1882.] 



KNOWLEDGE ♦ 



59 



2.cttfi£» to ti)t (BhitOV, 



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 Kkowlidsb, should reach the Publishing Office ntt later than Ike Saturday preceding 

 Ike day cf publication, ______^ 



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** In knowledge, that man only is to be contemned and despised who is not in a 



state of transition Nor is there anything more adverse to accuracy 



than fliity of opinion." — Faraday. 



"There is no harm in roakinp a oustake, but erreat harm in mating unue. Show 

 me a man who makes no mistakes, and I will show you a man who has done 

 nothing." — Liebifj. 



" God's Orthocloiy is Truth."— CJar/w Eingiley. 



TOBACCO AIsD COXSUMPTION. 



[431]— In mentioning the immunity of the Turks from consump- 

 tion, Mr. W. B. Wicken (411) has not noticed the fact that the 

 Turkish women have never '■ taper waists." If all the females of 

 cattle and horses were deformed, would any sane person expect 

 them to produce healthy or "sound" offspring? Now, fully 90 

 percent, of the women here are so deformed. From the practice in 

 youth of wearing stays and glove-tight dress bodies, their lung- 

 capacity is reduced, and all sorts of morbid conditions follow; yet 

 so strong is the force of habit, that the majority of the world 

 expect to find the children of such mothers healthy and unpre- 

 disposed to consumption, and the scientific even cast about to try 

 and discover some far-off and occult reason for the most natural 

 result! The marvel is that the nation is not more unhealthy. 

 Rather let them u.sc their influence to try and persuade young 

 men and women to stuily anatomy, and to go and look at the 

 statues in art galleries, and instead of calling a woman's natural 

 figure "clumsy," to fi.x that epithet on a dress which makes it 

 appear so. 



They will see there, also, that legs are no more exclusively 

 masculine than arms or fingers, and tliey may in time begin to 

 draw the ioference that a style of clothing which, from its innate 

 ngliness retiuires the sacrifice of health and strength to make it 

 presentable, is not the most advisable to persevere in upholding, 

 it they wish to preserve the supremacy of their race, and to stamp 

 out long disease. — I am, Sir, ic, F. W. Harberto.v. 



[432] — Tliere are no returns showing tho relative prevalence of 

 coDsamption among the smoking and non-smoking males of this 

 country, but some idea of the influence of tobacco may bo obtained 

 by comparing the deaths from phthisis of males (of whom, perhnp.s, 

 one-half are smokers) and females, who are, practically, nil non- 

 smokers. The deaths from phthisis in tho year 1876, for example, 

 in England and Wales were 30,413 males and 35,221 females. The 

 occupation of men is tho chief cause of tho greater prevalence of 

 phthisis among them, but, if tobacco had any practical power of 

 averting it, wo ought certainly to find its frequency less among men 

 than among women. J. J. Kipgf, M.D., B.A., London. 



MULTIPLICATION AND DIVISION OP DECIMALS. 



[433] — With your permission I venture to submit tho following 



facts relating to this subject to your arithmetical readers, with an 



apology if it happens that I am telling them anything that they 



already know. 



Arithmetic is an exact science, and, therefore, does not entertain 

 the idea that when applied to calculations based upon measure- 

 ments, it is working upon a more or less erroneous foundation. As 

 a matter of fact, however, all measurements are necessarily approii* 

 mations. If we reckon in the decitiial notation, our measurements 

 will be correct to po many decimal places, and no more. Suppose 

 then that we require to multiply the numbers 3G12-219 and 3141, 

 both of which being correct to the third decimal place, the error 

 in each factor (duo to the fourth, fifth, Ac, decimal places being un- 

 known) will cause corresponding errors in the product ; but the fact 

 is evident, that the error in the second factor (3141) will cause a 

 thousand times more mischief than the error in tho first factor, for 

 it is multiplied by a number a thousand times larger than is the 

 case with the other. Is it not wise, therefore, to cut down the first 

 factor to the same number of digits as the second, and multiply 

 3,612 by 3,141 ? 



Again, since the product of two approximate numbers can never 

 be depended upon to more digits counting from left to right than 

 there are correct digits in either factor, will it not be wise to sub- 

 stitute cyphers for all digits beyond four in the product of the 

 above numbers, and write 1134<:>, instead of 11345-292? This 

 makes our results appear to be often only very rough approxima- 

 tions ; but what is the use of deceiving ourselves ? 1 have seen the 

 heating surface of a set of boilers calculated in square feet, and tho 

 result published to tico decimal places, when a moment's considera- 

 tion would show that an error of only one-hundredth of an inch in 

 the diameter of the tubes (of which the heating surface mainly 

 consists) would vitiate the result to the extent of twenty or thirty 

 square feet. 



Logarithms appear to have this advantage over ordinary arith- 

 metic, namely, that they naturally fix the degree of accuracy as wel! 

 as the value of our results. Logarithms put ns to a lot of trouble if 

 we attempt to get more figures in our answer than are good for us. 

 — Tours, &c. A. N. Souesscalks. 



[434] — Supposing that the reader has leamt how to reduce a 

 vulgar fraction to decimal form, i.e., how to divide one integral 

 number by another not contained "exactly " in it, and to carrj- on 

 that division beyond integral quotient figures, and that he accepts 

 the truth of the statement, that " if the divisor and dividend be 

 both multiplied by any the same number, the value of the quotient 

 is unchanged"; " then the rule for division of decimals is, " mnltiply 

 the divisor and dividend by such a power of 10 as will remove all 

 decimals, and divide tho latter ))roduct by the former." 



I take the examples given in Knowledge, May 0, p. 576 : — 

 127-412) 15-315 



1000 1000 



255600 

 254824 



776 



From the above the following rule at once suggests itself: — 



1. If tho number of docimal places are not equal, make them 

 equal by annexing zeros. 



2. Then divide as in whole numbers, neglecting the decimal 

 points in division and dividend. So far, tho quotient will bo 

 integral. 



3. Any quotient figures found by annexing leros to the dividend, 

 or remainder, beyond this point, will be decimals, but the only re- 



