262 



♦ KNOWLEDGE ♦ 



[Oct. 26, 1883. 



capacious and full of yellow teeth. The arms werelong, attennated, 

 and wizened ; the nails more resembled the claws of a vulture, botli 

 in colour and form, than anything else." 



After stating how they used the elder of the two to induce some 

 more of the same tribe to come to the camp, he goes on : — 



*' The men were but little over four feet high ; all wore their hair 

 tied with a piece of creeper at the back of the head, and spreading 

 out like a peacock's tail. They had short bamboo bows, the strings 

 of which were formed of the sinew of some animal, and the arrows 

 were reeds hardened by fire, and tipped with quills of pea-fowls." 



He then says these strange beings belonged to a race called 

 Yanadi, and spoke in a harsh, guttural language. 



ANTHROPOMETRY. 



[970] — Mr. Grant Allen (in the Pall Mall Gazette) sums up the 

 researches of the Anthropometric Committee of the British Asso- 

 ciation by teaching ns that (broadly) the tallest men in Britain 

 are found on the coast ; and that this is a proof that these men 

 are descended from other races than those inland. Is it safe to 

 overlook another possible cause ? Dr. A. Haviland first had the 

 idea (more than ten years ago) of publishing Disease Charts of 

 Great Britain. The first was of heart-disease ; and.it was sho^vn that 

 this is much less prevalent on the coast than inland. Now, other 

 things being equal, a heart extra-nourished by fine sea-air should 

 produce a finer physique all through — consequently greater stature. 



" The very tallest men in the whole island are the Lowland Scots 

 of the sea-hoard." Wliy are they taller than Lowland Scots inland, 

 identical in race ? I remember hearing (30 years ago) a Tipperai-y 

 man boast that in the Militia of that county there was not one man 

 under 6 ft. 3 in. Is it inhabited by a race different to that round 

 about? Or is it not rather that the land of the " Golden Valley " 

 has better fed her children ? H.\llyariis. 



RE JACK KETCH. 



[971] — Yon write (Oct. 5, to E. D. Girdlestone), "but no soldier 

 ever gets [misprint for 'yet.' — R. P.] enlisted with the thought that 

 it would be a pleasant thing to him to take away life." I remember 

 reading in a laudatory newspaper account of " Garibaldi's English- 

 man" (Colonel Peard), that he had joined with the sole object oi 

 killing as many men as possible, being a first-rate shot. He had no 

 grudge against the Austrians, no care for Italian unity ; he looked 

 upon campaigning simply as so much man-stalking. I also remember 

 regretting very much that I could not join the Austrians as a 

 volunteer with the express mission of potting Colonel Peard, and so 

 ridding my country of one disgrace at least. But as it is not pro- 

 bable he was unique, it seems as if a thirst for bloodshed is some- 

 times one motive for taking military service. Halltaeds. 



[No rule without an exception, but the exception proves the rule. 

 Even here it was the shooting not the killing that was in question, 

 though the disgrace to humanity is none the less on that account, 

 s^ipposing the newspaper report truthful. — R. P.] 



DOUBLING OF POPULATION, CAPITAL, &c. 



[972] — Let E=ratio of any increasing geometrical series, and r= 

 increase per cent, per annuni, or per term. 

 Thenif E" = 2 



« = ?^1.'- (A) . 



3,- 



r=^^ (B) 



3u-l 



Example. 

 The annual increase of population in a certain town is 2'50645 

 per cent. Required the time in which the population will double 

 itself ? 



R = 1-025065 

 By logs. 



„^l og- 2 _ 301O30O _..,-,^^^^ 

 log. R 0107513 

 By formula (A) 



„=208 + 2-506-i5^210-50645^.,„.gg_g 



3 X 2-50645 7-51935 



The formula thus gives the exact answer to the second decimal 



place, the error being only —0011, or 35 h. 54 min. in time, an 



error which might generally be neglected ; but if great accuracy 



were desired, -005 added to the answer wonld render it witliin 



— of a unit of the result by logarithms. 



Example 2. 

 The population of a town doubles in 27-9994 years. Required 

 the annual increase per cent. 

 By logs. 

 0-3010300 

 gy.gc)Q_^ = 0-0107513 = log. of 1-0250C5 



1-025065 X 100 -100= 2-5065. 

 By formula (B). 



20S 208 



"" "27-9994x3-1 " 829982 °°"^''^^- 

 This formula gives the answer right to three places of decimals, 

 the error being — -0004. The simplicity of these formulae, which 

 render them easy to recollect, combined with their great accuracy, 

 render them valuable for many purposes, and more especially iry 

 cases where logarithm tables are inaccessible. T. J. B. 



CURIOUS MULTIPLICATION. 



[973]— Multiply 10,958,904 by 18,127,076; 15,068,493 by 

 34,605,731 ; 36,585 bv 19,849 ; 615,384 by 34,521 ; 30,136,986 by 

 1,058,581 ; 68,493,150" by 13.260,896. 



The peculiarity of the above examples is that in each case the 

 product can be obtained by the follo^ving rule : — Multiply each 

 figui-e of the multiplicand, beginning at the right, by its number in 

 order, counting from the right, and sec down the result in the 

 corresponding place in the product, carrying where necessary, 

 until you have multiplied the first or left-hand figure by the whole 

 number of the figures. Then, begin again at the right, multiplying 

 each figure by its number in order, counting the other way from the 

 second figure, and ending with that second figure. For example, to 

 multiply 36,585 by 19,849, set down 5, 2 x 8, 3 x 5, 4 x 6, 5 x 3, 4 x 5, 3 x 

 8, 2 X 5, 6, carrying where the product is more than 9, which gives 

 the answer 726,175,675. A. B. 



FIGURE MAGIC. 



[974] — The following variations of the familiar " Think of a 

 number, double it," &c., may be of interest, and an explanation of 

 the apparent mystery would be very acceptable to myself. 



A. " Think of a number." 



B. Thinks of, say, 373. 



A. " Treble it. Is the result odd or even ? " 



B. "Odd." 



A. " Add one, halve and treble, and say if result is odd or even." 



B. " Even." 



A. " Halve result, and sav how manv times 9 will divide the 



half." 



B. "Nine will go 93 times into the remaining'.half." 

 A. "You thought of 373." 



Nowj A. has been told that the trebled restilt was odd and even, 

 but numbers might have been thought of that would give us trebled 

 results. 



a. Even and even. 



h. Even and odd. 



c. Odd and even. 



d. Odd and odd. 



As procedure is to multiply the reply to the last question by fovir, 

 and if the questions about odd and even have been replied to as 

 a, i, c, or d, he adds 0, 2, 1, or 3 accordinglv. 

 Thus B has thought of 373. 



373 

 3 



1119 Result : odd. 



2)1120 



560 

 3 



2)1680 Result : even. 



9)840 



Now A multiplies 93 by 4, and having been told that the trebled 

 results were odd and even, C adds one, which makes up 373, the 

 number thought of by B. Inquirek. 



