SErTEMBER 28, 1S93] 



NATURE 



517 



Satisfactory reasons have still to be given for deserting the 

 jquaternion highway. The asserted weakness of Hamilton's 

 'calculus, as contrasted with the implied strength of its rivals, 

 "as still to be disclosed. 



With a view to bring us all to one mind. Prof. Alfred Lodge 

 suggests (Nature, June 29) that the quaternion be regarded as 

 the difference of its vector and scalar parts, so that the square 

 of a vector becomes minus the scalar product of a vector into 

 itself. It is not easy to see what ultimate advantage this change 

 of sign would bring. The most obvious disadvantage would be 

 that it would to a large extent render Hamilton's and Tail's 

 classical treatises of little service to the student. Moreover, it 

 would bring in the quaternion in a very artificial manner, as a 

 rkind of after-thought, so to speak ; it would, I think, confuse 

 ^he beginner by forbidding him to make use of powers of vectors 



in the way generally familiar in analysis ; it would accentuate 

 he imp irtance of the product at the expense of the quotient of 

 ectors ; and it would tend to obscure the significance of the 

 ersor. I am afraid it is too much to ask of any who have got 

 nccustomed to the quaternion method to introduce confusion by 

 such a change of sign. Up to a certain point, and along certain 

 lines, Gibbs's and Heaviside's systems lead to reults identical 

 fvith those obtained by quaternions. It has not been shown 

 ^hat they lead to these results more simply or more directly, or 

 fhat they are more easily mastered by the student than is the 

 palculus of Hamilton. And the same may be predicted of the 

 knodified quaternionic system suggested by Prof. Lodge. 

 ( Musselburgh, September 4. C. G. Knott. 



Grassmann's " Ausdehnungslehre." 



. Sir Robert Ball asks why no one has translated the 



f ' Ausdehnungslehre "into English. The answer is as regretable 



as simple— it would not pay. The number of mathematicians 



ivho, after the severe courses of the universities, desire to extend 



iheir reading is very small. It is something that a respectable 



few seek to apply what they have already learnt. The first duty 



bf those who direct the studies of the universities is to provide 



hat students may leave in possession of all the best means of 



ulure investigation. That fifty years after publication the prin- 



(.iples of the "Ausdehnungslehre" should find no place in English 



Inathematical education is indeed astonishing. Half the time 



•ven to siich a wearisome subject as Lunar Theory would place 



'.dent in possession of many of the delightful surprises of 



ismann's work, .and set him thinking for himself. The 



Ausdehnungslehre " has won the admiration of too many dis- 



inguished mathematicians to remain longer ignored. Clifford 



jiaid of it : " I may, perhaps, be permitted to express my pro- 



ound admiration of that extraordinary work, and my conviction 



;.hat its principles will exercise a vast influence upon the future 



of mathematical science." Useful or not, the work is "a thing 



iif beauty," and no mathematician of taste should pass it by. 



!! IS possible, nay, even likely, that its principles may be taught 



iiore simply ; but the work should be preserved as a classic. 



I should be glad to subscribe ;^io towards the expenses of 

 r.inslation. It others will join, perhaps some publisher will 

 ■ ; the matter up. Is there no machinery by which the uni- 

 iiies could be induced to subscribe? 



good book on the subject, entitled "The Directional Cal- 

 -," by Prof. E. W. Hyde, h published by Ginn and Co., 

 jn ; and a valuable and very clever elementary exposition, 

 • •■1 a geometrical basis, of important parts of the Calculus, by 

 »I. Carvallo, appeared in the NouvelUs Annales dc Matlic- 

 i^iatiques of January, 1S92. The latter will, in one day, enable 

 ,. student to comprehend the power and elegance of Grassmann's 

 i^ethods. R. \v. Genese. 



Astronomical Photography. 



The nature of chromatic correction adopted for visual tele- 

 copes ii uniform enough to make it possible to state what kind 

 )f photographic plate is desired for use with such telescopes. 



.■\. pla-.e which is sensitive to light between C and F in the 

 olar spectrum, with a marked maximum between D and b, and 

 .nsensitive to other light, would be suitable for nearly all visual 

 lelescopes, which might in other respects [e.g. aperture, focai 

 ength, position as affected by climate) be available for taking 

 pecial photographic records. With existing plates, so far as I 

 lave been able to acquaint myself with them, the sensitiveness 

 n the blue and violet is the difficulty. 



NO. 1248, VOL. 48] 



But whilst such a special plate as I describe would be warmly 

 welcomed, we must not forget that the proved goodness of the 

 photographic star-images of what may be called violet refrac- 

 tors, i.e. refractors corrected so that the minimum focus is for 

 violet light, is in great measure to be attributed to the fact that 

 light of short wave length is used. The increase in the diameter 

 ol star images with increased exposures or great brightness of 

 the star, may be, as Scheiner has lately suggested, due to de- 

 fects in the mode of support of the object-glass or mirror, but 

 doubtless the i^oodness ot the images with proper exposures 

 must be connected with the smallness of the scale of the diffrac- 

 tion pattern, and with the concentration of light to the centre of 

 the pattern, which may be got at smaller expense with a violet 

 refractor than with a visual. 



Probably few astronomers would have been bold enough, if 

 no photographic plates had been available except plates sensi- 

 tive only to yellow and green, to urge the preparation of plates 

 sensitive in the violet, on the ground that a violet refractor 

 would give much better results, because short » ave lengths were 

 used. And yet a comparison of the results obtained with violet 

 refractors and with reflectors would lead one to the view 

 above expressed, and, I believe, generally accepted. 



The increased range of sensitiveness of modern photographic 

 plates, with respect not only to the colour, but also to the in- 

 tensity of the light affecting them, is all in favour of the reflector. 

 A greater andjmore desirable advance than even the preparation 

 of plates to suit visual telescopes would, I think, be made if the 

 difficulties of supporting, adjusting, and maintaining a mirror 

 were overcome ; so that the measurement of star-images may 

 be regarded with as much confidence in the case of plates 

 exposed in reflectors as in refractors. H. F. Newall. 



Madingley Rise, Cambridge, September 25. 



Hering's Theory of Colour Vision. 



I AM very much surprised to see that Prof. Ebbinghaus, in 

 the last number of the Zcitschrift fiir Psychologic, announces 

 as new a discovery which has a critical bearing upon Hering's 

 theory of colour-vision — the fact, namely, that two grays com- 

 posed the one of blue and yellow, and the ;other of red and 

 green, and made equally bright at one illumination (by admixture 

 of black with whicnever of them turns out to be the brighter), 

 do not continue to be equally bright at a different illumination. 

 If two complementary colours were purely antagonistic — that 

 is, if the colour-processes simply destroyed each other, as pro- 

 cesses of assimilation and dissimilation must do, and if the result- 

 ing white was solely due to the residual white which accompanies 

 every colour and gives it its brightness, then the relative bright- 

 ness of two grays composed out of different parts of the spec- 

 trum could not change with change of illumination. The fact 

 that they do change is therefore completely subversive of the 

 theory of Hering, or of any other theory in which the comple- 

 mentary colour- processes are of a nature to annihilate each 

 other. This consequence of the fact, as well as the fact itself, 

 I stated at the Congress of Psychologists in London in August, 

 1892, and it was printed in the abstract of my paper, which 

 was distributed at the time, and also in the Proceedings of the 

 Congress. 



Prof. Ebbinghaus' discovery is apparently independent of 

 mine, for he supposes that the phenomenon cannot be exhibited 

 upon the colour-wheel. This is not the case ; with fittingly- 

 cnosen papers (that is, with a red and green which need no . 

 addition of blue or yellow to make a pure gray, and with a 

 corresponding blue and yellow) it is perfectly evident upon the 

 colour-wheel. The same paper circles which I used to demon- 

 strate it in Prof. Kbnig's laboratory in Berlin are, at the request 

 of Prof. Jastrow, now on exhibition at the World's Fair at 

 Chicago. While Prof. Ebbinghaus' discovery of the fact is 

 therefore doubtless independent of mine, I allow myself to 

 point out that mine is prior to his in point of time. 



Baltimore. Christine Ladel Franklin. 



"Megamicros." 



In Nature of August 24 the following extrtict from the 

 Bulletin dc I' Academic de Belgiqtie, No. 6 (1893), is given, 

 viz. : — 



"According to Laplace, if the dimensions of all the bodies 

 of the universe, their mutual distances and velocities were to 

 increase or diminish in a canstant proportion, these bodies 



