Nov. 2, 1883.] 



* KNOWLEDGE 



279 



LETTERS RECEIVED AND SHORT ANSWERS. 



Alex. A. Rodger. Your contempt for " Vegag and John Piskes," 

 <:t hoc genus omne, must extend to and include me also. Can you 

 not see that the God they speak of is but a symbohsation ? They 

 advance no dogma, would force no ideas about the nature of Deity 

 ou men unwilhng to accept even the thought of deity. But the 

 freedom of thougiit about which you are so earnest is a strange 

 sort of freedom if it means that they or I or any who think as we 

 do, are to be silent because tliere are some who can stand face to 

 face with the mighty mysteries of the universe and not feel that at 

 iho back of those mysteries there lies a greater mystery yet, the 

 mystery of the Infinite Unknown, "yea evermore Unknowable," but 

 as manifestly there to us as the sun is in the mid-heaven even when 

 his light so blinds us that we cannot see him because of his very 

 glory. If our widening recognition of the infinite extension of 

 the universe alike in space and time, our clearing perception 

 of the infinite range of the laws of the universe, the mys- 

 tery of universal gravity, the mystery of eternal evolution, are 

 to lead to the belief that there within the region of the known lies 

 all, then were it better — so far as the worth of life is concerned — ■ 

 that no advance towards wider knowledge should ever have been 

 made. But as reasonably might the student of some complex 

 mechanism, who had traced a few links of the connecting chains or 

 watched the movements of some half-dozen cogs, pretend that the 

 whole plan and purpose of the machinery was known to him, the 

 whole scope even of the mind and character of its constructor. I 

 have no wish to convince you that your view of the universe is nar- 

 row and unworthy. But in common honesty I must tell you 

 that if you or any other readers of Knowledge suppose my 

 refusal to admit religious discussions into these pages 

 involves the rejection of all reference to a Power outside 

 the known, and working (unknowably by us) in and through all 

 things, then you labour under a considerable delusion. You speak of 

 freedom of thought, by the way ; but the contempt and rancour 

 you express are altogether inconsistent with real freedom. — B. 

 Walkee. You enter another debatable region. You speak, how- 

 ever, of feelings of rancour and animosity wliich do not exist. Most 

 students of science simply do not concern themselves with the 

 questions you raise. I have mixed a good deal with them, and I 

 know that it is so. Y'ou might as reasonably talk of the feelings of 

 rancour and animosity entertained by fishermen towards land- 

 surveyors, or by any class of men towards another class in whoso 

 pursuits they happen to take no special interest. Do you ima- 

 gine that when Mr. Allen speaks of the evolution of some plant 

 or animal he is expressing the rancour and animosity which he feels 

 towards those folk (now few among the intelligent) who fancy evolu- 

 tion in some way inconsistent with doctrines dear to them, or that 

 when I speak of the tens of millions of years of which the crust 

 (God's work, and therefore His word) tells us,' that I want to hurt 

 the feelings of those who find a few thousand years of work as 

 much as they can believe God capable of ? So when Mr. Clodd 

 speaks of the origin of myths, or Mr. Foster speaks of what the 

 Speucerian school liolds (and I think rightly) to be the origin and 

 true meaning of moral laws, can you for a moment imagine that 

 they are moved by feelings of ill-will towards those who think, or 

 think they think, such ideas must be erroneous (let tho evidence be 

 what it may) ? H'/ich wo feel so, some system of reconciliation 

 auch as you suggest may be wanted. But it will, I fancy, be a 

 long time first. When you speak of " determined, indeed bitter, 

 opposition" where we are, in truth, absolutely unconcerned, you 

 remind mo of the way in which some school-girls quarrel, who, 

 when annoyed by perfect coolness, jiretend to see fierce anger. 

 " You needn't got angry, dear," they will say ; " your hair's coming 

 out of curl." Allow mo to assure you wo are not troubled by tho 

 anger you imagine : our hair curls quite sweetly still. — S. Griffim. 

 The advantages claimed for the Christy over tho Amici have 

 no real existence, though claimed — Paul gets what is taken 

 from Peter. — W. D. B. I said each star had been seen with a tele- 

 ecopc 2J iu. in aperture, not that such a telescope would show such 

 regions as appeared in my maps with all those stars simultaneously 

 visible. The chart results from picturing in a single view the stars 

 seen when such a telf.-^copo is laboriously directed to part after part 

 of tho hcavons. — E. I{.\ti.lii'f. I would gladly answer if I know, 

 but I do not know, whether condensed sea-water (meaning, I 

 suppose, distilled) is used on board any vossols for drinking pur- 

 poses. — K. Anderson. 1 quite agree with you. Tho system may 

 be necessary for many, as iu the training of children. Those 1 have 

 learned to love and estei'm most of all whom, thus far in my life, I 

 have known, have boon absolutely free from both the fears and the 

 iiopos to which yon refer. But many do\ibt whether that state of 

 mind is possible or even conceivable. The passago you quote is 

 indeed absurd — but tho reporter maybe in fault. "No telescope 

 can show Godl" Noj nor can tho conscience be analysed in a 



laboratory, or the soul investigated with a microscope. But he 



might with equal sense have said (to use Sydney Smith's illustra- 

 tion of nonsense) that you can't "ride to London on a pound of 

 pickled salmon." — Enquirer. I know nothing of the rules relating 

 to debts of honour, absurdly so called. I am sorry to leam that so 

 fine a game as whist should ever be played for stakes large enough 

 to be worth troubling about. — C. E. Hanson. No not like the 

 moon ; that stage would be a far later one. But the earth would 

 become entirely water covered through the washing away of all 

 her upraised portions, were it not for subterranean action renewing 

 the inequalities of level. The disappearance of water would, much 

 later, be brought about by the gradual withdrawal of the seas into 

 porous cavities in the cooled crust and nuclear regions. — Omega. 

 Thanks. I try to please as many as possible, — a Spencerian system 

 on a small scale. — G. M. Nearly always, when a communication is 

 not acknowledged in this'part of Knowledge, it may bo taken for 

 granted that it has been marked for insertion. But sometimes 

 considerable delay intervenes between this and the appearance 

 of the letter. It should be clear to you, however, that there could 

 not have been any idea of annoying you, in any case. Look at 

 my lecture advertisements and you will (or should) be prepared to 

 understand and forgive occasional delays. — Steam Roller. You 

 are right ; there must be continual, though slight, sliding : this is 

 no doubt intended. — R. W. J. It seems likely enough that in a 

 number of cases the cure was a mere coincidence ; but there are so 

 many much more remarkable illustrations of the influence of the 

 mind on the body that we must, take that into account. — Chas. A. 

 Edes. Many thanks for your very curious and interesting work on 

 " Papyrography," which I hope shortly to "notice." 



®iir iWatDcmatiral Column. 



THL PHILOSOPHY OF MATHEMATICS.* 



By Professoe A. Cayley. 



IN TWO PARTS.— PART II. 



(^Continued from page 205.) 



IT is interesting to consider two different ways in which, 

 without any modification at all of our notion of space, 

 we can arrive at a system of non- Euclidian (plane or two 

 dimensional) geometry ; and the doing so will, I think, 

 throw some light on the whole question. 



First, imagine the earth a perfectly smooth sphere ; 

 understand by a plane the surface of the earth, and by a 

 line the apparently straight line (in fact an arc of great 

 circle) drawn on the surface ; what experience would in 

 the first instance teach would be Euclidian geometry ; 

 there would be intersecting lines which, produced a few 

 miles or so, would seem to go on diverging ; and apparently 

 parallel lines which would exhibit no tendency to approach 

 each other ; and the inhabitants might very well conceive 

 that they had by experience established the axiom that 

 two straight lines cannot enclose a space, and the axiom 

 as to parallel lines. A more extended experience and 

 more accurate measurements would teach them that the 

 axioms were each of them false ; and that any two lines, 

 if produced far enough each way, would meet in two 

 points ; they would, in fact, arrive at a spherical geometry, 

 accurately representing tho properties of the two-dimen- 

 sional space of their experience. But their original 

 Euclidian geometry would not the less be a true system ; 

 only it would apply to an ideal space, not the space of their 

 experience. 



Secondly, consider an ordinary, indefinitely extended 

 plane ; and let us modify only the notion of distance. We 

 measure distance, say, by a yard measure or a foot rule, 



• Abstract of that jiortion of Professor Cayley's Address before 

 tho British Association at Sonthport which relates to tho philo- 

 sophy of Mathematics and to certain recent ideas respecting non- 

 Euclidian Geometry and space of more than three dimensions. 



