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A Treatise on Mechanics

Chapter 24: FOOTNOTES:
By Henry Kater
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Science - Physics

About This Book

The treatise presents a systematic exposition of classical mechanics, beginning with the sensory basis for understanding matter and defining fundamental properties such as magnitude, impenetrability, and force. It develops principles of statics and dynamics through logical argument and mathematical demonstration, treating equilibrium, motion, and the mechanical behavior of bodies and machines; it explains methods of measurement, comparison, and generalization, and illustrates principles with worked examples and experiments. Emphasis is placed on clear definitions, stepwise deduction, and practical application to common mechanical problems.

FOOTNOTES:

1 More exactly through 161/12 feet, or 193 inches.

2 This ratio is that of 31,416 to 10,000 very nearly.

3 Lardner on the Steam-Engine, Steam-Navigation, Roads, and Railways. 8th edition. 1851.

4 From the Greek words tachos speed, and metron measure.

5 Theatrum Machinarum, tom. ii. pl. 36. fig. 3.

6 In a strictly mathematical sense, the path of the point P is a curve, and not a straight line; but in the play given to it in its application to the steam-engine, it moves through a part only of its entire locus, and this part extending equally on each side of a point of inflection, the radius of curvature is infinite, so that in practice the deviation from a straight line, when proper proportions are observed in the rods, is imperceptible.

7 The variation produced in the height of the column of mercury (supposed to be 61/2 inches high) by an alteration of ± 16° in the temperature will be only ±  1/100 of an inch, or in other words,  1/100 of an inch will be the total variation from its mean state, by an alteration of 32° in the temperature. It is therefore probable that, in most cases of moderate alteration in the temperature, the centre only of the column of mercury is subject to elevation and depression, whilst the exterior parts remain attached to the sides of the glass vessel. It was with a view to obviate this inconvenience that Henry Browne, Esq. of Portland Place (I believe) first suggested the piece of floating glass.