[21]: Strictly speaking, this is only true when the divergence of the rods from the spindle is not very great, and, in practice, this divergence is never sufficient to render the above assertion untrue. This property of the conical pendulum arises from the circumstance of the centrifugal force, in this instance, varying as the radius of the circle in which the balls are moved; and when this is the case, as is well known, the periodic time is constant. The time of one revolution of the balls is equal to twice the time in which either ball, as a common pendulum, would vibrate on the centre, and as all its vibrations, though the arcs be unequal, are equal in time, provided those arcs be small, so also is the periodic time of the revolving ball invariable. These observations, however, only apply when the balls settle themselves steadily into a circular motion; for while they are ascending they describe a spiral curve with double curvature, and the period will vary. This takes place during the momentary changes in the velocity of the engine.
[22]: Mr. Brunton used moveable bars in a furnace constructed by him before he adopted the horizontal revolving grate. That plan, however, does not appear to have been as successful as the latter, as he has abandoned it. Mr. Oldham states that his furnace has been in use for several years without any appearance of derangement in the mechanism, and with a considerable saving of fuel.
[23]: It is strange that this absurdity has been repeatedly given as unquestionable fact in various encyclopædias on the article "Steam Engine," as well as in by far the greater number of treatises expressly on the subject.
[24]: Some of the preceding observations on inland transport, as well as other parts of the present chapter, appeared in articles written by me in the Edinburgh Review for October, 1832, and October, 1834.
[25]: Wood on Railroads, 2d edit.
[26]: Mr. Booth received a part of the premium of 500l., but has not participated in any degree in the profits of the manufacture of the engines.
[27]: Mr. Robert Stephenson, whose experience and skill in the construction of locomotives attaches great importance to this condition. It has lately, however, been abandoned by some other engine-makers, for the purpose of getting rid of the cranked axle which must accompany it.
[28]: The estimate commonly adopted by engineers at present is 9 pounds per ton. I have no doubt, however, that this is too high. I am now (November, 1835,) engaged in an extensive course of experiments on different railways, with a view to determine with precision this and other points connected with the full developement of their theory; and I have reason to believe, from the observations I have already made, that even 7-1/2 pounds per ton is above the average force of traction upon the level.
[29]: A contrivance might be applied in changes of level in railroads somewhat similar to locks in a canal. The train might be rolled upon a platform which might be raised by machinery; and thus at the change of level there would be as it were steps from one level to another, up which the loads would be lifted by any power applied to work the machinery. The advantage in this case would be, that the trains might be adapted to work always upon a level.
[30]: On the occasion of races held at Newton, a place about 15 miles from Liverpool, two engines were sent, with trains of carriages, to take back to Liverpool the visitors to the races. Some accident prevented one of the engines from working on the occasion, and both trains were attached to the same engine: 800 persons were on this occasion drawn by the single engine to Liverpool in the space of about an hour.