August 8, 1889] 



NATURE 



34 



40 



yellow, red, &c., the colours resembling those of Newton's rings. 

 The central disk is far the brightest part, and there is no real 

 break in the colours, though the first purple is a good deal 

 darker than its neighbours. The easiest way to see these 

 ■colours is to sprinkle a slip of glass with Lycopodium seed and 

 look through it at a bright point of light. The above descrip- 

 tion applies equally well whether the obstacles are spherical or 

 <;ylindrical. The latter form is nearly approached in Nature by 

 the fine needles of ice of which many clouds must be largely 

 ■composed. With other forms of obstacle the colours would be 

 more or less blurred, but in any case the bright central disk 

 would survive. 



When recently engaged in investigating such phenomena, I 

 ncticed that the rings formed in my eye were of an utterly 

 different character. There are two narrow rings, apparently in 

 •contact — the inner green, the outer red ; the apparent breadth of 

 each being about 20', and the radius of the intermediate circle 

 about 2° 3c', Within the green ring is a broad dark space, and 

 then comes the ordinary colourless haze surrounding the light. 

 The rings are not quite continuous, and certain short arcs are 

 much brighter than the rest. But the arrangement of these arcs 

 seems quite irregular, and is different in the two eyes. With 

 this exception the two eyes behave alike. The green and red, 

 though faint, are of good quality, not unlike a very faint pris- 

 matic spectrum. They are rather capricious in their appearance, 

 requiring a dark background and a moderately bright light. A 

 small arc light some thirty yards from my window generally 

 shows them well, though they vary a good deal in brightness, 

 and at times I cannot see them at all. 



The question was, how the colours were produced. After 

 pondering the matter for some time, and rejecting one 

 explanation after another, the true solution suddenly flashed 

 upon me. The colours are the first spectrum of a dif- 

 fraction grating, and the ring form is due to the bars of the 

 grating lying in different directions in different parts of the eye. 

 The idea was readily put to the test. Cutting a small hole, one- 

 tenth of an inch square, in a piece of paper, I held it in front of 

 the eye. When the aperture was in the centre, the coloured 

 rings vanished ; when it was drawn to one side co the very edge 

 of the pupil, two bright spots appeared on the circle, one above, 

 the other below the light. The rest of the circle was invisible. 

 As the aperture was moved round the outside of the pupil, the 

 two bright spots revolved round the circle, preserving their 

 angular distance of 90° from the aperture. This shows that the 

 bars of the grating radiate from the centre of the pupil and are 

 only found near its edge. From the dimensions of the rings we 

 may deduce that the lines are spaced at the rate of about 75 to 

 the millimetre, or 1900 to the inch. Since the coloured ring is 

 not uniformly bright, the grating must be imperfectly developed 

 behind some parts of the outer edge of the pupil. But trial 

 with the diaphragm left no doubt that the structure was present 

 to some extent all round. I then compared the coloured rings 

 wiih the spectra seen on looking at a light through an ordinary 

 diffraction grating of 3000 lines to the inch. The appearance 

 was very similar, though in the latter case of course the red and 

 green were much brighter, and were accompanied by a com- 

 paratively faint violet band. The breadth of the red and green 

 bands relatively to their distance from the light agreed very well 

 with the measurements given above. 



Another evening I prepared some diaphragms with annular 

 apertures of which three. A, B, C, had the inner and outer 

 diameters respectively 107 and 8'6 mm., 99 and 76 mm., 8'l 

 and 6'i mm. In A the central stop was large enough to hide 

 the light and of course extinguish the rings too. With B when 

 held centrically the rings were very plain — indeed yellow could 

 be made out between the green and red — while the light was dis- 

 torted and enlarged by both spherical and chromatic aberration. 

 With C the rings were visible but not distinct. I found too that 

 with B 1 could see the rings round the naked flame of a bright 

 paraffin lamp only two or three feet away, for the pupil enlarged 

 till it cleared the stop. But w ilh C, I had to move two or three 

 yards away before the rings appeared. These experiments show 

 the diffracting structure to exist in a ring, whose diameter lies 

 between 81 mm. and 76 mm., and that it does not extend far 

 inside the lower limit. Further, the diameter of the pupil when 

 the rings are visible may be decidedly less than 8 "6 mm. The 

 structure is not on the inner edge of the iris, but it may lie either 

 in the cornea or in the crystalline lens. The latter is known to 

 be built up of closely-packed radial fibres from 0'co56 mm. to 

 O'oi 12 mm. in breadth (Helmholtz, " Physiologi.^che 0[ tik," § 5). 



It seems probable that some modification of these near the edge 

 of the lens form the diffracting layer. I have since found that 

 at a distance of a hundred yards from the electric light the pupil 

 can be made to clear the central stop of A. There is then seen 

 a narrow circle of light, too faint to show colour. I was not 

 able to get a good enough measure of its diameter to decide 

 whether it was smaller than before. 



I can hardly fancy this curious structure in the eye to be a 

 rare peculiarity. One of my friends saw the green ring well 

 defined round the electric light one evening, and with practi- 

 cally the same radius as I. He was not sure about the red. 

 Inside the green he described the colour as very dark purple, 

 almost black. Probably this was a contrast effect, but possibly 

 it was the violet of the spectrum. In Sir John Herschel's 

 " Meteorology " I find the following passage. After speaking of 

 coronse round the sun, he says : "Occasionally the cornea of the 

 eye itself becomes filmy by the diff'usion over it of minute parti- 

 cles, which (such at least is our personal experience) exhibit 

 round a candle two or three beautiful coronas, the second of 

 17° 57' 'ri diameter, of vivid colours and most perfect definition." 

 This description makes me feel suspicious that the rings were of 

 the same class as mine. It suggests separate spectra such as are 

 produced by a diffraction grating. Further, the accuracy of the 

 measurement implies a tolerably narrow ring, whereas in ordin- 

 ary corona?, if the second green had a diameter 18", the second 

 blue and second red would have diameters 15° and 23" respect- 

 ively. His dimensions do not agree with mine, but imply bars 

 or lines at distances of about 0"oo7 mm. Fibres of this breadth 

 are found in the crystalline lens. James C. McConnel. 



Davos, Switzerland. 



Use or Abuse of Empirical Formulae, and of 

 Differentiation, by Chemists. 



As I believe that I am one of the "ingenious and clear- 

 sighted" chemists who, Prof. Lodge suggests, may be "run 

 away with by a smattering of quasi-mathematics and an over- 

 pressing of enrpirical formulae," I hasten to assure him that he 

 is quite wrong in his surmises. 



With every word of Prof. Lodge's remarks on the proper 

 method of examining curves I heartily agree ; with his stric- 

 tures on the abuse of formula; I more than agree : I should 

 advise chemists not even to use them. 



The method of examining the continuity of any curve by 

 plotting out the experiments themselves, and then differentiating 

 the curves representing them, is the method which I have applied 

 in nearly every case, and applied it, I believe, for the first time 

 to questions of a chemical nature. The only difference be- 

 tween my modus operandi and that which Prof. Lodge suggests 

 is that, instead of differentiating the curves by a mechanical 

 integrator, I take readings from them at definite intervals, and 

 find the differences between these readings ai-ithmetically. 



I do not consider, however, that this is the safest method of 

 examining results. The method which was introduced to the 

 notice of chemists by Mendeleeff, which was used subsequently 

 by Crouipton, and on which I have placed my chief reliance, 

 consists of differentiating the experimental numbers themselves, 

 and not the curves which may be drawn to represent them. If 



jj and s.^ be the densities of p^ and p^ per cent, solutions. 



lip 

 ds 



A - Pi 



at a percentage ^ ' ' - is given by 



Each of these two methods has its own special advantages, but 

 the balance is generally strongly in favour of the last one. It 

 does not necessitate the drawing of the original curve, which 

 drawing may often be considerably modified by the " taste" of 

 the drawer ; it will sometimes bring about the recognition of 

 breaks which might be overlooked in the original curve, for 

 though the diflerential curve can show no breaks which do not 

 exi>t in the original curve, it may often, as a consequence of its 

 very nature, show breaks charly, which would be recognized 

 only with difficulty in the original curve ; and, lastly, the proper 

 depiction of the original curve is often a 1 ractical impossibility, 

 as, for instance, with the densities of sulphuric acid solutions, 

 where the scale which would have to be adopted to give the 

 experimental error a fairly visible magnitude would involve 

 dealing with a curve some 3000 inches long. 



Prof. Lodge could, no doubt, have told us more than he has 

 i done of the difficulties and dangers of diflTereniiation in any 

 I form, and, perhaps, the extensive practical experience which I 



