60 



SCIENCE. 



[N. S. Vol. IY. No. 81. 



which process we have learned from Mr. 

 Spencer to expect with such confidence. 



We may first note the prevailing tend- 

 ency in the division of units of length. In 

 land surveying, where a change of the mode 

 of measurement causes more inconvenience 

 than elsewhere, the advantages of the deci- 

 mal division are so strongly felt that hun- 

 dreds of feet and tenths of a mile and 

 a foot are being used to a considerable 

 extent instead of rods and inches. This 

 is true, I think, to a greater degree in 

 the West than in the East. Even in 

 common speech it is more usual to esti- 

 mate a distance as, say, sixty feet or two 

 hundred feet, than in yards or rods. The 

 division of the foot into tenths has come into 

 use in spite of the inconvenience of a unit 

 so nearly like the inch, yet so difficult to 

 reduce to it. The subdivision of the inch into 

 twelfths originally in vogue is almost un- 

 used, while tenths of an inch are supersed- 

 ing not only the line, but also the fractions, 

 of quarter, eighth and sixteenth. Fine 

 measurements are more often expressed in 

 hundredths of an inch, and even where the 

 old terms are used in speech they are often 

 written .50 or .125. This change has been 

 made not by scientists, but by machinists 

 and practical men, who have most occasion 

 to use such measurements. 



In weights the same evolution toward 

 the decimal system is noticeable. The ton 

 of 2000 pounds, because it is capable of 

 decimal division, has almost entirely driven 

 out the ton of 2240 pounds. A Western 

 man does not know of the existence of the 

 ' long ton ' except from his arithmetic. The 

 bushel has become in common practice a 

 unit of weight and, being a useless incum- 

 brance, is being displaced by the hundred 

 weight. Measurements of grain and vegeta- 

 bles are taken in pounds and hundreds of 

 pounds, and then, if necessary, reduced to 

 bushels. 



Units of volume apparently have not been 



subjected to decimal division, but it is more 

 customary to speak of ten, one hundred or 

 five hundred quarts or gallons than it is to 

 use other multiples, and receptacles are 

 made to correspond with this custom. In 

 the measurement of area the same is true. 

 Our city streets, blocks and lots are meas- 

 ured in multiples of ten more often than of 

 any other number. 



In the measurement of time, where the 

 laws, not of Nature, but of the Chaldeans, 

 have prevented the use of decimal division, 

 the existing duodecimal division is almost 

 ignored. The division of the hour into 

 halves, quarters and thirds, which appears 

 to Mr. Spencer such a great advantage, is 

 entirely disregarded by railroad men and 

 o a large extent by everybody. ' Ten 

 thirty' and 'nine forty-five' are rapidly 

 superseding the expressions ' half past ten ' 

 and ' a quarter before ten.' We even write 

 5:25 and 9:41.5 as though it were in decimal 

 notation. As for the third of an hour I 

 never heard of its use either in speech or 

 practice. Days are coming to be used in 

 multiples of ten both in business and in 

 ordinary life. We go for a ten-days' trip 

 or give our notes for one hundred days in- 

 stead of using weeks or months. 



In arithmetical operations decimals are 

 being used more and more in the place of 

 vulgar fractions. This is a commercial age 

 and country, and ' the business man' thinks 

 in per cents. He says his health is fifty 

 per cent, better than the day before and he 

 discounts the newspaper twenty-five per 

 cent. ISTotwithstanding the statement of 

 Sir Frederick Bramwell that the decimal 

 system is absolutely incompatible with 

 mental arithmetic, the ordinary man per- 

 sists in using it, and if vulgar fractions are 

 given him to add or subtract he will change 

 them over to decimals before performing 

 the operation and the result back again 

 rather than use them. In some of our best 

 schools children are taught the use of deci- 



