# Rudimentary mechanics

### Popular passages

Page 172 - It is better, on this account, in graduating the bottle, to make two scratches as represented in the drawing, one at the top and the other at the bottom of the curve : this prevents any future mistake.
Page 7 - If two forces be represented, in magnitude and direction, by the sides of a parallelogram, an equivalent force will be represented, in magnitude and direction, by its diagonal.
Page 26 - The evolutions of the performer are found to be facilitated by holding in his hand a heavy pole. His security in this case depends, not on the centre of gravity of his body, but on that of his body and the pole taken together. This point is near the centre of the pole, so that, in fact, he may be said to hold in his hands the point on the position of which the facility of his feats depends. Without the aid of the pole the centre of gravity would be within the trunk of the body, and its position could...
Page 80 - ... There is, therefore, a practical limit to the increase of the power, and that degree of sharpness only is to be given to the tool which is consistent with the strength requisite for the purpose to which it is to be applied. In tools intended for cutting wood, the angle is generally about 30°. For iron it is from 50° to 60° ; and for brass, from 80° to 90°.
Page 146 - Kepler found that the periodic times of any two planets (te the times occupied in revolving round their whole orbits) are proportional to the square roots of the cubes of the longest diameters of those orbits ; or, as it is commonly stated, " the squares of the times are as the cubes of the mean distances ;" for it will be observed that the mean distance of a planet from the sun is half the major axis (or longest diameter) of its orbit, for it comes to its greatest and least distances at the two...
Page 68 - No. 2 revolves twice, No. 3 three times, and so on ; thereby producing an enormous inequality in the wear of the axles. 68. To remedy these defects, it was suggested, that if the wheels were made to differ in size in proportion to the quantity of rope which must pass over them, they would revolve in the same time, and might therefore be all fixed on the same axis, and would require no divisions between the different sheaves of the same block. For this purpose, the sheaves would require to have their...
Page 167 - That particles of fluid, on escaping from an orifice, possess the same velocity as if they had fallen freely in vacua from a height equal to that of the fluid surface above the centre of the orifice.
Page 123 - I allude to my time-measurer, the precision of which is so great, and such that it will give the exact quantity of hours, minutes, seconds, and even thirds, if their recurrence could be counted ; and its constancy is such that two, four, or six such instruments will go on together so equably that one will not differ from another so much as the beat of a pulse, not only in an hour, but even in a day or a month.
Page 39 - ... be compounded of the ratios subsisting between the arms of each lever ; or, in other words, the power multiplied by the continued product of the alternate arms commencing from the power, is equal to the weight multiplied by the continued product of the alternate arms, beginning from the weight. For example, in the following arrangement (Fig. 23) we have three levers, two of the F'g- 23. second kind, AF, A...