18 J. 



KNOWLEDGE 



[Dbc. 30, 1881. 



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" In knowlrdce, that man only is to bo contemned and dcBpieed who is not in ft 



Btate of tran!iition Nor is there anything more adverse to accuracy 



t-han ftiity of opinion." — Faraday. 



) hami in raakini; a mistake, but preat barm in making none. "^^ 



le a man who makci 

 othing." — Liebig. 



[niakes, and I will show joa a man who has done 



(Buv Corrrjjponlrfnrt Columns. 



THE PRIMARY COLOURS.— RED AT THE BLUE END OP 

 THE SPECTRUM. 



[140] — I venture to suggest the following explanation of tlie 

 difficulty raised by M. W. Laing, letter 71, p. 96. The sensitive 

 ends of the optic nerve take the form of cones ; each cone is divided 

 into three parts, and each part is able to vibrato independently of 

 the others. As a violin string of a certain length, thickness, 

 density, and tension is only able to vibrate a certain number of 

 times in a second, and is set vibrating by those vibrations of air 

 only which synchronise or keep time with the string's periods of 

 vibration, vibration for vibration, or every second, third, fourth, 

 &c., air vibration to each string vibration, so each part of the cone 

 is act vibrating by those vibrations of ether which synchronise with 

 its periods of vibrations, and by those only. The sensation of red 

 colour is produced by the vibrating of the thick end of the cone, 

 green, not yellow, by the middle, and blue by the thin end, these 

 three being the primary colours ; about 392 billions of ether vibra- 

 tions in a second synchronise, vibration for vibration, with the 

 periods of vibration of the thick end of the cone, and about 757 

 billions with the thin end of the cone. Now, it is evident that with 

 784 (twice 392) billions of ether vibrations in a second, every 

 alternate ether vibration would synchronise with each vibration of 

 the thick end of the cone, and the result would be a weak red, 

 contiguous to and beyond the blue of the spectrum. Thus we 

 should have about 



392 billions of other vibrationa in a second, represented by rod. 

 575 „ ,, „ „ green. 



757 „ „ „ „ blue. 



784 „ „ „ „ red. 



Higher numbers of vibrations arc probably absorbed or reflected by 

 the refracting media of the eye (i.e., the conjunctiva, cornea, 

 aqueous humour, crystalline lens, and vitreous humour). 



In giving yellow as a primary colour, the " commissioners" were 

 probably guided by their knowledge of pigments and their com- 

 pounds, whiob knowledge only misleads in the matter of coloured 

 lights. 



I trust tliat my explanation, be it right or wrong, is " plainly 

 worded," and the assumed facts " exactly described " ; but I cannot 

 hope to rival " M. W. L." in these matters. 



W. Rayment, Amateur of Sc. 



THE MOON'S ROTATION. 



[159] — CO. K. — [39]— Newconib, in his " Popular Astronomy," 

 says : — " Tbc most remarkable feature of the motion of the moon is 

 that eho makes one revolution on her axis in the same time that she 

 revolves round tho oarth. . . . The reason of this peculiarity is to 

 bo found in tho ollipticity of her globe. That she should originally 

 have beeu set in revolution on her axis with prooisoly tho same 

 velocity with which she revolved around tho earth, so that not the, 



slightest variation in the relation of the two motions should oror 

 occur in tho course of ages, is higlily improbable. . . . Tho effect of 

 the attraction of the earth upon tho slightly elongated lunar globe 

 is such thot if tho two motions arc in the beginning very near 

 together, not only will tho axial rotation accommodate itself to tbo 

 orbital, revolution' around the earth, but, as the latter varies, the 

 former will vary ^. with it, and thus the correspondence will be 

 kept up." 



Uerschel, " Outlines of Astronomy " (S. 436*), refers to arcmark 

 made by Professor Hansen, viz., " that the fact of the moon turning 

 always the same face towards the earth is in all probability the 

 result of an elongation of its figure in the direction of a line join- 

 ing the centres of both the bodies acting conjointly with a non- 

 coincidence of its centre of gravity with its centre of symmetry." 

 He then gives a practical illustration. 



" Suppose, then, its (the moon's) globe made up of materials not 

 homogeneous, and so disposed in its interior that some considerable 

 preponderance of weight should exist oxcentrically situated, then it 

 ^vill be easily apprehended that the portion of its surface nearer to 

 that heavier portion of its solid content under all the circumstances 

 of a rotation so adjusted will permanently occupy the sitaation 

 most remote from earth." — A. T. C. 



FOUR FOURS, SINGULAR NUMERICAL RELATION. 



[151] — It may be as new to some of the readers of Knowiedce 

 as it was to myself when first shown the other day that all the 

 numbers to twenty inclusive (and many upwards), with the single 

 exception of nineteen, may be expressed by four fours, using any 

 signs necessary except those of squaring and cubing, in which 

 figures are required. Only four, but at the same time, the whole 

 of the four figures are to be used. I do not say that it is impossible 

 to obtain the number 19 in this way, but neither myself nor the 

 gentleman who showed me the above has been able to do so. With 

 the hope that this may prove interesting to at least some of the 

 readers of your valuable paper, — Tours, &c., CtJPmus Scientl«. 



[Our correspondent gives the solutions for all numbers from 1 to 

 20, except 19. These shall appear next week. In the meantime 

 v.c leave tho problem as an exercise to our readers. — Ed.] 



THREE SQUARE PUZZLE. 



[152] — A great number of letters relatingto this puzzle have been 

 received, nearly all of which we should like to print, but we have 

 nearly tweniy pages of correspondence already in type, besides the 

 correspondence received since No. 8 appeared. We have, there- 

 fore, absolutely no choice but to omit matter which otherwise would 

 suit our pages exceedingly well. 



Mr. Langley's puzzle has been solved and explained fnlly and 

 exactly by J. 0. M., W. T. Y., Mathematicus, F. F., J. S., and 

 others. T. Turner, Thomas Mactaggart, and J. T. E. point out 

 that it is in Todhunter's Euclid, p. 266. There is a pretty way of 

 obtaining Mr. Langley's pieces, which none of these mention. It is 

 simply taking the fig. of Euclid I., 47, and conceiving the largo 

 square turned over round the line liC, giving 



We thus liavc tho five pieces of Mr. Langley's figure, and, at tho 

 same time, see how they arc to be arranged to fill the square BE. 

 Wo leave 2 where it is; put 1 where BAC is, 4 on Eab, and then 

 5 and 3 together cover tho triangle lEc, divided as shown by the 

 lino cd. R. A. Pbociok. 



THE QUERIES IN "KNOWLEDGE" (Abstract). 

 [153] — Perhaps you will forgive my making a few observations 

 on Knowledge. Like many, doubtless, I have profited very much 

 by such essays as those in the first half of each number. But, Sir, 



