Jlxe 12, 1SS5.] 



* KNOWLEDGE ♦ 



513 



LETTERS RECEIVED AXD SHOUT ANSWERS. 



MiiS Kate H. CiiAXm.EK. Tndoubteilly the Amnioiiiiiphonp is iu 

 the market, bnt I really do not know where it is sold iiiysolf. Write 

 to any high-class London music-sellers — Keith it I'rowse, or the like. 

 — M . Jackson. Streeter, the Bond-street jeweller, wrote a book on 

 " Precious Stones," which ought to answer your purpose. — J. JI. B. 

 It would really appear from your letter that the cuckoos must have 

 held a species of convocation about Dorking. If this bo so, it may 

 to some e.\tent account for their conspicuous absence from — or 

 silence in — other parts in the South of England during the month 

 just past. — Db. Bakn.irdo. An important engagement on Epsom 

 Downs on Wednesday precluded the possibility of my availing 

 myself of the invitation with which you kindly favoured me. 

 — H. B. Is V. S really one whit more genuine than v. 7 H 

 To ask ichy water crystallises at an angle of 60° is 

 to pnt an idle question. No true student of Science 

 ever pretends to attempt to penetrate to final causes. — Senf.x. 

 presumably the reviewer considered that all who would read his 

 essay would be tolerably familiar with the results of modern 

 criticism. I do not feel personally justified in inviting him to 

 repeat a notorious fact in any form of words whatever. — G. M. L. 

 It would be a simple impertinence to suppose that the reviewer 

 was ignorant of Dr. Lightfoot's essay. With regard to your second 

 point, see reply to " H. B." above. — An;. J. Uakvky. I'robably 

 owing to my own mental infirmity, I fail to follow you in your argu- 

 ment that if we had always been accustomed to mesmerise ourselves 

 " insanity, consumption, cancer, and other diseases would never have 

 to take itjot." — Db. Lewixs. Intellectually constituted as are the 

 overwhelming proportion of mankind, your theory would fall upon 

 but barren ground indeed, were I to proclaim it as persistently and 

 prominently as you continue to urge me to do. To give a single 

 illustration why : I trust to you not to mention it, bnt in strict con- 

 fidence I may tell you tiat I was at the Derby on Wednesday week, 

 and, infer alia, saw a gentleman on the course who had had a fight 

 \vith another gentleman, with the result that the first gentleman's 

 nose was bleeding copiously. Now, it strikes me that the fist of 

 his antagonist had a verj- objective existence indeed for him, and 

 that had I (of course, at the risk of having my own head punched) 

 assured him that his unpleasant condition was wholly subjective, 

 and had its beginning and ending in his *' Ego," he might have 

 doubted my sanity, had he done nothing worse. — General Babbage 

 points out that the entire sum spent by the Government in connection 

 with calculating machines went in the construction of the Differ- 

 ence Engine, and that the late Charles Babbage developed the 

 Analytical Engine entirely at his own cost and charge. Whether 

 the country ever obtained anything in the slightest degree equiva- 

 lent for the very considerable sum expended from the National 

 Exchequer is a point on which General Babbage and I must agree 

 to differ. — J. Cliffobd Williamson. I know nothing whatever of 

 theaddress of the maker of the " Hand-grenade Fire-extinguisher." 

 — H. R. Shakmax. Received with thanks. — Hallyjkds. If I 

 "have fetched a lusty blow," (ic, it was done unintentionally. I 

 am not in the least a man to "cry stinking fish," which I should 

 assuredly have done had I fetched the blow in question. I 

 entirely agree with the spirit of your letter, even if I do not insert 

 it. — CoMMEXTATOB. Letters will appear. Thanks for very 

 picturesque photograph.— -Sexe.x. As there is really nothing in 

 the very interesting account you send which might not with 

 advantage appear in print, why not ask the author's permission to 

 publish it ? 



The following paragraph, which has gone the rounds of the 

 papers this week, forms a fitting sequel to our article in No. 18G on 

 " Overhead Electric Wires " — " The Press Association states that 

 the Government do not intend to follow up the recent report of the 

 Select Committee on Overhead Wires by any legislation, consider- 

 ing that the recommendations passed by the majority of the Com- 

 mittee were impracticable, and would invade private rights to an 

 extent for which the Government cannot make themselves 

 responsible." And the following extract from the Electrical Review 

 is typical of many notes which have appeared during the past five 

 years or so, and forms a striking comment on the assertion that the 

 danger from overhead electric wires is very small, and has been 

 greatly exaggerated : — " A telephone lineman had a painful expe- 

 rience the other day at Philadelphia. He was on a pole, tightening 

 wires, and imagining that in the daytime the electric light wires 

 were free from danger, he caught hold of one, the result being that 

 he received a shock which rendered him insensible. Ue hung on to 

 the wire until his fingers were badly burned, when he fell and was 

 caught on a wire by the strap of his climbers. He remained sus- 

 pended in the air, head down, for several minutes, when he was 

 rescued and taken to a hospital, where he was restored to conscious, 

 nesg. One finger was burned entirely off, and another and the 

 thumb were amputated." 



<J^ui' aaill)i2ft Column. 



By Five of Clubs. 



REASONS FOR THE ACCEPTED ACE LEADS. 



TT^ROII a long suit, or in the case of a forced load from three 

 P cards, headed by Ace, Ace is only played in two cases, viz., 

 from Ace to Five at least, not including tho King, and from Ace, 

 Queen, Knave, with or without others. 



It is easy to see why Ace should be led, .as a rule, from Aco with 

 four more cards. The objects of tho jilay from a long suit arc first 

 to make as many tricks as possible in tho suit, and socomlly to 

 establish the suit' Now, if a small card is led from a Uvo-card suit 

 there is a considerable chance that the Ace will bo ruffed. The odds 

 are, indeed, in favour of the suit going round twice. If the reader is 

 very anxious to know what the chances are, let him rejoice in tho 

 following statement: — There arc 2',)0,884,H98,30l possible ways 

 in which the cai-ds of a suit may be so arranged that one 

 player has five, and there aro only two kinds of arrange- 

 ment by which one player holding five, each of tho others may 

 hold two at least, viz., by tho renuiining eight cards lying 3, 3, 

 2 in the other hands, or 1, 2, 2. Now tho actual number of ways 

 in which the former arrangement can bo obtained is 98,531,079,072; 

 while the other arrangement can be obtained in 07,182,320,040 

 ways ; hence the arrangements by which all the three other 

 players will hold at least two cards of the suit are 105,710,405,712 

 in all, or considerably more thari half the total number of arrange- 

 ments possible. Jlorcover, of the remaining arrangements, by 

 which the suit will run shorter than two cards in one of the other 

 hands at least, nearly one-third put the short suit in partner's 

 hand, who would not ruff. The arrangements by wliicli the other 

 eight cards are distributed in the other hands, so that one hand 

 has less than two, are : First, 4, 3, 1, in the other handp, 

 which can happen in 82,111,732,500 different ways ; secondly, 

 5, 2, 1, which can happen in 20,154,697,992 ways; thirdly, 



4, 4, 0, which can happen in 7,895,358,900 ways ; fourthly, 



5, 3, 0, which can happen in 5,084,058,408 ways ; and 

 lastly, 6, 2, 0, which can happen in 4,134,297,014 ways. 

 One-third of these cases, which amount to 119,980,744,874 in 

 all, are favourable. The remaining cases, of course, viz., where 

 the eight cards are distributed 0, 1, 1, or 7, 1, 0, or 8, 0, 0, in 

 the other hands are all unfavourable, they amount severally to 

 4,478,821,674, to 089,049,504, and to 17,876,428. Adding these 

 three sets to two-thirds of the preceding five sets, we get 

 85,172,910,922 unfavourable cases in all, or less than one unfa- 

 vourable case in three. Vet tho chance which exists that the Ace 

 will be ruffed in nearly one case out of three is too great to be un- 

 necessarily risked. By leading the Ace at once, and then a small 

 card, the Ace is almost certain to be made, and there is a good 

 chance of so far exhausting the suit that either the command will 

 remain with the original leader, or a third round taken out by 

 partner will leave him with two long cards in the suit, which, when 

 trumps are extracted, will be as good as trumps, or may be effec- 

 tively employed in forcing out trumps. 



The lead from Ace to Ace, (^ueen. Knave, with or without others, 

 is obviously good ; for after the Ace has made, one or other of the 

 Queen-Knave sequence can be led, forcing out the King, and then the 

 suit remains in all probability established. If partner holds the 

 King guarded, he would probably not play it on the Queen, unless 

 he saw that it was absolutely essential ho should give his partner the 

 chance of leading the Knave, when he would take the trick with 

 the King and lead the little card. Usually, however, he would re- 

 frain from taking his partner's trick ; and thus if the leader had 

 originally five cards in the suit, his long suit would be blocked. To 

 avoid this it is customary to lead the Knave from the Queen- 

 Knave sequence, after Ace has made, when the suit was 

 originally Ace, Queen, Knave, and two others at least. Then 

 partner puts on the King, and the long suit is prac- 

 tically established. Of course, if beside the Queen and 

 Knave, the leader holds the Ten, he leads that card instead 

 of the Knave, where he originally held five, the Queen, however, 

 if he only held the Ace, Queen, Knave, and Ten. The principle is 

 obvious, though it may be remarked that many players doubt the 

 wisdom of tho convention by which Knave, or lowest of Queen- 

 Knave sequence, follows the Ace when the original hand contained 

 more than four cards. Cavendish was led to suggest the innovation 

 by observing the bad effect of his own play on one occasion when, 

 as partner to a player who followed Ace by Queen, he played his 

 King's solitary guard to the Queen, and had then to capture the 

 Knave without any power of giving his partner a lead again, by 

 which the two long cards in the suit would have been available for 

 two tricks certain. 



