Feb, 



1882.] 



KNO\AALEDGE ♦ 



301 



CHINESE CALCULATION. 



[257] — In reply to yonr question respecting Chinese Calctilatiun, 

 let me state that in Sir John Bowring's " Tieatise on the Decimal 

 System in Nnmbers, Coins, and Accounts," there is a good descrip- 

 tion of the Chinese Kwan-pan. or abacus, nud mode of using it. lie 

 tells us that the following is the Chinese multiplication table, the 

 eimplicity of which recommends the whole scheme. Ten tens are a 

 hundred ; ten hundreds a thousand ; ten thous.'ind a wan = 10,000 ; 

 ten wans a zih = 100,000; ton zihs a chaon = l,Oa>,000. Ue 

 adds ; — " At early morn, one of the tirst sounds heai'd in the shops 

 of all the towns and cities of China is the shaking and cleaning of 

 the swan-pans, i>reparatory to the business of tho day. As, in 

 Christian lands, tho sound of the bells calls the worshippers to 

 Church, as, in Mahoniedan countries, the voice of tho Muezzin from 

 the minarets bids tho devout Mussulmans to prayers, so, in " the 

 middle kingdom," tho rattling of tho abacus announces that another 

 morning's labours are begun. 



With that instrument the Chinese youth has been as familiar as 

 with his hermetrical classics, the first and most popular of his school 

 books. From it he has i-eceivcd the most correct impressions of 

 the relations of numbers to one another ; and he has acquired the 

 habit of moving the balls on the wires of his swan-pan with con- 

 siderable dexterity "and rapidity ; wonderful are the ease and accuracy 

 with which all calculations are made and recorded. In my own 

 person I have had to settle a great variety of accounts with various 

 classes of people in China, and 1 never remember to have detected 

 an error ; and in cases where my reckoning has disagreed with that 

 of the Chinese, I have invariably found that their account was 

 correct, and my own erroneous. In China it might almost be laid 

 down as an axiom, that a mistake in an account is in itself strong 

 evidence of fraudulent intentions. I have compared my obscrva- 

 tioBB with those of persons of the longest and most extensive 

 experience as to the general correctness of Chinese accountancy ; 

 and my opinion has been fully coufinned, that among Cliinamen 

 intending to be honest, an error in reckoning is almost unknown. 



HONQ-KONG. 



COMMDNICATION WITH THE MOON. 

 [258] — It was Gruithuisen, the continental astronomer, who 

 maintained that in his observations on the moon, by means of a 

 large achromatic telescope, he had perceived invmense cities, edifices, 

 and artificial structures, apparently the works of some being exist- 

 ing tliere ; and from these appearances he concluded that the moon 

 formed a home for reasonable creatures, with whom we might cor- 

 respond. This idea he communicated to Gauss, who replied that 

 correspondence might be carried on, but with signs which all 

 rational beings must have in common ; such as the right-angled 

 triangle, with the properties of which (Euc. I., 47), the Selenites 

 mH£t be acquainted. Tho plains of Siberia, or the Great Desert, 

 might be selected for the purpose ; and the requii-ed figure — a right- 

 angled triangle, a circle, or an ellipse — be formed by channels dug 

 in the plain and filled with, say naphtha. Even if the object was 

 not attained, the work would provide employ for the hordes which, 

 objectless and homeless, roam those vrilds. But, provided that tho 

 moon is inhabited, and that by rational beings, our intentions and 

 efforts would be most likely misunderstood. But why correspond 

 with those that are not ? Hkkbert R. Wellee. 



PROBABILITIES. 



[259] — Seeing an article in a recent number of Knowledge 

 on luck and probabilities, I venture to ask yonr opinion on the 

 following i>roliiem, which has occasioned animated discussion in 

 more than one instance ; — 



A bete B an even sum of money that in three cuts of a pack of 

 cards he will turn up an ace, a knave, or a nine. Of course, it is 

 immaterial what particular cards are decided on. 



I have seen this done over and over again, the stake being a 

 shilling, and it has raiely happened that either of tho parties has 

 lost or won to any extent ; in fact, so close was tho running, that 

 an Irish bystander came to the conclusion that the odds were even. 



I should very much like to see the correct calculation of the 

 chances, as I have known many attempts made to solve tho 

 problem. 



At first sight the chances appear all against^the cutter, and the bet 

 is usually taken with alacrity, but I imagine that the odds are 

 slightly in his favour, though I don't know why. 



Barracks, Dundalk, Jan. It, 1882. Chaeles A. Edes. 



[The solution would run somewhat as follows : — The chance that 



at a single cutting one of the three cards will be out is -r^, since 



52 

 there are four of each of the cards named (no suit being men- 



tioned in the conditions), or =^ ; therefore, the chance that none of 



13 



10 



the cords will bo cut at a given trial is — . Hence, the chance that 



(by tho well-known rule for such cases), 

 1000 

 "2197 

 The odds are, therefore, 1107 to 1000 against A — that is, againtit 

 turning up one of the named cards in three trials. 'l"he betting 

 should have been about C to 5, or, moro exactly, £5. 19s. 8Jd. to £5 

 ag.-iinst A. — Ed.] 



MESMERISM. 



[260] — As a constant reader of your valuable paper 1 should like 

 to be allowed to ask a few questions about mesmerism. 



My reason for so doing is because, ou Saturday evening, 1 put 

 one of my boys in what 1 believe is called a mesmeric trance. In 

 joking with him, 1 told him to keep his eyes on a white spot of 

 paper in tho centre of a penny. I then made a few passes in imi- 

 tation of those I had seen made by professional mesmerists, when 

 I was astonished to see hiui drojt into a trance, from which no 

 amount of shaking, pinching, &c., could wake him. At first, being 

 considerably startled, I did not know what to do, but recollecting 

 how I had seen mesmeric subjects awakened, 1 blew on his 

 forehead, tapped him on the head and said " Right." He at once 

 awoke, but for some time (half-an-honr) was somewhat dazed, 

 doing things almost unconsciously. Being rather startled at finding 

 1 possessed this power, 1 should like to ask a few queries, viz. : — 



1. What is mesmerism ? 



2. What ultimate effect has it on the subject ? 



3. How is the subject restored to his senses ? 



And any other information on the subject that will be useful. 



A Stastled Oke. 



Wigmore Schools, West Bromwich, Jan. 16, 1882. 



P.S. — I may mention that I have previously been a disbeliever in 

 mesmerism. 



[As animals can be mesmerised — to use this rather absurd term 

 for want of a better — it is certain that there is some physical effect 

 to be interpreted. Unfortunately, many professional mesmerists 

 mix tricks with what they can do without trickery. — Bu.] 



TERRACES IN DORSET VALLEYS. 



[261] — Anyone travelHug in Dorset must have observed ou tho 

 sides of the vaUeys a nmnber of terraces, sometimes rising on 

 above another like steps, varying in number and also in size. I 

 have noticed some as large as giant earthworks, with slope as 

 smooth and top as level as any garden terrace. Others, again, are 

 a few feet in length and about one in depth. They are a peculiar 

 feature of that county, but 1 have seen occasional outliers in 

 Yorkshire and Cornwall. What is their origin ? 1 have seen it 

 asserted in a newspaper article, in an otf-hand way, that they are 

 artificial ; but there is no conceivable end commensurate with the 

 immense labour the construction would have entailed. They might 

 be old sea-beaches, if only they were all horizontal. Can anyone 

 say whether there is any accepted theory about them amongst 

 geologists ? S. H. W. 



ICE. 



[262] — In your current number, p. 252 (208), " A Fellow of the 

 Royal Astronomical Society" appears to have made a slip. It may 

 be a fact, though very improbable, " that ice does not vary in 

 volume, as other solids do, with variation of temperature." But 

 this is by no means a corollary from the other fact, that water in 

 becoming ice undergoes a greater chango of volume than most 

 other substances do in the act of crystallisation. 



There are other known substances — notably certain bismuth 

 alloys — which expand on crystallisation, and remain permanently 

 larger than before congelation. Does " A Fellow," Ac., apply tho 

 same assertion to those, and does he consider that ice remains 

 constant in volume at all temperatures at which it is ice, or docs 

 he think that it continuously expands with decrease of temperature ? 



An Engineer. 



SHORTENING OF THE DAY. 

 [263] — Laplace satisfied himself by reference to ancient astro- 

 nomical records (meaning, no doubt, those of Hipparchus, who 

 lived about 125 B.C.) that no alteration in the length of the day ha 



