the axis, and move freely on a strong polished wire, supported by two short arms, projecting a little from two upright pieces about three feet in length, in order that the descending weights may proceed without interruption beyond the edge of the table.

Six equal weights were attached to as many threads, and each pair of threads was passed in opposite directions round the different portions of three pullies. The first pulley was so formed that its large portion was to its smaller as 3 to 2, the second was in the ratio of 5 to 2, and the third as 4 to 1; and the three weights, of which the threads were coiled round the smaller part of each pulley, being suffered to rise at the same instant, the middle weight rose evidently much faster than either of the others. Dr. Young however remarked that the greatest velocity would not in all cases be practically desirable, on account of the injury that the machinery would sustain from the shock in stopping it.

VOL. II. SECOND SERIES.

H

Sub

Substance of an Essay lately published respecting the Con struction, Hanging, and Fastening of Gates and Wickets, &c. with Supplementary Improvements. Communicated by the Author THOMAS N. PARKER, Esq. M. A. With a Plate.

"Studium quibus arva tueri." Virg. Georg. I. 21.

ON the Principles here laid down, a Gate is eon

sidered as a lever of the second kind; and when suspended by hooks or pivots precisely perpendicular to each other, it will be at rest wherever it may be placed: but by the smallest variation of the hooks from their perpendicular position (provided it be sufficient to overcome the friction) a gate will acquire one determinate line of rest, and an opposite line of equilibrium; and consequently, from any part of a circle which a gate so suspended may be made to describe, it must have a constant tendency to fall to that line of rest.

When a gate is in its line of rest, or opposite line of equilibrium, the hooks and the centre of the gate's gravitation will be in one and the same vertical plane; and when the hooks are perpendicular to each other, it can admit of no doubt, that they must be in the same vertical plane with the centre of the gate's gravitation, because they will be so with any third given point what

soever..

The requisite velocity for the fall of a gate which opens but one way, is obtained by an extra length of the lower thimble, or more properly, by the horizontal distance of two perpendicular lines, one falling from the centre of each of the hooks or pivots upon which a gate is suspended; and the proportion is not to be determined so much

by

by the length and weight of the gate, as from the distance of two hinges from each other: about a quarter of an inch must also be added to the extra length of the lower thimble for what is lost in the hanging of the gate, exclusive of the perpendicular difference of the two pivots *.

A gate nine feet long should rise at the head in opening, about six inches, by which it will acquire a sufficient tendency to fall to its line of rest; and supposing the hinges to be 40 inches asunder, it follows, that as the length of the gate is to the difference between the height of the head of the gate when in its natural line of rest, and the height of the head of the gate at its greatest elevation, or opposite line of equilibrium; so will be the distance of the two hooks to double the clear extra length of the lower thimble: that is, reducing it to inches, as 108:6:: 40: 2t: therefore, this extra length of the lower thim

* The velocity given to the gate's fall by the extra length of the lower thimble, is calculated for such hinges as are rounded off and well finished; it being now ascertained " that the smallest surface will have the least friction." See Mr. Vince's Experiments on the Motion of Bodies affected by Friction." Vol. LXXV. Philos. Transac. of Royal Society of London.

↑ As it will scarcely be possible in common practice, to be more exact in hanging a gate than to a twelfth part of an inch, I have omitted all greater fractions; that is, the integer of one inch will in no case be divided into more than 12 parts, which I propose to make a general denominator for all broken numbers.

And it may not be amiss to observe in this place, that the compound nature of a gate's motion, which proceeds necessarily from the position of its hinges, or the two centres of its suspension, with respect to each other, cannot readily be defined with an accuracy perfectly mathematical: but it will be found capable nevertheless of plain and satisfactory explanation, abundantly near enough to the truth for every practical purpose