68 



KNOWLEDGE. 



February. 1913. 



parallels. Some mathematicians have even discussed some 

 problems of motion, using the three coordinates, x, y, and z, 

 and the fourth w to represent a fourth dimension, and their 

 results are given in dynamical works, just as we find problems 

 as to the motion of bodies under laws of force differing from 

 that of nature (inverse cube, inverse fifth power, direct 

 distance, and so on) set for the edification and amusement 

 of students. Of a somewhat different character is the 

 question as to the curvature of space, which, we are told, 

 may possibly be some day detected by astronomical observa- 

 tions. At present, however, we find that the Euclidian 

 " homaloidal " space agrees most closely with the space of 

 experience and is the simplest concept, but there are other 

 concepts which within the limits of observational error give 

 results differing but little therefrom. If some day the existence, 

 say, of stars with negative parallaxes be definitely ascertained 

 ' lying on the other side of nowhere," some mathematicians 

 may regard this as a proof of the non-Euclidian nature of our 

 space, but meanwhile astronomers generally will be likely to 

 find a simpler explanation. 



Walthamstow. 



F. W. HENKEL, B.A., F.R.A.S. 



THE FOURTH DIMENSION. 

 To the Editors of " Knowledge." 



Sirs, — I notice in the November number of " Knowledge," 

 that Mr. John Johnston still continues the (as I think) 

 unprofitable exercise of criticising a theory, with the arguments 

 for which he has not taken the trouble to acquaint himself. 

 Mr. Johnston says that "Our experience of dimensions gives 

 us the law that where there is one there must be three, but it 

 gives us absolutely nothing else. There is nothing in it to 

 lead us to believe, or even to suggest to us, that there are 

 other dimensions." On the other hand, I say that the exist- 

 ence of any number of dimensions (say n) implies the existence 

 of one more dimension (« + l), and so on, ad infinitum. In 

 support of that statement I have brought forward certain 

 arguments, to which I have referred Mr. Johnston. Now, 

 these arguments of mine may involve a fallacy. I may have 

 misapplied the principle of the continuity of natural law, or 

 committed some other logical mistake. If so, I am quite 

 willing to relinquish a belief in the real existence of the fourth 

 and higher dimensions ; since this belief does not form an 

 integral part of my philosophy, but is merely an appendage 

 thereto, supported only by its own specific arguments. But if 

 this be the case, let Mr. Johnston point out the fallacy in my 

 argument ; not content himself with making bland assertions 

 and negations without first finding out what this argument is. 

 If Mr. Johnston does not wish to do this, then let the 

 correspondence cease, since it is only a waste of time and the 

 valuable space of your journal ; for I must confess I am not 

 sufficiently anxious to convince Mr. Johnston of the correct- 

 ness of my views as to the fourth dimension to the extent 

 either of restating them in a letter, or of sending Mr. Johnston 

 a gratuitous copv of my book. 



H. STANLEY REDGROVE. 

 The Polytechnic, 



Regent Street, London, W. 



P.S. — Reading Mr. Johnston's letter my eye caught that of 

 its companion signed " Geoma." I thought that Professor De 

 Morgan had annihilated the last circle-squarers, and that the 

 species was now extinct. "Geoma" may easily satisfy him- 

 self of the inaccuracy of his " theorem " by measuring the 

 diameter of a cylinder with calipers and its circumference 

 with thread, since it is quite easy to get the value of the ratio 

 (*) by this means correct to two places of decimals : that is, 

 3-14. Of course, as I e<pect all your readers know, it has 

 been conclusively proved by the higher mathematics that the 

 value of this ratio is an incommensurable quantity, and that 

 to five places of decimals its value is 3- 14159. 



A BAROGRAPH RECORD. 



To the Editors of " Knowledge." 



Sirs, — The wet weather we have experienced since the 

 15th of July, though that day was fine and bright with us, is, 

 probably, a fair A , 



//PhJ/frn JJh SJ*l. 



fyPo 



• 7 



7° 



Jo\ 



sample of the kind 

 of weather that 

 originated the leg- 

 end of St. Swithin. 

 My Barograph 

 has been com- 

 paratively un- 

 changed during 

 this period of rain 

 and wind, but the 

 accompanying re- 

 cord (see Figure 

 68) of a thunder- 

 storm here on the 

 night of May 11th 

 and 12th last, is 

 quite unpreceden- 

 ted during the last ten years 

 your columns. 



JOHN GLAS. SANDEMAN. 



Whin-Hurst, Hayling Island. 



ON COOKED FOODS. 

 To the Editors of " Knowledge." 



Sirs, — I read with much interest, the article in the October 

 number of " Knowledge," by Katharine I. Williams, but 

 would like to ask how her values would stand if the vegetables 

 were cooked conservatively and did not come in contact with 

 the water in the process. 



It is not denied that the old-fashioned method of cooking 

 vegetables is wasteful and foolish in the extreme. 



Figure 68. 

 and may be worth notice in 



13, Shaftesbury Road, 

 Hornsey Rise, N. 



A. GAUBERT. 



SCHOOL SCIENCE SOCIETIES. 



One of the topics discussed by the Association of Public 

 School Science Masters at their meeting, held at the London 

 Day Training College, on the 8th and 9th of January, was the 

 aims and uses of School Science Societies. The general 

 principles were dealt with by Mr. W. M. Hooton, of Repton, 

 and after considering the general advantages of such societies 

 and their kinds, he spoke of the limitations imposed by 

 organised games, which, very many will agree, stand greatly 

 in the way of the boy whose tastes and inclinations would 

 lead him to acquire knowledge first hand and in his own way. 

 Mr. Hooton emphasised the point that, in his opinion, organised 

 games did not so much use up the time of the boys as their 

 energy, and left them too tired for other pursuits. In either 

 case the result is the same. With all due respect to 

 Mr. Hooton's contention, we think that a trustworthy boy 

 who would prefer taking a ramble in order to study some 

 scientific subject as a hobby, to playing games should be 



allowed to do so. Mr. Hooton also testified to the good 

 training obtained by boys in preparing lectures and illustra- 

 tions. Mr. F. C. Headley, of Haileybury, when discussing 

 School Natural History Societies, dwelt on the need for 

 unspoilt country to be within easy reach. He said that at 

 private schools many boys with a definite bent for Natural 

 History had the enthusiasm starved out of them. Liberty and 

 leisure, he claimed, were important things. Some of the leading 

 boys should be enlisted as supporters, and it should be made 

 clear to them that Natural History leads on to the study of 

 evolution and to many difficult problems, and is not merely 

 an amusement for little boys. 



Geological Societies were advocated by Mr. C. I. Gardiner, 

 of Cheltenham; Photographic Societies, by Mr. T. H. 

 Oldham, of Dulwich, and Astronomical Societies by Mr. G. 

 Hewlett, of Rugby. 



