This section is from the book "Turning And Mechanical Manipulation", by Charles Holtzapffel. Also available from Amazon: Turning and Mechanical Manipulation.

Quantities expressed decimally would be more easily written down, and more exactly defined than the compound fractions such as 3/4 and 1/14 of an inch - or than the still more obscure method, of 3/4 of an inch full or bare as the case might be, which latter nearly sets all attempts at exactness in defiance

The smaller aliquot fractions of the inch such as the 1/20 1/22 1/24 1/26 1/28 1/30 etc., of an inch, although in themselves very precise, do not from their nature, so readily admit of definition or comparison, as the quantities 2. 3. 4. 5. 6. 7. 8. 9. or 10 hundredths of an inch; because, in the vulgar fractions every one has a specific relation to the inch, whereas the decimal terms have one general relation, decimals being sometimes considered as the numerators of fractions, all having the constant denominator unity, or 100, 1000, Ac.: and therefore the latter, or the decimal terms, constitute a simple arithmetical series, or one in which the intervals are alike, but this is not the case with vulgar fractions.

It would bring all foreign measures within reach of our workshops. For example, in the United States of America, and Russia, English measure is employed, and no-difficulty would be felt in reference to these countries. And as most of the National Foot measures, are more than 11 inches English, and leas than 13, even if they are considered for the time as equal to our own foot, and without any adjustment being attempted, the average error would not exceed about five per cent. And further, when two of Holtzapffel and Co.'s engine-divided scales, the one of the particular foreign measure, and the other of English inches, are laid side by side, they show visually, as on a slide rule, the correspondence between any quantity of such foreign measure with our own, as more fully explained in the author's pamphlet "On a New System of Scales of Equal Parts," in which this and numerous other employments of scales of equal parte are treated at length.

The decimal scheme would allow the exact weight in every superficial foot of sheet metals and other substances to be readily arrived at - Thus, as a cubic foot of water weighs 1000 ounces troy, the specific gravities of lead, copper, silver, etc., denote at the same time how many troy ounces are severally contained in one cubic-foot of the same The specific gravity divided by 1200, gives the Weight of a plate or film, the one hundredth of an inch thick, and thence a table may be readily computed, fry addition alone, to show the weight of plates of any thickness in troy ounces.

These calculations would bo correct at once for gold and silver, as these metals are estimated by troy weight; but for other substances requiring avoirdupois weight, the numbers expressing the specific gravities of the substances must bo previously altered by one of the usual methods, namely, either by multiplying them by 192, and dividing the product by 175, numbers which represent the ratio between troy and avoirdupois ounces; or else instead thereof, the specific gravities of substances may be multiplied by the decimal constant usually employed for effecting the same end.

In this method also, constant multipliers may be readily found for thus determining from the specific gravities of the several materials, the exact thicknesses of plates or sheets of the same, which shall precisely weigh one ounce or one pound, either troy or avoirdupois as may be required. This has already been done by Mr. Hay ward as regards crown glass; for assuming its specific gravity to be 2 52, when the glass is of the thickness of .1525, (or one tenth and a half nearly.) it weighs 32 avoirdupois ounces to the superficial foot, and thence by Mr. Hay ward's calculation are obtained the following numbers - the first line denotes the weight of crown glass in ounces, in every superficial foot, the second line the corresponding thicknesses in thousandths of the inch, ranging from about 5 to 152 thousandths -

Crown glass of | 1 | 2 | 4 | 8 | 12 | 16 | 20 | 24 | 28 | 32 | ounces. | |

Measures | •00476 | •0095 | •019 | 038 | •0571 | •0762 | •0952 | •1333 | •1429 | •1524 | inch. |

The above and the intermediate terms are sometimes engraved on Messrs. Chater & Hay ward's gages, alongside of the line of graduations which denotes thousandths: and at other times, instead of the weight per foot are engraved divisions indicative of the 8th, 9th, 10th, 11th, 12th, etc. of the inch; which quantities are of course obtained by simply dividing 1000 by those respective numbers.

Tables might, in the above manner, be very readily computed, that would show the weights in every superficial foot of the metals and other materials for all defined thicknesses; and also other tables for showing how thick the metals should be, in order to weigh exactly so many ounces to the superficial foot These matters could be also arrived at by the employment of scales of equal parts, laid down in the proportions of the specific gravities of the substances; and in the opinion of the author they could be worked out with even greater simplicity and universality, by a decimal proportional instrument he has some time since contrived, which is applicable to the visual development of all ratios that have reference to decimal arithmetic, including those of interest, discount, profit, and other calculations to which the term Per Cent. is applied.

In conclusion, the author begs to add that he does not suggest any alteration whatever, as regards those measures for which the division of the foot-rule into eighths and sixteenths may be found sufficiently precise and minute. But he would ask whether for more minute measurements, greater convenience and distinctiveness would not result, from the general employment of measures expressed in hundredths of the inch, than from the employment of the many gages for specific uses, the sizes and numbers of which are entirely devoid of system, and which gages may be considered as unknown beyond the particular trades in which they are employed.

How confusing would it be, if the measures by which broad cloths, linens, cottons, silks, velvets, carpets, and other textile fabrics, are manufactured and sold, were all different instead of being uniformly the yard measure; and yet this incongruity fully applies to the various articles whose measurements are described under the mystical names of Number, Size, Gage, and other appellations, which assume different values in different branches of manufacturing art; as for example, in the various kinds of sheet metals, various kinds of wires, in tubes, joiners' screws, and vast numbers of small manufactured articles, the various sixes of which are arbitrarily designated at Nos. 1. 2. 8. 4. etc.

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