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[[circled number in page corner: 120]]
The Principle on which Mr. Harrison forms the alterations of the third sort is, that the longer vibrations of a balance moved by the same spring, are performed in less time. This is contrary to the received opinion among Philosophers and Workmen. But if Mr. Harrison is right, yet whether the method he has proposed will correct the errors, or not, is to me quite uncertain. 

The last alteration before-mentioned is ingenious and useful; but that it can be made to answer exactly to the different degrees of heat, seems impossible. 

From the Cambridge Journal for Sept. 21st 1765 WILLIAM LUDLAM. 

[[Margin note: Advantages arising from a new position of the fusee in [[strikethrough]] a [[/strikethrough]] common matches. By M.Le ROY. Gents Mag. for Aug.[[st]] 1766. p. 369.]]

  The size and number of teeth of the wheels, and of the leaves of the pinions, are not the sole objects which require our attention in such machines as consist of toothed wheels, and especially in clockwork; besides which, there is another very simple principle, which it is surprizing it should not have hitherto been considered, though perhaps as necessary as any other, to the perfection of those machines.
  This principle is the position of wheels and pinions upon their arbor, at an equal distance as far as possible, the utility whereof may be thus explained.

[[margin note: Pivots [[gull]] their holes]] [[second margin note: V. Thilos. Trans. No. 112 Vol. 1. p.465. of Lowthorp's Abridgment]]
 
  The several wheels which compose a machine, are designed to transmit from one to another, the force which the first of them received from the [[strikethrough]] other [[/strikethrough]] moving power. The pivots receive a [[strikethrough]] considerable [[/strikethrough]] constant pressure towards one certain side of the hole, in which they turn round; from whence necessarily ensues a tendency in them, to wear, enlarge, and gully the hole on that side which they rub against, and that when they have once begun to wear it, the cavity is very quickly enlarged, because the surface of the hole becoming irregular, occasions a greater resistance, and a greater friction. 
  Every wheel of a watch is fixed upon an arbor, which terminates in two pivots, and these turn in holes drilled in the plates of the watch. Each arbor is charged [[strikethrough]] with [[/strikethrough]] both with a wheel and pinion; and it is the pinion which receives the action of the immediate preceding wheel, and transmits it to the wheel fixed on its own arbor.

[[margin note: A Problem.]]

  Now at what place of the length of the arbor ought the wheel and pinion to be fixed? This has every been thought quite indifferent, however it is certain it cannot be so; and as it commonly falls out, that when we act at hazard, we make a bad choise, or at least, not the best; just so has it happened on this occasion, and the usual arrangement or caliber, in this respect, carries with it several inconveniences which could not escape the penetration & enquiries of M. [[underline]]le Roy [[/underline]]