February, 1913. 



KNOWLEDGE. 



65 



or even -17, but the former would be ample for even 

 " spotting " diatoms, giving a circle of confusion of about 

 the one hundred and forty-third part of an inch. 



The point to be noted above all is, that for good working 

 distance and depth of focus the lower the angle the easier the 

 work. Empty amplification is a great mistake, empty aperture 

 is a greater, and much more expensive and equally valueless. 



A four-millimetre objective, e.g., of N.A. -65 or -74, is far 

 more convenient than one of N.A. -90 which will only work over 

 No. 1 covers, whilst the former have working distances of a full 

 millimetre. But the craze for " angle " is still with us, and 

 many would rather take a quarter of an hour in coaxing a 

 quarter-inch to resolve Angulatum than put on a one-twelfth 

 inch and do it in one minute. Where, however, the 

 student wants efficiency, convenience and moderation in price, 

 he will get low angles for dry objectives based on N.A. -15 

 per one hundred magnification. A one-sixth inch that 

 will not work over any cover, even a No. 3, is a nuisance in a 

 laboratory, and an unnecessary nuisance, too. 



Meanwhile, opticians laugh in their sleeves and play to the 

 gallery, and above all rake in the coin that foolish men throw 

 away. If their clients will spend two pounds on a two-thirds 

 where one pound would buy an equally useful one, or three 

 pounds on the one-sixth where thirty shillings might have 

 sufficed, they cannot complain. Meanwhile the student has 

 wasted two pounds ten shillings : that is, half the cost of a good 

 one-twelfth inch oil immersion which some day he must buy. 

 Let him remember that useless aperture is a useless possession. 



There is also another matter which these investigations 

 bring out, and one which is of great practical importance, 

 namely, the limit of useful magnification, and on this we must 

 touch briefly. 



At present the highest numerical aperture is 1 • 50. It will 

 therefore be seen that if for every one hundred of magnification 

 we allow a numerical aperture of -20, the highest useful power 

 will be seven hundred and fifty. Anything beyond that reveals 

 no further structure, according to Mr. Conrad Beck's formula. 

 With him agrees Professor Abbe. By Mr. Nelson's formula, 



the limit of useful power will be only = 577, a 



•26 



much lower figure. 



Let us now take facts. Most opticians make a two-millimetre 

 semi-apochromatic of N.A. 1.30 at £5, and one of N.A. 1 -40 at 

 a varying price. They are, of course, oil immersions. The 

 resolving power of the former is about one hundred and 

 twenty-five thousand, and of the latter, one hundred and thirty- 

 five thousand, as given in the tables. By photography these 

 limits may be extended to one hundred and sixty-five thousand 

 and one hundred and seventy-seven thousand eight hundred 

 respectively. 



The test diatom, Amphipleura pellucida, varies but slightly 

 in its markings between ninety-five thousand and one hundred 

 thousand lines per inch. It also varies a little in other ways, 

 some being strongly marked, others being more feeble and 

 difficult. 



Now, we have several photographs of this diatom taken by 

 acknowledged masters, with every appliance at their disposal. 

 These photographs ought to show about thirty-three per cent, 

 more than can be seen visually, so that what is not there in 

 the photograph is almost certainly beyond the limits of 

 ordinary vision. 



In Dr. Spitta's " Microscopy," we have on Plate IV, Figure 2, 

 a photo of the diatom with a Zeiss two-millimetre apochromatic 

 of N.A. 1 -30X 750. This photograph, then, ought to show as 

 much as the eye would see with the same objective, and under a 

 magnification of one thousand. It shows fine lines only, and 

 Dr. Spitta tells us in his text that this is what such an objective 

 should show, and I do not for one moment doubt that this 

 is all we ought fairly to expect. But notice, we have got above 

 our theoretical limits of useful magnification and still get only 

 lines shown. 



In Messrs. Leitz's Catalogue of Photomicrographic 

 Apparatus, another photograph is found taken with an apochro- 

 matic two-millimetre objective, the N.A. of which is not given, 

 but is either 1 • 32 or 1 • 40. The magnification was one thousand 

 one hundred and fifty, and a deep blue screen was used, 



needing an exposure of six minutes. This would give us as 

 much as the naked eye, X 1400 or so. Still we get lines only, 

 and again I insist that I do not doubt we see all that can be 

 expected. There is a faint suspicion that the lines are 

 serrated as if nearing resolution, but that is all we can say. 

 But again notice, we have got to nearly twice the old 

 theoretical limits of useful magnification and still get lines 

 only. 



We turn again to Dr. Spitta's volume, and on Plate VI, 

 we find a magnificent photograph " taken (using blue light) 

 with a Zeiss two-millimetre apochromat N.A. 1-40 X 2,800." 

 He also notes that the dots are about the one-hundred- 

 thousandth part of an inch diameter " and that " these 

 are very difficult to see without the use of oblique green light, 

 even when employing the finest objective. A first-class semi- 

 apochromat should then show the dots furnishing an image 

 almost as good as that afforded by the apochromat," and so 

 on. I may add, the diatom is mounted in realgar, and is a 

 picked specimen of the well-marked type. The magnification 

 Shows as much as one of three thousand five hundred does 

 visually, i.e., nearly seven times the old theoretical limit ; and 

 now we get fresh structure, namely dots. 



Thus, the old theories must be revised, or at least 

 modified ; seven hundred and fifty is not the extreme limit 

 of useful magnification. We may increase it to at least 



1-50X100 .... , .1-50X100 , , nn ... 



= l,154,orperhapsevento =l,500,with 



•13 H H -10 



advantage. Our objectives will in this latter case be of much 

 lower aperture, especially compared with the focus, but this is 

 no difficulty, and the wise student will still use a low aperture 

 for the usual two-thirds (sixteen-millimetre) objective, one of 

 N.A. -65 to -75 for the one-sixth inch (4-2-millimetre), 

 and one of as high as he can afford for the one-twelfth inch 

 (two-millimetre) oil immersion. From the last alone he will 

 expect the utmost resolution. The others will show him all 

 that the eye can see without unduly forcing them by high 

 oculars, and altogether he will have a battery that will save 

 his eyesight, his patience and his pocket, and that will, above 

 all, never disappoint him or fail to show him all' that can be 

 shown. 



The specialist may go a step further and obtain a one- 

 sixteenth inch oil immersion for the very highest power, not 

 in place of the one-twelfth inch, but to supplement it and to 

 prevent the use of too high an eyepiece. But it will be a 

 luxury and not a necessity — a specialist's motor compared to 

 the general practitioner's gig. For general work he will find 

 low apertures and medium eyepieces give him everything that 

 he can wish, and that the craze for higher apertures is the 

 mark of the dilettante and not of the worker, of the ignoramus 

 and not of the savant. 



E. Ardron Hutton, M.A. 



PHOTOGRAPHY. 



By Edgar Senior. 



PHOTOGRAPHY WITH A PIN-HOLE. — Having for 

 some time past devoted a considerable amount of attention 

 to the above, it was thought that the subject might be found 

 interesting to readers of " Knowledge " generally, as well as 

 to those in search of methods, more or less novel, for obtaining 

 photographs. Of course, it is not for one moment claimed 

 that the definition given by a plain aperture — or so-called pin- 

 hole — even approaches that of a high-class lens, yet the results 

 are by no means fuzzy or blurred, as the illustration, Figure 67, 

 from a pin-hole photograph taken by Mr. Alfred S. Gannon, 

 the subject being " St. Brelade's Church, Jersey," testifies. 

 Then again, as we do not in nature meet with that uncom- 

 promising sharpness which so many photographs exhibit — a 

 plain aperture will, in many cases be found to give more 

 artistic results, possessing those qualities termed by artists 

 " atmosphere," " breadth of effect," and so on, and in the case of 

 the photographing of buildings it is to be highly recommended, 

 since the image will be an exact facsimile of the object, with 

 an absence of that distortion so frequently seen in photographs 



