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THis Chapter I design for the use of such, as would convert old Bal∣lance Clocks into Pendulums, or would make any old work serve for the tryal of new motions, or would apply it to any other such like use.
§ 1. To do this, you may draw a Scheme of your old work: and so you will see what Quotients you have, and what you will want. To do all which, there are sufficient instructions in the pre∣ceding Chapter. A few instances will make all plain.
§ 2. Let us chuse for instance an old Ballance clock to be turned into a Pendu∣lum of 6 inches. The old work is, The Great-wheel 56, the Pinion 7; the next Wheel 54, the Pinion 6; the Crown-wheel 19, &c. The Scheme * 1.1 of this work is in the Margin. The Quotients and Crown-wheel and 2 Pallets multiplied together continually, produce 2736, which are the Strokes of the Ballance, in one turn of the Great-wheel, by Sect. l. § 4, 5. of the last Chapter. And by the Quotient of the Dial-wheel (which is 12) it appears, that the Great-wheel goeth round once in an hour. Or you may find the Beats in an hour, by § 5. last cited. Having thus found the Beats in an hour, of the old work, you must next find the Beats in an hour, of a 6 inches Pendulum; which you may do by
* 1.2 Chap. 5. § 4. following; or by Mr. Smith's Tables, according to whom the number is▪ 9368. Divide this by 2736, and you have the Quotient, which * 1.3 is to be added to the Scheme of the old work. This Quotient is 3 and near ½▪ as you see in the Margin.
The work thus altered, will * 1.4stand as you see in the Mar∣gin, viz. a Pinion 6, and a Contrate-wheel 21, must be added.
According to this way, the old work will stand as before, only the Crown-wheel must be inverted.
§ 3. But because the Crown-wheel is too big for the Contrate-wheel (which is unseemly) therefore it will be best, ▪to make both the Contrate, and Crown-wheels new; and encrease the number of the Contrate-wheel, but diminish that of the Crown-wheel. To do which, pitch upon some convenient number for the Crown-wheel. Multiply all the Quoti∣ents, and this new Crown-wheel number, as before; and divide 9368 by it. As,
Suppose you pitch upon 11 for the Crown-wheel: if you multiply 8, 9 and 11▪ the Product is 792; which multiplied by the 2 Pallets, makes 1584, which are the Beats in one turn of the Great-wheel, or * 1.5in an hour. Divide 9368 by it, and you have near 6 for the Quotient * 1.6 of your Contrate-wheel. The work thus ordered, will stand as in the Margin.
If you would correct your work, to find the true num∣ber of Beats in an hour, &c. you must proceed, as is shewn Sect. 2. § 6, and latter end of § 7. of the last Chapter.
§ 4. But suppose you have a mind to change the former old Watch, into a 30 hour piece, and to retain the old Ballance-wheel (which may be often done:) in this case, you must add a Contrate-wheel, and alter the Pinion of report. For the Contrate-wheel, chuse such a Quotient, as will best suit with the rest of your work; and then multiply all your Quo∣tients, Crown-wheel and •• Pallets toge∣ther, and so find the number of turns in the Great-wheel, as before. Then say by
Sect. 2. § 6. part 5. before, As the Beats in one turn of the Great-wheel, To the Beats in an hour:: So are the hours of the Dial, To the quotient of the Pinion of Report.
Thus in the old work before; to the old quotients 8 and 9, you may add ano∣ther of 8, for the Contrate-wheel. Those multiplied, as was now directed, make 21888, for the Beats in one turn of the Great-wheel. And then for the quotient of the Pinion of Report, say in numbers thus, 21888. 9368:: 12. 5. * 1.7 The quotient for the Pinion of Report is somewhat more than 5, which overplus may be neg∣lected, as you see by the Scheme of the whole work in the Mar∣gin.
If you desire to know what number of turns, the Fusy must have in this work; Say by the last quoted §▪ part 1, in numbers thus, 21888. 9368:: 30. 13 almost. So that near 13 turns will do.
If you would correct your work, to know the exact Beats, &c. you are refer∣red to directions in the end of the last pa∣ragraph.
§ 5. I shall add but one thing more, to what hath been said in this Chapter, and that is, to change the Striking part of this old Movement, into a 30 hour piece.
A Scheme of the old * 1.8 work is in the Margin.
And to alter it, the best way is, to double the number of Striking pins, making the 8, sixteen pins: and the Hoop of the Detent-wheel double, that the Pin-wheel may strike two strokes, in its going round once.
The greatest inconvenience here, will be to bridle the rapidity of the Strokes; because a quotient of (2 only, added to the old work, will be sufficient for this purpose: which being an inconvenient number, 'twill be necessary to be content with the old numbers, or make more Wheels and Pinions new, than may be thought worth the while.
If you would find what number of turns, the Fusy will require; you must find how many Strokes are in 30 hours, by Sect. 3. § 2. R. 6. before. These are 195; which divided by the 16 Pins,
gives somewhat more than 12 turns of the Fusy.
Lastly, for the Pinion of Report, you must pursue the directions in the last quo∣ted place, R. 5.
The work thus altered, * 1.9 will stand as in the Mar∣gin.
Horol. Dis. p. 54.
V. Sect. 1▪ § 6.