Is this then inadvertency? or is it uncandid nationality? I hope, the former.
A further remark on the utility of this System as a first motion, may be of use in this place. It respects the geering of the fixed and moveable wheels A B, and F, on the perfection of which depends the truth of the statement, that the stud, a, describes a diameter of the large wheel. Now, perfection is too much to be expected from common teeth when of the necessary strength; so that my Patent Geering is an indispensable complement to this Invention: as by its use, the principle is made practically true; this line becoming really straight, and this motion, under proper circumstances, being unattended with noise or commotion. In a word, I cannot move a step in this mechanical field, without meeting with instances where the new System shews its superiority to the old: whence it becomes a duty for me to commence the consideration of this subject in the very next part of this publication.
OF
A SYSTEM OF CONCENTRIC PULLEYS,
Already known as White’s Patent Pulleys.
These Pulleys have been frequently described since I first entered my specification at the Patent Office. The Authors of the Encyclopedia Britannica; the Rev. Mr. Joyce, in his juvenile philosophy; and Dr. Gregory in his mechanics, have all adverted to them. In the latter work, I find the following quotation from my own description, thus introduced:
A very considerable improvement in the construction of pulleys has been made by Mr. James White, who obtained a Patent for his Invention, of which he gives the following description: “Fig. 4, Plate 7, of this work, shews the Machine, consisting of two pullies, Q and R; the former fixed, the other moveable. Each of these has six concentric grooves, capable of having a line put round them, and thus of acting like as many different pulleys having diameters equal to those of the grooves. Supposing then, each groove to be a distinct pulley, and that all these diameters were equal, it is evident, that if the weight 144 were to be raised by pulling at S, till the pulleys touched each other, the first pulley must receive the length of line as many times as there are parts of the line hanging between it and the lower pulley. In the present case there are 12 lines, b, d, f, &c. hanging between the two pulleys, formed by its revolution about the six upper and six lower grooves. Hence as much line must pass over the uppermost pulley as is equal to 12 times the distance of the two. But, from an inspection of the figure, it is plain that the second pulley R S, cannot receive the full quantity of line by as much as is equal to the distance betwixt it and the first. In like manner, the third pulley receives less than the first, by as much as is equal to the distance between the first and the third; and so on to the last which receives only 1⁄12 of the whole: for this receives it’s share of line n, from a fixed point in the upper frame which gives it nothing: while all the others in the same frame receive the line partly by moving to meet it, and partly by the line coming to meet them.”
“Supposing now these pulleys to be equal in size, and to move freely as the line determines them, it appears from the nature of the system, that the number of their revolutions, and consequently their velocities, must be in proportion to the number of suspending parts, that are between the fixed point above-mentioned, (n) and each pulley respectively. Thus the outermost pulley would go twelve times round in the time that the pulley under which the part n of the line passes, (if equal to it) would revolve only once; and the intermediate times and velocities would be a series of arithmetical proportionals of which, if the first term were l, the last would always be equal to the whole number of terms. Since then, the revolutions of equal and distinct pulleys are measured by their velocities, and that it is possible to find any proportion of velocity on a single body running on a centre, viz. by finding proportional distances from that centre; it follows, that if the diameters of certain grooves in the same body be exactly adapted to the above series, (the line itself being supposed inelastic and of no magnitude) the necessity of using several pulleys in each frame will be obviated, and with that some of the inconveniences to which the use of the common pulley is liable.”
“In the figure referred to the coils of rope, by which the weight is supported, are represented by the lines a, b, c, &c. a is the line of traction commonly called the fall, which passes over and under the proper grooves, until it is fastened to the upper frame just above n. In practice, however, the grooves are not arithmetical proportionals; nor can they be so, for the diameter of the rope employed must be deducted from each term, without which, the small grooves to which the said diameter bears a greater proportion than to the larger ones, will tend to rise and fall faster than the latter, and thus introduce worse defects than those which they were intended to obviate.”
“The principal advantage of this kind of pulley is, that it destroys lateral friction, and that kind of shaking motion which are so inconvenient in the common pulley; and lest, says Mr. White, (I quote Dr. Gregory) this circumstance (of a long pin) should give the idea of weakness, I would observe, that to have pins for pulleys to run upon, is not the only, nor perhaps the best method: but that I sometimes use centres fixed in the pulleys, and revolving on a short bearing in the side of the frame, by which strength is increased, and friction much diminished: for to the last moment of duration, the motion of the pulley is circular, and this very circumstance is the cause of it’s not wearing out in the centre as soon as it would, assisted by the ever increasing irregularities of a gullied bearing.—These pullies when well executed, apply to Jacks and other Machines of that nature with great advantage: both as to the time of their going and their own durability: and it is possible to produce a System of pulleys of this kind, composed of six or eight parts only, and adapted to the pocket, which by means of a skain of sewing silk, would raise more than a hundred weight.”
There are several real and solid advantages attending the use of this pulley; some of which are only hinted at in this description. I have thought, therefore, it might be useful to introduce here an account of some trials which the System underwent a few years ago at Portsmouth—at the request of an Officer of the Navy, who had re-invented it with some ingenious additions to my ideas. Not being at present in correspondence with that Gentleman, I hardly think myself at liberty to mention his name; but fully so to give an extract from the report which followed these experiments—in which the superiority of the System in respect of power, is made evident, although some less favourable circumstances prevented its adoption on that occasion.
“With a view to comparison, it was settled with Lieutenant S. that his blocks should be made to correspond with the treble and double 16 inch blocks of a 24 gun ship, which carry a 41⁄2 inch rope. The sheeves in the new blocks are fixed upon the pin, revolving therewith, and are of different diameters proportioned to the velocity of the parts of the rope that pass over them; they are also reeved with a double rope so that there are two grooves of each size, the diameter of the smallest groove in this tackle being 28⁄12, and of the largest 15 inches. The diameter of the sheeves of the common blocks would have been (as usually made) 91⁄8 to the bottom of the grooves, but were reduced at the request of Lieutenant S. in the treble block to 81⁄8, and in the double block to 87⁄8, in order that the sum of the diameters of the sheeves in each tackle should be the same. The Lieutenant intending in the first instance, to have used a roller under the pin, for the purpose of diminishing friction, but afterwards laying aside this idea on account of it’s complication, was the reason that he had not made his sheeves in the same proportion with the common blocks: the weight and length of the respective blocks are as follows:
| Weight. | Length. | |
|---|---|---|
| Lieutenant S.’s |
treble blocks
|