February, 1913. 



KNOWLEDGE. 



63 



until the morning. Some which I kept alive in a box, found at 

 first some difficulty in thus suspending themselves from the glass 

 cover, but this was at length overcome by making a lattice- 

 work path of silk across the underside of the glass along 

 which they were able to walk and from which they hung their 

 houses every evening. A number of eggs laid by the moth 

 of one species on the flowers of one of the Compositae 

 hatched out as the flowers were maturing, and the larvae, one 

 thirtieth of an inch in length, immediately began to cut up 

 the feathery pappus and constructed the most perfect little 

 houses, which they somehow managed to enlarge as required 

 by their growth, without alteration of the original design. In 

 Figure 66b, the house is made of pieces of the stems of fine 

 grass arranged in parallel lines. Figure 66c is apparently 

 made of some kind of fibre worked together obliquely and 

 partly covered with silk. Figure 66d is presumably made of 

 fine fibres but is so completely covered with silk as to prevent 

 them from being seen. Figure 66e is formed of two kinds of 

 sticks fastened together lengthwise. Figure 66f is chiefly 

 constructed of the dried spikelets of grass overhung with a 

 roofing of grass leaves. Figure 66g is obviously made of 

 sticks, the ends of some of which are seen projecting through 

 a thick covering of silk, and Figure 66h, consisting chiefly of 

 the small dried leaves of a Mimosa, has been cut open, 

 showing the chrysalis inside. 



The natives of Southern India, where Psychidae similar to 

 Figure 66a are not uncommon, regard these creatures as the 

 embodiment of the souls of men who having during their 

 human lives been addicted to the stealing of firewood, are 

 passing their next period of existence attached to a bundle of 

 sticks. The Kaffirs of Natal, however, have given them the 

 common name of Mahambanendelwhana, which, being trans- 

 lated, means " he that goes with his little house." Friends 

 who sometimes complain of the long names given to insects 

 by entomologists, will possibly think that this is no improve- 

 ment. R, T. L. 



ON THE RELATION OF APERTURE TO POWER 

 IN THE MICROSCOPE OBJECTIVE.— That opticians 

 are human they would themselves admit, and to supply what 

 the public demands is the essence of business with them as 

 with everyone else. Moreover, competition is keen, and hence 

 each tries to give his customers a better bargain than can 

 elsewhere be obtained. 



Now, by a "better bargain," the microscopical customer 

 only too often understands objectives of higher numerical 

 aperture, since stands, eyepieces, and condensers of similar 

 quality are now much the same price everywhere. But A puts 

 into his a two-third inch of N.A. -30 and a one-sixth inch of -88, 

 B gives N.A. -28 and -74 respectively, whilst C gives -25 

 and • 65 for these same lenses. The one-twelfth oil immersion 

 is almost invariable everywhere nowadays, being of about 

 N.A. 1-30, and costing five pounds. 



In the above case A would often get the order, the tyro 

 arguing that increased N.A. meant more resolution, and there- 

 fore better results. It is altogether forgotten that behind 

 everything is the human eye, and that this admits of improve- 

 ment within but narrow limits. Let us see what those limits 

 are. 



The standard distance for ordinary eyesight is ten inches. 

 Most people can with but little practice, by the aid of a rule 

 divided into tenths, prick off divisions as small as the one- 

 hundredth part of an inch. We may take this as fairly easy. 



Now let us go a step further and ask how closely can we 

 read a millimetre scale ? Remember a millimetre is practi- 

 cally one twenty-fifth of an inch. Can we without a vernier, 

 or lens or any other extraneous aid, read it closer than to one- 

 fifth of a division, i.e., one hundred and twenty-fifth of an 

 inch ? Very few would say that this was possible with ease, 

 and, above all, certainty. Rule, e.g., a few lines of different 

 lengths. Obtain a glass scale with millimetre divisions on the 

 lower surface (so as to avoid parallax) then measure the lines 

 and put the measurements down on paper. Ask others to do 

 the same, and you will find that the fifth of a millimetre is 

 about the average of good ordinary eyesight, and that even 

 if one has large powers of accommodation and can, for instance, 



read ordinary print at, say, five inches distance, yet the milli- 

 metre scale will still defeat us if we attempt to read it closer 

 than fifths. 



Let us go elsewhere for confirmation. Vega forms the 

 brightest of a small triangle of stars distant from each other 

 less than two degrees. The one N.E. of Vega is e Lyrae, a 

 noted double double. Most people cannot see it double at all. 

 Many astronomers can separate them without artificial aid. 

 Smyth says : " The naked eye sees an irregular-looking star 

 near Vega, which separates into two pretty wide ones under 

 the slightest optical aid. " So," adds Webb, " I see it, and 

 probably most observers," but notes that Herschel, Bessel 

 and " many others have divided it with the naked eye." The 

 distance is three minutes twenty-seven seconds. This angle 

 corresponds almost exactly to one hundredth of an inch at a 

 distance of ten inches. 



Now let us return to the microscope. In Mr. Conrad Beck's 

 Cantor Lectures on " The Theory of the Microscope " page 

 40, we read, "It is generally considered that for every one 

 hundred magnifying power the numerical aperture should not 

 be less than about -2 N.A. 



Now, a numerical aperture of -2 should resolve nineteen 

 thousand three hundred lines to the inch. With a power of 

 one hundred we must be able to separate lines - 1 ib8 = tJ3 of 

 an inch. This agrees well with Professor Abbe's calculations, 

 which are based on the assumption that the human eye can 

 distinguish intervals, having an angle of two minutes or jif-j at 

 ten inches. Mr. E. M. Nelson puts the ratio as a magnification 

 of one hundred to -26 N.A. Now, -26 N.A. will resolve 

 twenty-five thousand lines per inch. In this case, therefore, 

 we get the limit of resolution of the eye itself given as two 

 hundred and fifty lines per inch. Professor Abbe's researches 

 date from 1874-5 ; Mr. Nelson's opinion dates from 1883 ; 

 whilst Mr. Conrad Beck's lectures were given in December, 

 1907. 



We may approach the solution of the question by asking at 

 the very commencement what eyepiece magnification and what 

 tube length must we predicate ? As regards the latter we have 

 no choice, the six-inch tube (one hundred and sixty milli- 

 metres) being now almost universal. Eyepieces, too, are now 

 almost universally the same and give, with the one hundred 

 and sixty millimetres tube, powers of 3, 4, 5-5, 7, and 9. 

 Professor Abbe gives the upper limit of eyepieces as ten with 

 N.A. -10 and only four with N.A. -90. His researches, as I 

 have just said, date from 1874 when the substage illumination, 

 at least on the Continent, was of the most primitive descrip- 

 tion. At the present day, whilst the experienced worker con- 

 fines himself as far as possible to low and medium eyepieces, 

 he does not hesitate to use the higher if required to reveal 

 structure. Much, however, depends on his objectives. 



Passing over the lower power lenses, which are used only as 

 finders, we come to those useful medium powers ranging from 

 the one-inch to the half-inch or four-tenths of an inch, which 

 consist usually of two doublets. 



These admit abundance of light and often possess a work- 

 ing distance equal to three-quarters of their focal length. 

 They can scarcely be said to be used for highly critical 

 work and will bear an eyepiece magnification of at any 

 rate more than ten. Professor Abbe gives such moderate 

 powers an eyepiece amplification of 5-5 to 9 and since his 

 day the excellence of objectives has advanced all along the 

 line thanks to the Abbe-Schott glass and other causes, so that 

 nowadays every objective of four-tenths of an inch or lower 

 will bear an eyepiece magnifying ten on the one hundred and 

 sixty millimetres tube. Even then we must be careful as to 

 the illumination or we shall only get a foggy glare. 



Dry objectives of high power ranging from, say, one-quarter 

 of an inch to one-tenth of an inch now almost invariably con- 

 sist of a hemispherical front with two correcting systems of 

 lenses behind. It is not easy to make such a combination 

 much lower than -60 N.A. and they range as a general rule 

 from -60 to -90 N.A. It is with these that the greatest 

 improvement of all has taken place. The new optical glass, 

 and especially the use of fluorite in one of the back combina- 

 tions, have led to such an advance in the colour corrections 

 of these series that nowadays one can often scarcely see the 



