>24 



• KNOWLEDGE ♦ 



[Nov. 23, 1883. 



work is not known to me. — C. Davison*. All those ideas about 

 earthquake predictions based on mere coincidences, — about as 

 trustworthy as the sun-spot influences on commercial crises and 

 other such nonsense. Captain Delauney is a mere paradoxist. — T. 

 Ki.NMER. — We do not undertake to work sums.— C. Stketto.v. Thir- 

 teen if the trains start simultaneously, otherwise fourteen. Thanks 

 for date information, but the lines are known, and the reference to 

 first table in Prayer-book rather complicates matters. — J. C. M. D. 



Letter forwarded. — A Lady Mathejiatician- '' By-and-by, 



' strange 1 ' says she, ' what a noise there is in my ears, as if ten 

 thousand paper-mills were going.' A little after she was at it 

 again, ' Look, look, what is that I see yonder ? It is just like the 

 flame of a tiei-y furnace.' To whom the dame replied, ' Prithee, 

 child, if you would have us allow you any sense at all, do 

 not affect to show more than Xatnre has given you.' " 

 ^sop. You see two or more can play at the polite " nonsense ! " 

 game. In fact, three or four. For you and I are 2, and Messrs. 

 Foster and Clodd are 2 : but you may believe in Mill's cheerful 

 universe where 2 and 2 may be 3 instead of 4. Quaternions 

 belong to the common sense of mathematics, and the square 

 root of a negative number is only inconceivable if you insist 

 that the square root shall be a number of a certain kind, just 

 as the lenjrth of a line at right angles to another may become 

 inconceivable if you insist that that length shall be regarded as 

 measured along the other. The square root of a positive number is 

 utterly inconceivable if the number represents time, or shillings, 

 or pecks of potatoes. But the ideas which you seem to think 

 conceivable (though Cayley and Helmholtz knew better than to say 

 that) are about as conceivable as time progressing sideways, or as 

 squared time, or the cube root of ten degrees of heat. If' you will 

 give us an essay on the quadrature of a time-circle I will tell you 

 just how you are mistaken as regards Messrs. Foster and Clodd. — 

 Uncertain. Considering that the whole question is, Where are the 

 Umits ? how shall we begin our inquiry by defining the limits .' To 

 use your illustration, it is as though France and Spain desired to 

 determine their border line, and some one started at the outset the 

 objection that the question could not possibly be dealt with till it had 

 been settled what is France and what is Spain, which could not be 

 done until the border line had been determined. — J. B. FiNL.lY would 

 be obliged if Mr. Grant Allen would name the printers and probable 

 cost of Dr. Hull's Geological Charts. — X. T. Z. You might as 

 justly argue that the return motion of a point along a line gives a 

 second dimension. — Thos. Padmore. Thanks. The points you note 

 are interesting. They correspond to the fact, which has been shown 

 by other observations, that the outline of Jupiter is variable. — C. 

 CoLLiNGwooD. Thanks, letters printed. — H. Chaplin. There seems 

 to me no objection to the belief that downfalls of the kind would 

 onJy happen occasionaljy, when the walls chanced to be unusually 

 precipitous. Most moimtain j-anges would be free from danger. 

 There may be much heat internally still, and almost certainly there 

 is much water.— E. T. L. Calcula'te the effect ; and " please find 

 enclosed" in calculation the disproof of your earth-piloting theory. 

 — A Poor SxroENT. Vide Natttical Almanac for right ascensions 

 of Ceres, Vesta, Juno, and Pallas, at any given date. Your "pre- 

 sent time" is so vague. Periods. 1 (Ceres), 4-61 years; 2 (Pallas), 

 4-62 years; 3 (Juno), 4-36 years; 4 (Vesta), 303 years.— J. J. 

 ScAEGHL. Certainly not fiery rain, but whether showers of 

 falling stars looking like rain, or some purely local phenomenon, 

 information too vague to enable me to say. — A Constant Reader. 

 Oh come I I say ! — look here, now ! — it's all very well to give me a 

 formula, and to say h is so and so, d something else, and I such and 

 such ; but what does the " tottle of the whole " mean ? Is it the 

 discharge per second in gallons, or cubic feet, or what ? Because 

 if you will tell me what it is, I will tell you what you want to know. 

 — W. Gibson. I cannot find the duplication of the cube in your 

 enclosure. Are you clear as to what the problem is ? — S. L. B. 

 I quite agree with you that the use of imaginary quantities differs 

 entirely from such questions as quadrimensional space, non- 

 Euclidean geometry and so forth. But I fear the subject would 

 hardly please the readers of Knowledge. It seems generally for- 

 gotten that when we apply algebraical treatment to geometrical 

 problems, we are not free to assume that everything involved in 

 our geometrical subject matter is necessarily expressed in our ana- 

 lytical formula?, and that these formulas necessarily express nothing 

 more than is involved in the geometrical relations we use them to 

 illustrate. Thus when we take the equations x- + i/' = i~ and ,r. = d, 

 to represent a circle with radius r, having the origin of co-ordinates 

 (right angled) at its centre, and a straight line at distance d from 

 one of the axes, we must remember that these equations do not in 

 reality express these geometrical relations but only illustrate them. 

 They are relatiuns between matters measurable numerically, but not 

 themselves numerical. In dealing with them we get other numerical 

 relations, not all of which necessarily illustrate the geometrical 

 relations we are dealing with. Thus if d is greater than r, so that 



we obtain for the value x = d, y = \/H — d- an imaginary value 

 so far as the geometrical illustrations involved are concerned, we 

 need not therefore imagine that we have found evidence about 

 imaginary space. It is worthy of notice that even the square 

 root of a positive quantity has no analogue in space relations, if the 

 positive quantity represents a straight line. So with time. Our 

 numbers may represent time past or present ; but when we get to 

 their squares, cubes, or square roots, they have no relation whatever 

 to anything connected with time. The expressions a.', a', v'a, &c., 

 are fully as imaginary as the expression v — a if a represents a 

 time -interval. Yet this does not prevent our dealing with 

 a', a?, V a in problems relating to time, and getting correct and 

 real solutions. — Frederick Thompson. I see no reason why your 

 "pot of potatoes " should be scattered over the floor; so am at no 

 pains to explain their quiescence. You think we rotundists want 

 to immolate our opponents (save the mark I) as heretics. If you 

 think that, you would think anything. I feel about as anxious to 

 immolate the Flattists as I do to set fire to Earlswood Asylum. 

 But wait at least till you have squared matters with Hampden 

 and Parallax before you come rounding on me. You doubt 

 whether there is any North Pole ! Xow, they respect it as the 

 centre of everything. Why you will malign, next, the very meri- 

 dians ! But seriously what can you suppose it matters to me 

 whether you understand or fail to understand the nattire of the 

 world you live on ? — Hy. Lancaster, Ed. Radfohd. You choose the 

 hardest worked person you can find to do what you could easily do 

 yourself. Do you imagine I keep a list of all the advertisements 

 which have appeared in Knowledge ? It is not so, I asstire you. — 

 A. McCallum. Permit me to say that if I use Knowledge occa- 

 sionally for mj' own purposes I pay for the privilege, and full 

 value too. If I did not feel free to do so much as that, I 

 should drop Knowledge rather quickly. The article on the 

 Spencerian philosophy appeared in the last volume of ray 

 essays published by Messrs. Chatto & Windus. — L. S. M. P. Quien 

 Sale ? 



O^ur ZM)\^t Column, 



By " Five of Clubs." 



THE question of the value of the signalling system at Whist has 

 brought us many very interesting communications, from 

 among which, with thanks to the rest, we select the following : — 



CONVEXTIONAL RULES AT WHIST. 



Some months ago there was a very able discussion in the Fieid 

 upon the policy of leading Ace originally, from Ace to four. 

 There was, of course, the objection that such a lead simulated the 

 lead of Ace, from Ace to five or more. On the other hand, some 

 writers gave their experience that by leading a small card, from 

 Ace to four, they had frequently not made a trick in the suit, the 

 first trick having been won by the adversaries, and the Ace 

 trumped upon the second round. I took no part in the discussion, 

 but I may say, en passant, that I am in fa^-our of leading a small 

 card from Ace to four originally, and also in the course of the 

 hand, unless, in the latter case, the play of the previous suits has 

 shown an irregular division of the cards, in which event the Ace 

 might be in danger. I am in favour of leading a small card as 

 above because I am in favour of uniformity at Whist. I lay no 

 stress whatever upon the argument that uniformity gives informa- 

 tion to the adversaries as well as to the partner. 



Success at Whist depends upon the faculty of combination and 

 the rapidity and accuracy with which correct inferences can be 

 drawn from the fall of the cards, and if information is to be with- 

 held because the adversaries may make use of it for the purposes 

 of their strategy the whole science of the game is gone. But there 

 may be, and frequently is, what I call an ahuse of imiformity ; where, 

 in order that his hand may be counted or his cards known, a player 

 will under all conditions and without reference to the score play 

 according to conventional rule. Good players will, however, fre- 

 quently deviate from recognised play, and indulge in what I hope I 

 may be permitted to call the common-sense of Whist. 



■To illustrate the last observation I send you a game in which I 

 played .4. It will be obser\-ed that I had Ace to five and did not 

 lead the Ace, and that I had five trumps and did not lead one. 

 Both conditions were combined in my hand, which might have 

 induced one set of players to lead a trump notwithstanding the 

 Knave turned, and another set to lead the Ace of the suit. In my 

 judgment either play, although in the direction of uniformity, would 



