270 



KNOWLEDGE. 



Jui-v. 1911. 



predicting the effect upon tlie speaking qualities 

 which of certain constructions in telephonic cables 

 have been based upon the researches of Heaviside 

 and Pupin, and chieflv reduced to simplicit\' In the 

 work of Dr. Kennelly, of Harvard University. U.S.A. 

 The writer of this article delivered last \'ear to 

 a large class of practical telephone engineers a course 



of Post-Graduate Lectures on this subject on behalf 

 of the Universit\' of London, and these Lectures have 

 just been published b\- Messrs. Constable & Co., 

 in a book entitled "The Propagation of Electric 

 Currents in Telephone and Telegraph Cables " in 

 wliich a full discussion of the scientific questions 

 in\-ol\ed in loaded telephone cables is given. 



CORRESPONDENCE. 



THE FOURTH DIMI-XSION. 

 To flic Editors of " Knowledgk." 



Sirs, — I much appreciate the article of Mr. .\nnison on the 

 Fourth Dimension : I regard it as peculiarly fortunate that I 

 happened to refer to the subject in my letter on The Eternal 

 Return. Just recently I devoted a fair amount of thought to 

 the subject of meta-space. approaching it from the geometrical 

 side. The principal difficulty is, I thinU. that of determining 

 what analogies are justifiable. For instance, it may be 

 argued : .^ line can revolve about a point in two-dimensional 

 space (2 D. space), and a plane can revolve about a line in 3 D. 

 space ; therefore, a volume can revolve about a plane in 4 D. 

 space. This seems straightforward, but actually we need to 

 examine more closely the meaning of the word " revolve." 

 Suppose we say that " to revohe round " means " to move 

 continuously at constant normal distance from." Then we 

 must be careful when talking about a body revolving about a 

 line. A body moving in a circle should not be said to move 

 at constant normal distance from a straight line, but from a 

 curved line — any other coplanar, concentric circle, in fact. 



Thus, instead of expecting a Euclidean plane to be a 

 fulcrum and axis in 4 D. space, we should regard a sphere and 

 " meta-cylinder " as such. 



Now, of course, it is possible to obtain rotation " about a 

 sphere " in 3 D. space, except that, practically, it is difficult to 

 devise suitable mechanism. However, my own incomplete 

 geometrical investigations have shown that, even in 3 D. space, 

 very curious projected motions arise from a point revolving 

 " spherically." For instance, suppose we have a ball revolv- 

 ing about an axis lusing common parlance), and that this axis 

 is revolving about a line bisecting it at right angles, the two 

 component angular velocities being the same ; then differently 

 situated points move in differently shaped loci " in space." 

 Each " pole " for instance, has the following locus. 



Front elevation. — A figure of eight. 



Plan. — Two coincident circles, of diameter equal to half 

 that of sphere. 



Side elevation. — Two coincident half-sine-curves. 



This may seem irrelevant to the subject of the fourth 

 dimension, but actually it is not. When one realises the 

 vast number of 3 D. motions which, either by projection or 

 section, are similar in 2 D. space, one realises the magnitude 

 of the task of trying to identify 4 D. figures and motions by 

 their 3 D. ni.anifestations. 



I hope this letter is not unduly long, but I should just like 

 to say this: As I hinted in the last sentence of my former 

 letter, we must not lose sight of psychological considerations in 

 these matters. However. I think that something profitable 

 might arise from cogitation along the following lines. Instead 

 of utilising the analogy of 2 D. beings who " sense " 3 D. objects 

 by their sections in a 2D. world, we should rather deal with 

 3 D. beings whose " introspectible consciousness" (forgive the 

 term I) is limited to two dimensions whilst they actually live 

 and move m three. The analogy must not be pushed too far, 

 but think of men, who. whilst living and acting (to a limited 

 extent) in a 3 D. world, sense objects (including one another) 

 by means of shadows cast on a wall ; also remember how easy 

 it is for visual space and " loco-motor " space to be dissociated, 



as, for instance, when shaving or arranging one's hair, one 

 thinks of the visual operation as occurring " in the mirror." 

 Unfortunately, there is a lack of written matter on the fourth 

 dimension: although I may be allowed to mention Mr. C. H. 

 Hinton's " Fourth Dimension " (Sonnenschein). 



J. JOHN ELLIOTT. 



THE SELENIUM PHOTOMETER. 

 To the Editors of " Knowledge." 



Sirs, — I desire to make a few remarks with reference to 

 your note on the application of the Selenium Photometer to 

 the measurement of starlight. 



First, let me protest against the use of the term Selenium 

 " cell " to the selenium resistances, which are commonly 

 employed in photo-electricity. In 1895 I used. at the Daramona 

 Observatory. Westmeath, a selenium cell, properly so called, 

 for comparing the lights of stars (see the Proceedings of the 

 Royal Society Volumes LVIII and LIX). This cell contained 

 a liquid : and in the cell the light of a star generated an electro- 

 motive force, the cell being thus quite distinct from the 

 ordinary selenium resistance, in which increased conductivity 

 is produced by light. In the Proceedings of the Royal 

 Society, Volume LXXXL 1908, I described a form of selenium 

 resistance, called a selenium bridge, which is suitable for star 

 measurement : and I also pointed out a fallacy involved in the 

 usual employment of selenium for comparing two lights. I am 

 afraid that no notice has been taken of this fallacy. In the last- 

 named paper are given the results of exposing a selenium 

 bridge to the infra-red, red, yellow, blue, and ultra-blue parts 

 of the spectrum of one and the same source of light. The 

 effects of red and blue are enormously different, the red pro- 

 ducing much greater effect. Hence it will be seen that if we 

 compare the light of Sirius or Vega with that of Aldebaran or 

 Betelgeuse. we are not doing justice to the former stars if we 

 merely allow the total light of the star to fall on the selenium, 

 and measure it by the electrical effect produced. We should 

 proceed quite differently. We should split up the various 

 lights into their spectra, and compare two stars, colour by 

 colour. 



This, of course, requires large telescopes, of which this 

 country possesses none available ; but in America the thing 

 could be done properly. 



I send you a copy of my 1908 paper, from which you will see 

 how necessary it is to use spectra when comparing two stars, 

 and how suitable the selenium bridge is to the purpose. The 

 bridge is so narrow — as narrow as the thinnest flake of mica — 

 that the light in any line of a spectrum can be measured. 



Another thing of vital importance is to keep aqueous vapour 

 from the surface of the bridge, or other form of selenium 

 resistance ; otherwise we get spurious conductivity. I rather 

 think that this fact has not been attended to in America ; but 

 I have actually constructed iin electric liygroinetcr depending 

 on the presence of vapour on the bridge. 



I have been hoping to use the selenium bridge here in the 

 Radcliffe Observatory, for spectrum comparison of stars ; but 

 the telescope available is only one of small aperture, and other 

 work has prevented observations. 



GEORCH-: M. MINCHIN. 



