Nov. 3, 1882. 



♦ KNOW^LEDGE 



381 



'Any and 'Arrict note ? What change liave I proposed that would 

 add to their opportunities of being annoying ? I am glad to say 

 that not one letter in fifty which has reached us takes your riew 

 about arrangeincnts which keep out all alike. I think, for my own 

 part, the wall is the chief offence. It deprives the public of the 

 general view of the grounds, which is their chief beauty. Inside, 

 there is ranch that is in such bad taste, — inartistic effects, tawdry 

 colour*combinations, hideous false ruins, and so forth, that the 

 public lose less by the late opening than they otherwise might. — 

 Elt. H. Jules. The rainbow can be photographed after a fashion; 

 only the violet and blue part come out well. It is in one sense 

 true that the rainbow exists only in the eye of the observer ; so 

 does every image of optical effects; but the very fact that there is 

 an image in the eye shows that an imago would be formed on the 

 photographic plate. — Jas. Deas. Undoubtedly a solar spot, un- 

 less yon saw it move, in which ease it was ]irobably a distant 

 bird. — D. 31. J. Many thanks for your very kind expressions 

 about Knowledge. Yon are quite right ; when we asked the 

 opinion of our readers about the weather chart, we received so 

 many letters from those who otherwise would not have written to 

 us, and these letters were so kindly written, that we learned how 

 very small a part of our readers the grumblers are. — A Scbscribee. 

 Prof. Young's book on the sun is now published by Messrs. Kegan 

 Paal & Co.— N. W. S. You will find that the solution involves what 

 I said. The illumination varies as the square of the distance in- 

 versely, and also as the sine of the angle LBA directly ; but the 

 sine of this angle varies inversely as the distance LB. This 

 introduces the inverse distance yet a third time, altering the 

 inverse square to the inverse cnbe. — Sciolist. I stop at your 

 first statement. The comet of 1843 may, you say, have 

 obeyed another sun, and what happened may have been due to some 

 change in that other sun (one of its foci, you say). Are you aware 

 that before that comet could have felt the influence of any other 

 sun appreciably (even though that other sun were the nearest of all 

 the stars) some five millions of years would have to elapse ? Edina. 

 A simple way of ascertaining whether a room is damp or not is to 

 bring into the room a polished glass or mirror at a temperature 

 cooler than that of the room, at a time when the room has for an 

 hour or so been free from living occupants (whose breath might 

 otherwise moisten the air). If the room is damp, a slight mist will 

 form on the glass. — C. G. W. Thanks for your letter about the 

 comet. You ^vill see that we show our readers where to look for it. 



ELECTBICAL. 

 Dextist. I do not remember having read or heard that electricity 

 has the power you mention, but I certainly should recommend you 

 not to try it in the way you suggest. The shocks from a coil are 

 exactly the reverse to ana;sthctic in their influence, even when 

 applied to the least sensitive parts of the body. When applied to 

 any of the organs of the head, they develope more or less intense 

 pain, and, by virtue of their intermittent nature, there is a constant 

 tendency to motion. You propose that the patient's hands shall 

 rest on the arms of a chair in connection with one of the coil-wires, 

 the other wire being connected to the forceps. The forceps being 

 insulated (this you may do by encasing the handles in vulcanite, 

 or by wearing a thick india-rubber glove), you would apply them 

 to the gum in the \icinity of the tooth to be extracted. Has it 

 never occurred to you that every time a shock is imparted to a dead 

 body (as, for instance, to Galvani's frog) that body is subjected 

 to a convulsive movement ? Would not the effect bo even greater 

 in the case of a living body, especially one unaccustomed to such 

 influences ? The battery of which you enclosed a sketch is what is 

 generally known as the "Bottle Bichromate" (on account of its 

 shape), and is expensive because there is usually a deal of work 

 about it. For a simple or less expensive fomi sec next answer. — 

 J. H. Waed. Pleased to hear you succeeded with coil. You could 

 scarcely get a bichromate cell by following the instructions given in 

 K.N'OWLEDGE for June 23, seeing that those instructions were for 

 making a Leclanche cell. The number of cells required to heat 

 two inches of platinnm wire would depend on the diameter of the 

 wire. To make a simple bichromate cell with two zinc and three 

 carbon plates, the plates may bo separated by means of strips 

 of paraffined wood, i to S of an inch in section. The strips may 

 bo 80 arranged as to allow you to fix a clamp across the two 

 zincs. The carbon plate in the centre should not bo in contact with 

 this clamp, but a conical-shaped hole should be scooped out, into 

 which a copper wire should be fixed by pouring in a little molten 

 lead. The external carbon plates may bo treated in the same way, 

 and the three wires clamped together, or a clamp screwed on 

 to them, and a wire from the central plate attached to it. A stout 

 india-rubber band will hold the set together, little i)ieces of paraflined 

 wood or ebonite being placed between the plates at their lower ex- 

 tremity.— W. G. PiNFiELi). The source of electricity in the 

 dynamo machine is to bo found in the steam-engine which 



drives it. Friction lias nothing to do with the generation of 

 the current, a question which is entered into in previous 

 articles in Kxowledge on induced electricity. There Bboold 

 be no wear, unless it be that due to friction at the bearings. 



<!^ur ©aftigft Column. 



By " Five of Clubs." 



[1ST ODDS. 



ACOEEESPONDEXT, "A. B.," sends the following reasoning^ 

 (given in a letter to the Asian) for analysis. The writer 

 is showing how the odds on the rubber, after one game has been 

 played, are calculated :— " Supposing A to have won the first game, 

 there are four different ways in which two games can be played, 

 and only four : — 



2nd game. 3rd game. 



(1) A wins B wins A wins the rubber. 



(2) A wins A wins A wins the rubber. 



(3) B wins A wins A wins the rubber. 



(4) B wins B wins B wins the rubber. 

 From this we see that in three of the cases A wins the rubber, 



and only one in which B wins. Hence the odds on A should be 3 to 

 1." Of course, in cases 1 and 2 the third game is not played, but is 

 Only given to show the different ways in which two games can be 

 played. 



On this, A. B. remarks, " It seems to me that the first two cases 

 are really one and the same, as the third game is not played ; and 

 that, therefore, only three ways are to be considered, viz. : — 



Supposing ^ B to have won the game — • 



2nd game. 3rd game. Enbber. 



^ B win - -IB win. 



r Z win A B win A B win. 



r Z win r Z win 1" Z win. 



which would make it 2 to 1 on J. B ; but I suppose I am wrong in 



mv deduction. 



The reasoning of the Asian correspondent is correct. We must 

 consider both ways in which the two games might be played for 

 .1 B to win, although in one case there is no occasion to play the 

 second. The correctness of the result may, perhaps, be best shown 

 thus :— 



Suppose there were4n trials to determine experimentally the true 

 odds, n being some very large number. Then we know that in about 

 half, or 2n, of these trials A B would win the first game. In all 

 these 2n cases (about) .1 B would win the rubber. In the other 

 half, or about 2n cases, Y Z would win the first game, and a third 

 game would have to be played. Of the 2n (about) third games thus 

 played, A B would win about half, or n games, and in each of these 

 cases they wotild win the rubber. Thus in all they would win the 

 rubber in about 2»n- n or 3n cases out of the 4n, while Y Z would win 

 in about ?i cases. Thus the odds in their favour are 3)i to n, or 

 3 to 1. 



Note, that all the law of probability assures us of is that A B will 

 win (the players being assumed of equal skill) in about 3n cases 

 out of 4)1, or in 3 )i±r cases, i' Z winning in >iTr cases, where, if 

 n is very large, r will be very small compared with n. Thus the 



proportion of wins to losses will be 3n±r to nTr, or 3±- to 1^-, 

 where - may be made as small as we please by sufficiently in- 



Ekratcii. — Page 307, col. 1, lino 6 from foot, for " Ace, King, 

 Knave, nine," read " King, Knave, nine, five." 



ANSWEES TO COEBESPOXDENTS. 

 Walter.— The law is explicit. It says, "on his own or any 

 other pack." Therefore, if the trump card is placed face 

 tlowuwards, quite apart from the dealer's cards or any of 

 the others, it is not a misdeal. — A. Welleslev. Your 

 suggestion seems to us excellent. Will see what printers 

 say to it, and follow it if possible.— Vac.nol. It would scarcely 

 have been right, though it would have turned out well for 

 Mr. U. (who was Y, by the way,— and we think IT to play as he 

 did), to have played the King second-hand to trick seven of last 

 week's game. The presumption was that our Editor did not hold the 

 Ace and four others, the usual lead in that case being the Ace. If he 

 did not, Y Z'b game was sure ; for from the play 1' knew that Z held 

 the winning Heart and the winning Spade, so that the trick wanting 



