432 



• KNOWLEDGE ♦ 



[MAncii 17, 18-- 



Can " F. C. S.," or any other rondor, any what i« tho diffcrcnco of 

 atarch in n noft, wiixy potnto nnd n dry, flour}' ono ; and (^ivo any 

 nxuon for tlip dilTiTi<nri', otlior Mian minliglit and a minimum of 

 moiatnn' y Kaiimkk. 



HOC vvY/ALy.. 



fSaO]— Liout.-Col. W. II. (»iik.'«' Sdlntion (soo letter 2HH, p. :«i3) 

 in till" fiillnn-inif : — Wi- liavr to llnil four jmirH of Hr|iiare8 having u 

 common ililTi'rcnoc. Tliin common differonco will bo : — 

 Kimtly. A multiplo nf 21. 



Secondly. Tho piiidnct of four conspciilivc terms of nn in- 

 creasing arithmetical progression. 

 Thirdly. The proiliict of cncli of four pairs of factors. 



Now 21 —3 X 7. Also, 1, 3, 5, 7. is tho lowest arithmetical scries 

 of four terms that includes 3 and 7. Also 1x3x5x7 is tho pro- 

 duct of eacli of four pairs of factors, namely, 105 x 1, 35 x 3, 21 x 5, 

 and 15 x 7. The product of this series gives tho lowest number of 

 shillings that satisfies all the re(|uirements of tho problem. Tliero- 

 fore, each husband has spent 5 guineas more than his wife. 



N.B. — Half the sum and half tho difference of each pair of factors 

 will give the number of hogs bought bv each man and his wife ; so 

 wo got 53 and .'>2, 19 an<l Hi, 13 and 8, and 11 and 1. 



[Correctly solved also by J. A. Miles, C, and J. R. Campbell. — Ed.] 



Tho original jiuzzlo (sec letter 198, p. 232) admits of the following 

 arithmetical solution : — 



The number of shillings in 3 guineas is G3. We have, therefore, 

 to find .3 pairs of S(|uare8 with a common difference of 03. Now, 

 63 is the product of 63 x 1, 21 x 3, and 9x7, Halt the sum and halt 

 the difference of each of the.'O pairs of factors will give the number 

 of hogs bought by each man and his wife, namely 32 and 31, 12 and 

 9, 8 and 1. Hy question, H bought 32, and K 9 ; also E bought 12, 

 and (i 1. Therefore, II and A, E and K, C and G, are the respective 

 husbands and wives. 



William Emerson published tho original puzzle and its algebraical 

 solution nearly 120 years ago. 1 append his solution as he gives it. 



Let 

 l)er II" 

 4tr. 

 5-^ 



6-./ 

 But 



per 12" 



= hogs some man bought, a: — y=wife's hogs, 

 the money for the man's=:cx. 

 II — 2xy + !/ 1/ = wife's money. 

 zx = x.r — 211/ + 1/ y + 03. 

 2x1/ = 63+ ijy. 

 aa + yij 

 X = — T = whole number. 



63- vv 

 x — y = — „ = whole number. 



In this case y must be an odd number, 

 = 1, 3, 5, 7, <S;c., but it cannot be 5. 

 Ifi/ = 1, x-y = 31, 1 = 32. 

 i/ = 3, x — y= 9, .r = 12. 

 V = 7, x — y= 1, r= 8. 

 A has 32 hogs, and Q 9, 

 Also B has 12, and P 1. 

 Whence B and Q '^ 



and V > are man and wnfe. 

 A and R ; 



Herbert Eees Philipps 



[331] — T.et i=the number of guineas each husband laid out 

 more than his mfe = 21.r shillings. 



Call tho four men A, B, C, and D, and their four wives o, b, c, 

 and d. 



Let p = the number of hogs A bought more than n. 

 „ 9= „ „ B „ „ h. 



„ r= „ „ C „ „ c. 



„ «= ., „ D ,, „ ,1. 



Now, by the conditions of the question, p, q, r, and .«, are four 

 consecutive terms of an increasing arithmetical progression. There- 

 fore it follows that p is less than rj, 



q is less than r, i-c. 

 But the number of hogs bought by each man is equal to the 

 number of shillings given for each hog, therefore — 

 p hogs cost p' shillings, 

 and q hogs cost q' sliillings, 

 and as by the question — 



p'=21i, 

 and (j'=21ii!, 



P' = l', 

 and p = q, 

 but it has been shown that p is less than </. 



Therefore, as things which are equal to one another cannot be 

 greater or less than one another, the question is an impossible one. 



J. A. Miles. 



THE PERFECT WAY IX DIET. ) 



[332] — When a Fellow of tho Royal Astmnomieal Society (285) 

 writes of tho abolitionists of the barbarism of the slaughtor-hooso 

 as being "as weak numerically as they are intellectually," is he i 

 really ignorant of the facts (1) that to all intents and purpose* 

 two-thirrls of the human species are, and always have been (at 

 nil evonts, since tho times when they emerged from the universal ' 

 prinueval barbarism), nolentmrolr'nlpg, abstinents from flesh-meots: 

 that it is the richer classes in all communities alone who support 

 the slaughter-house ; while the poor, because of the sellishness of 

 the rich, are starving upon the minimum amount of non-desh foods i 

 (upon badly-cookcd potatws and cabbages, it may be) ; (2) that I 

 there are such names in historv as Pythagoras Sakya-Mani (the I 

 founder of a religion tho most philosophical and most humane, in < 

 its essential doctrine, that has ever been preached on the earth, and 

 which has some 30O,UOO,0(X) followers), Plutarch. Seneca. Porphyry 

 (the most erudite philosopher of antir|uity), Clemens of Alexandria, 

 Chrysostom, (jassendi (whom Boyle characterises as " the greatest 

 philocopher among scholars, and the greatest scholar among philo- 

 sophers"), Mandcville, FIvelyn (Acelaria), Bay, Linne, Halley, 

 Cheyne, Voltaire, Howard, Wesley, Rousseau, Franklin, Shelley, 

 Graham, Hufeland, Struvo, Daumen, Lamartine? 



Before this critic attempts again to pronounce upon the value of 

 a creed which has engaged the earnest attention, and in very many 

 cases the entire approbation, of the most profound thinkers of all 

 tho best times, let me exhort him to study, with some attenlion, at 

 least, such writings, e.g., as Plutarch's "Essay on Flesh-eating" 

 (Ilfpi rpc yiapKo^ayia^), the most remarkable ethical production of 

 antiquity; Seneca's " Letters," Ac. ; Gassendi ; Shelley's " Essay"; 

 Professor V. W. Newman's " Lectures" ; and last, not least. Dr. 

 Anna Kingsford's " Perfect Wav in Diet." — Howard Wii.lums, 

 M.A. 



UNIVKRSITY OF LONDON MATKIC. EXAM., JAN.. ISV. 



[333]—" Out of 800 candidates, less than 300 passed." Ought 

 not this result to lead to some inquiry as to the manner in which 

 the examiners performed their duty ? From the Arithmetic and 

 Algebra paper given by Dr. John Hopkinson and B. Williamson, 

 Esq., M.A., I wish to place two questions before your readers for 

 their consideration. 



No. 5 question is the following : — " Six terms are in arithmetical 

 progression, and also in geometrical progression, and their sum is 

 51. What are they ? " "The only solution ajipears to be that which 

 we find in the multiplication table: — " Six times 9 are 54." No. 9 

 question occupies nine lines, and is as follows : — " Suppose that 

 gold is worth 15 times as much as silver, and that silver is worth 

 100 times as much as copper. Find the proportions of the metals 

 in a certain coin worth 4s., having given that a coin with double as 

 much gold, the same quantity of silver, and 5 times (or 5 million 

 times?) as much copper, would be worth 7s. 9d. ; a coin ha\nng 5 

 times as much gold, the same silver, and twice as much copper (?) 

 would bo worth 19s. ; and lastly, that a coin with the same gold^ 

 double the silver, and one-half the copper (a half-millionth would 

 do c<inally well) would be worth 4s. 3d." If we construct the 

 equations, and from (4) subtract (1), .ind next multiply (1) by (2), 

 and from the product subtract (2), the results will be found incon- 

 sistent, unless we assume that the quantity, or rather "proportion," 

 of copper is nil '. 



Will you, sir, or some of your readers, characterise questions 

 such as these ? If the object is to baffle and bewilder candidates, 

 by "rejecting" 500 out of 800, the examiners are shown to have 

 attained their end. But will the London Matric. Exam, continue 

 to stimulate tho acquisition of " knowledge," if conducted on this 

 principle ? — A Te.\cher. 



MATHEMATICAL PARADOX. 



[334] — The following mathematical paradox is tho shortest, and 

 at the same time the most difficult, I have met with. It seems to 

 have seriously perplexed even so accomplished a mathematician as 

 Lacroix. I should like to hear the opinions of some correspondents 

 before giving mj' own. 



( + „).= (_„). 

 .'.2 log. ( + o)=2 log. (-a) 

 .-. log. ( + a) = log. (-a) 

 a result which is not true. S. L. B. 



INTELLIGENCE OF A MONKEY. 

 [335] — One of the tricks we were in the habit of playing him 

 was this : he had a cord suspended from the ceiling, with a loop just 

 large enough for him to get through ; then one of us passed his 

 chain through tho loop something like a dozen times in different 

 ways; wo then watched tho result. After getting into the loop and 



