232 



♦ KNOWLEDGE ♦ 



[Jan. 13, 1832. 



ivo tond Iioppwl out, not very long ngo. No nlhigion hnd Ijoen 

 iiuidi< to nnyiliiiiK of the kind previously, mid lie could havo hud no 

 motive for saying wlmt was untrui". 



I proRunio tliespfofisilifonius Mints in " thocnij?" aro well known, 

 although I find no particulnr notice of them in geological works in 

 my possession ; but considering the colls in them and the channels 

 by which they are approached from outside, is it possible for a new 

 tenant to bo inducted and dovoloped such as tho toad ? 



If Sir W. Thomson could 8|>eak seriously of a Colorado beetle 

 surviving a voyage through space in a meteoric stone (see report of 

 British Association Meeting at Plymouth, 1S77 — Mathematical anil 

 Physical Section), I hope you will pardon mo if 1 havo strained a 

 point on the capabilities of a toad. — Yours, Ac, Vf. B. 



"A CcBious Fact.— Many years ago a friend of my father's built 

 a country house, which he fitted up and furnished according to his 

 ownt.i3te; to aecorapli.sh this ho caused to be brought from Italy 

 a piece of pure white marble, out of which a nianteljiiece was con- 

 structed for his own particular sitting-room. The manteli)iece was 

 of singularly pnro marble, in one block, and free from (law, save 

 in one part. Shortly after its crc>ction, the owner of the houso 

 noticed a small damp-looking stain, no bigger than the nail of his 

 little finger in the very centre of the mantelpiece. This, however, 

 was so Blight a blemish that it did not trouble him, till, as months 

 and years went by, it became evident that the mark slowly but 

 aurely increased in size. For twenty years tlie good man of the 

 house sat in his arm-chair facing the curious .stain and marvelling 

 what caused its certain spread. At the lapse of that period it had 

 increased to the size of the palm of his hand, and he could no 

 longer rest in patient contemplation of it. Masons were sent for 

 and desired to take down the marble and break it in two, so as to 

 disclose the mystery. This was done, and to the amazement of all, 

 out hopped an enormous toad ! " — " H. A. F.," in Chatterbox. 



INTEREST OX A PARTUING.— AX APPLICATIOX OP 

 LOGARITHMS. 



[197] — As the nature of compound interest is little understood 

 by many, we will assume that a farthing was placed out, at com- 

 pound interest at 5 per cent., payable yearly, commencing at 

 the Birth of Christ, and extending over time till the end of the 

 year 1880. Now, tho moan diameter of the planet Jupiter is 

 88,(>4.5 miles ; the weight of a cubic foot of pure gold equals 

 17,486 oz. ; and the value of the gold being at the rate of £3. 18s. 

 per ounce ; how many globes of pure gold, each as large as 

 Jupiter, would that interest purchase ? 

 The principal and interest of £1 for one 



year 103 log. 0021189 



Multiply by the years 1880 



1695120 

 169512 

 21189 



Baised to the ISSOth power 



Subtract the log. of the farthings in a £. 960 



Log. of the amount of interest for the 

 gi%-en time, eipials 7120-1- 



7129 4- (thirty-three more figures). 



Diameter of Jupiter in miles 88615 log. 



Feet in a mile equals (1760x3) 52S0 „ 



Feet in Jupiter's diameter 



Baise this quantity to the 3rd jiower 



The diameter raised to tho 3rd power 



Add tUe log. of 1- (31 116) -5236 „ 



Solid contents of Jupiter 



Weight of a cubic foot of gold in oz 17t86 „ 



Value of one ounce of this gold, £3. 18/. 39 



Valne of a solid globe similar to Jupiter 



equals 3661 -h 



3661 -H (twenty-six figures) 



Amount of Interest (Log.) 36S5.30t9 



Valne of Jupiter 30563609 



Log. 19 17331 =- 6 289 1-10 



It therefore appears that tho interest upon a furthi 



39-835320 

 2-982271 



ng for 1,880 



years, at 5 percent., would purchase 1,917,331 solid globes of pare 

 gold, each as largo as the planet Jupiter. — Yours, Ac., Pascal. 



[The calculation is a pretty illustration of tho valne of logarithnu. 

 The mean diameter of Jupiter is much loss than 88,fX)0 miles, lo 

 that the legal representatives of the original owner of the farthing 

 can claim from tho bankers with whom that farthing was placed 

 at interest, a much greater number of gold Jupiters. But that ia a 

 detail. — Eo.J 



TUE HOG PUZZLE. 



[198] — The following problem may Ber\-e to amuso some of the 

 many young readers of Knowledgk who aro conversant with the 

 elements of Algebra. It was given mo by a young lady, but the 

 analysis is my own. 



Question. — Three Dutchmen. Hendrick, Elas, and Cornelius, and 

 their •wives, Gurtriin, Katriin, and Anna, purchase hogs. Each buys 

 as many aa he (or she) gives shillings for one. Each husband pays 

 altogether three guineas more than his wife. Hendrick buys 23 

 more hogs than Katriin, and Elas 11 more than Gurtriin. Require 

 the name of each man's wife ? 



I call this a " puzzle," because I venture to think that nineteen out 

 of twenty would attempt its solution by the common process of simul- 

 taneous equations, and would certainly fail, because there are more 

 unkno^vn quantities than tho number of independent equations it ifl 

 possible to construct. The solution is, however, obtained in a very 

 simple manner, thus* : — ■ 



For brevity, denote the men and women by their initials H, E, C, 

 G, K, A, and let the corresponding small letters h, c, r, g, A-, a, 

 represent the number of hogs (equal to the payment for one) pur- 

 chased by each respectively. 



Then /i', e', c', ;r, k'', a' aro the sums expended by each. 

 Thus H purchases h hogs for h- shillings ; E, e hogs for e' shillings, 

 &c. Also 3 guineas = 63 shillings. 



Observe (1) that It, e, r, g, k, a must be positive integers; and 

 (2) that if m and n are any positive integers, such that 

 711- — 11 - = 63 

 or (m-m) (m-j0 = 9x 7 = 21x3 = 63x1, 

 there are three, and only three, possible values of m + n correspond- 

 ing to three of m—n. 



If m-H?i=9, m—n. = 7, which gives in =8, n = l 

 ,, m-H7i = 21, m— » = 3, ,, m = 12, 7i = 9 



„ m + n = 63, ra-n = I, „ »ii=32.n = 31 



Suppose now m to be the price (in shillings) paid for a hog by a 

 man, and n that paid by his wife. It follows that m may have 

 three values, viz., 8, 12, 32, corresponding respectively to three 

 values, 1, 9, 31 of n. Also, since each man is the husband of some 

 woman, and each woman the wife of some man, whatever arrange- 

 ments may exist between the quantities h, e, c, and g, k, a, each is 

 susceptible of three values. Any one of the quantities, h, e, e, may 

 have a value of 111, provided its corresponding quantity in the 

 groups, g, k, a, has the corresponding value of 11. 

 But there are two equations of condition. 



A-it = 23 (1) 



"-." = 11 (2) 



Referring now to the values of m and 11, we find that to satisfy 

 (1) we must havo A = 32, 1: = 9; 



(2) e = 12,., = l. 



Wo may infer from this that c= 8, a = 31. 

 But to verify our inference, substitute for h, c, k, g in the general 

 equation 



y -^ e' -H c' - (3' -f i' -1- a') = 3 X 63 

 the values just found, and we have 



a'-c»=89r, 

 which can be satisfied with no other possible values of a and c than 

 = 31, c = 8. 



Having obtained the number of hogs each man and woman has 

 purchased, we at once observe that — 



Ji'— n' = 63, ond therefore that A is the wife of H, 

 e^-k'-GS, „ K „ E, 



c'-i7» = 63, „ G „ C. 



Y'ours, &c., I. R. CAUPBELt, 



MOCK SUNS. 



[199]— On Monday, Dec. 19, 1881. between two and half-past in 

 the afternoon, on Wandsworth Common, 1 saw two s|wctra, irreg 

 in shape, with apparent diameters about twice that of the sun, one 

 on each side of and apparently oiiuidistant from the sun. They 

 were at the same apparent height from the horizon as the sun. and, 

 liv guess, appeared to be 25° from the sun. The colour-bands wen> 



• The young reader should try to make out the solution for 1 ' 

 self, before rending what follows. 



