April 27, 1883.] 



KNO^VLEDGE 



253 



and remaining thcro during the 30th and the 1st of May. On May 

 2nd she travels into Pisces, which she does not quit until the oth, 

 whin slie passes into Aries. During the later morning hours of 

 the 7th she moves into Taurus, through which her path lies on the 

 8th and part of the !lth, travelling into Gemini on the latter day. 

 She contiuues in that constellation throughout the 10th, and on the 

 succeeding day will be found iu Cancer, where we leave her. 



" Let Knowledge grow from more to more." — Alfbed Texxvson. 



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MULTIPLICATIOX [759]. 

 [791] — By referring to the English Mechanic for April or May, 

 ■1875, under article " Singular Mathematical Fact," two rules are 

 given as communicated by me, signed " S. J." 



The first rule I learnt more than si.tty years ago, and have found 

 it very useful ; the second rule I devised for the article : — 

 38 x3C= (38 + 6)3 = 132 

 and t; X 8 = 48 



1363 product. 



87x34 = (S7 + 4)3 = 273 



and (87-30)4 = 228 



2958 product. 



The two rules may be applied to multiplicands and multipliers 

 consisting each of three figures. James Smith. 



P.S. — The editor, I believe, was abroad during April and May, 

 1875. — J.3. (See the " Geometry of the Two Rules.") 



EASY MULTIPLICATION. 

 [792] — I was much interested in Jlr. Green's method of multiply- 

 ing numbers up to 19 x 19. I find it much easier to calculate in his 

 lT»y up to 99 X 99 than by the usual system, in all cases where the 

 left-hand figures are the same. Slightly alter Mr. Green's statement 

 [this part was mine. — R. P.] and sav — 



(10a + 6) (10a + c) = 10'a(10a + 6 + c)+bc 

 Thus 97x95= 90(90 ■!- 7 + 5) + 35 



(90 X 102) + 33 

 9180 + 35 = 9215. 

 If we have to multiply different left-hand figures, say, 

 (lOo+b) (lOc + d), and the larger (a) be taken as multiplicand, 

 the statement is rather more complicated, viz. : — ■ 



10c (10 a + 6 + d) + d (lOo-lO c) + bd 

 Thus, 35x24 = 20 (30 + 5 + 4) +4 (30-20) +20 

 = (20 X 39) + 40 + 20 

 = 780 + 60 = 810 

 But Is this easier than the usual method ? A. G. T. 



STOKED ENERGY. 



_ [793] — Your note to letter 733 seems hardly to explain the ques- 

 tion asked ; the initial state of the two spnings is different, while 

 the final state is the same. From this it is evident that they must 

 both go through a series of changes, during which energy is given 

 off, till they are both in exactly similar condition ; and, I think, 



the final states being the same, we are justified in supposing that 

 any molecule of the coiled sjiring uncoils at the moment of its solu- 

 tion. Now, in the case of the coiled sjjring, the energy given out is 

 equal to the sum of that due to chemical action and that due to 

 the peculiar configuration of the mass ; and in the case of the 

 uucoiled spring it is oqu.al to that due to chemical action only. The 

 amount of heat duo to chemical action is constant, i»nd that due to 

 the peculiar configuration is equal to the thermal equivalent of the 

 mechanical work the spring would do in uncoiling. Hence, we see 

 that more heat would bo developed in the case of the coiled spring, 

 and that, as the chemical action takes place under similar condi- 

 tions, the time of solution would bo the same. 



S. Skinner. 



VALUE OF GOLD. 



[794] — Early in this century gold was made the sole standard of 

 value in England. All commodities are measured by it. We price 

 everything in it. Gold, like other commodities, is ruled by supply 

 and demand. 



For thirty years past the production has been falling off, and is 

 now less than one-half what it was. Meantime, the consumption 

 in the arts, ic, has been increasing, and it is estimated that at 

 present twelve or fifteen millions sterling of gold disappear in this 

 way annuall}'. For the past ten years this demand has been 

 eclipsed in importance by the demand for coinage. Germany, 

 America, and Italy havo been securing immense stocks of gold. 

 The metal, therefore, becomes scarcer, while the desire to obtain it 

 increases day by day. There is a growing appreciation of it ; 

 people are willing to give more land, or tea, or whatever it may be, 

 in exchange for it. In other words, prices of everything are falling, 

 and must continue to fall till the appreciation be checked. Thus 

 the agricultural industry suffers, and it will not make their hard- 

 ships the easier to bear, when they learn that their fellow-subjects 

 and competitors in the Indian portion of the empire are reaping 

 largo profits because they work under conditions exactly the con- 

 verse of those described above. 



In India silver is the standard of value, and this metal is depre- 

 ciating while gold appreciates. While the English farmer must 

 part with more corn in exchange for less money, the Indian gets 

 moro money for less com. 



Jlr. Goschen's speech has evoked articles in the Statist and 

 Spectator of the 24th ult., and iu the BuUionist of March 10 

 and 17. — I am, Sir, yours, &c., Padl F. Tidhan. 



LEARNING LANGUAGES. 



[795] — In the papers and letters which have appeared in Know- 

 ledge on the subject of Icaruing languages, the Kamiltonian 

 system is highly recommended. There is no doubt of its being an 

 excellent system, but it appears to me to go only half-way to per- 

 fection. The Robertsonian method preceded it, and earlier stUl the 

 " Methode Jacotot" — much used many years ago in France. By 

 this plan the memory is largely called into play, and words onoe 

 learnt are not likely to be forgotten. In a house wo find a store- 

 house or cupboard — a most necessary requirement. Vft; store our 

 tea, our sugar, fruit, spices, i-c, therein, and these are ready for use 

 when we want them. In a similar manner, the mind should have 

 placed in it a store of words — and not only of words, but of phrases, 

 of different parts of speech and their inflections, so that we may 

 take them out again when wanted. By the Ilamiltouian method 

 you get the meaning of words quicklj- at the time, but they are 

 generally forgotten again, nntil repeated translation fixes them in 

 the memory. By the Jacotot system they are put in the cupboard, 

 or mind, at once, and drawn upon when required. It may be said 

 that the task would be a heavy one — to learn a book by heart — but 

 for this there is no occasion, for when a person can say six pages of 

 a book by heart, ho knows half the language, its phrases and 

 inflections. 



I may state my own case. I read and speak French. I can read 

 well the language of Dante and Goldoni, and thoroughly enjoy the 

 Spanish of Cervantes. 



I read, for instance, every day, say, a page of Teleraaque inter- 

 linearly, and learnt by heart also two sentences. But I also repeated 

 by heart the two that I had learnt the day before, and the two 

 before that, always saying oft by heart daily the whole I had learnt; 

 so that after a time I had read the whole of the book, and was able 

 to repeat, say, six pages by heart. These I have never forgotten, 

 and in those six pages I consider I have learnt the best part of a 

 language. 



Thus a very little additional trouble to the student by the Hamil- 

 tonian method will give him a speedier result. W. P. Bain. 



[Mr. Bain's method is an excellent one, as I know from ex- 

 perience of my own. — R. P.] 



