is hinged so as 

 to let down and allow the mirror to project when the 

 microscope is in a raised position, the instrument lying 

 flat when the case is closed. The stage is focussed by 

 a rack and pinion instead of the body. The eye-lens 

 of the ocular is compound, and consists of two lenses, 

 the one next the eye being plano-convex, and the other 

 double convex. The instrument is the only example of 

 its type in the Society's collection. It resembles a 

 larger m.icroscope which belonged to Sir David 

 Brewster, and which is now in the British Museum. 

 .A small pocket microscope, presented by an anony- 

 mous donor, was also exhibited. It is a brass box 

 alx>ut 1 1" high and ij' in its greatest diameter. It 

 contains a simple microscope for viewing small insects 

 impaled on a steel point, and two other magnifiers, 

 and a diminutive line box. These magnifiers were 

 not uncommon 30 or 40 years ago, and were fre- 

 quently made of ivory, and were probably the pre- 

 cursors of the modern pocket lens. An immersion spot 

 lens by Reichert was exhibited, suitable for high 

 powers and for showing ultra-microscopic particles. 

 Messrs. W. Watson and Sons exhibited a new 

 metallurgical microscope, and the new Cathcart 

 Darlaston microtome, as described in " Kxowledge " 

 for November, page 597. A paper by Mr. James 

 Murrav on " Some Rotifera from the Sikkim Hima- 



