For brevities fake, let M Stand for Movement, whether Watch or Clock. F The Fufie. A The Great VVheel. a The Pinion of Report on the Arbor. E The Second VVheel. e The Pinion on its Axis. I The Contrat VVheel. i The Pinion on its Axis. O The Crown-Wheel, carrying o Its Pinion on its Axis. B The Dial VVheel carrying the Hand in 12 hours. ↑ Turns. N Notches, or Beats of the Ballance. Con. Continuance, and Length in Time of the Watches going. The Work stands both in Letters and Figures, as in the Example. a) B (d 4) 36 (9 e) A (f 5) 55 (II i) E (g 5) 45 (9 17 Crown VVheel Where every Wheel is Divided by the Pinion it moves from, A the Great Wheel, to O the Crown-Wheel, viz. 55, by 5 equal to 11, equal to f5 45 69 5 equal to 8, equal to k- But B divided by a gives 9, that is, B by a, equal to d. WH RULE I Here f 11, g 9, k8, o 17, and 2 Pallats Multiplyed into each other fucceffively, produce 26928 equal to N, the Notches or Beats made in one Turn of the Great VVheel: And 26928 Multiplied by 9, is equal to 242352, the Beats that are made in one turn of the Hand, whether 12 or 24- Laftly, Divide 242352 by 12, it gives 20196, the Beats in one Hour; and 20196 Divided by 60, gives 336.6, the Beats in one Minute. All this is plain enough, and is the foundation of the whole Work, and by it may be eafily found how many Turns any Wheel or Pinion makes for one Turn of the Fufte or Hour-wheel. RULE II. A S the Beats for one Turn of the Great Wheel, or Fufie. 26928 20196 So is the Continuance of the Time of the Watches going 16 ho. 9 of Report. These Thefe Proportions holding, then any Three given (not of the fame kind) you may find a Fourth. As by Example. To know the Continuance of the Watches going, that hath 12 Turns in the Fufie, and 26928 Beats in one Turn, and 20196 Beats in an Hour. Say, As the number of Beats of the Ballance in an Hour ls to the number of Turns in the Fufie, So is 12 Turns of the Fufie To the Continuance of Time of the Watches going. For 20196 26928: 12: 16. But if it be demanded by the Beats, and the Time of the VVatches going, to know the Turns of the Fufie: Then it will be, As 26928: 20196 16 12. Or, if it be demanded what Quotient fhall be laid upon the Pinion of Report. Then say, As 16 12 :: 12: 9 Or, 26928: 20196 Note, That the fewer Beats are taken, the longer fhall be the Continuance of the VVatches going at an Equal Time. RULE III. Concerning PENDULUMS. THE HE Spring in a Watch drawing harder at the first, than at the last: And likewife in Clocks with VVeights and Strings, there is added the weight of the String gotten every moment to the Clock VVeight; and for that no Motion can be Made by hand fo fit, but there will come fome unequalnefs, as you may hear by the Beats either of VVatch or Clock. To juften and regulate thefe inequalities, Monfieur Hugens invented the way of applying Pendulums to either, for which his name will be ever in venerable esteem. Pendulums whofe Vibrations are of the fame Degree and Minute, are Equal, or if they rife not above a Degree; And the Squares of their Vibrations are in proportion to their Lengths: For a Standard or Rule, the aforefaid Monfieur Hugens gives the length of a Pendulum that shall Swing Seconds, to be 881 to the Parisian Feet, 864. The English Feet to Paris Feet, by a Table of Sir Jonas Moors are, As 1000 to 1068, Therefore, As 864 881 :: 1.068: 1089: And 1.089 Multiplyed by 3, is equal to 3.267, i. e. equal to Three Feet, Three Inches, and two Tenths of an Inch. The late Honourable Lord Bruncker, and Mr. Hook, found the Length to be 39 Inches, and .325 Parts, which a little exceedeth the other, and it may be was juftned by Monfieur Hugen's Rule for the Center of Ofcillation: For Montons Pendulum that fhall Vibrate 132 times ina Minute, it will be found likewife 8.1 Inches, agreeing to 39.2 Inches, English: Therefore, for certain, 39.2 Inches may be called, The Univerfa! Measure; and relyed upon to be the neer Length of a Pendulum that shall Swing Seconds every Vibration: With this Caution and Rule. As ་་ As the length of the String from the point of the Sufpenfion to the Centre of a Round-Ball, Is to the Radius ; So is Radius To a Fourth Number. Let two Fifths of that fourth Number, be added to the former Length, for the Length of the Pendulum. Having this Standard. The next RULE is this. THat "Hat the Lengths of two Pendulums, are in Proportion to the Squares of their several Vibrations; which will be equal to the Beats of the Ballance; therefore the Beats that shall be propofed in a Minute being given, to be 50; and it be demanded to give the Length of a Pendulum, The Analogy is, As the Square of 50, viz. 2500 Is to the Square of 60, viz. 3600, So is 39.2 To 56.4, the Length required: For, As 2500 3600 :: 39. 2: 56.4 And if the Length be given, to find the Swings or Beats in a Minutej The Analogy is, As the Altitude given, To the Altitude known, So the quare of the Vibrations known, To the fquare of the Vibrations required, The fquare Root whereof is the Answer. And because the two middle Terms ftand in all fuch Questions, and will be always 141120; therefore divide 141120, by the Square of the Swings in a minute, it gives the length fought: or, by the length, it gives the fquare of the Swings. And thus a Swing may be hang'd by any Clock, upon a Pin, so that it may freely Vibrate to Regulate the fame Clock. 48)--4 (12 56-7 (8 54 6 (9 21 The Numbers of the Great Wheel 56. The great Wheel turning a Pinion of 7, fixt to The Crown VVheel 54,turning a Pinion of 6,fixt to The Ballance wheel 21. The Quotients 8, 9. 21, and 2 Multiplyed into each other, produce 3024, Equal to the Beats in an hour: Becaufe the great wheel turns once in an hour. Other . Otherwife 12, 8, 9, 21, 2, Multiplyed into each other, produce 36288.-12) 36288 (3024, and 60) 3024 (50.4 Beats in a Minute: And (as was thewed before) the Length of the Pendulum will be 55.5 Inches. a Fix a Weight upon a Wyre, running into a Rod, that shall have four Feet 7.5 Inches below the Pin whereon it plays 5 and about a Foot (or above) a Wyre beaten flat, with feveral holes to fit to the Top of this Rod; and to a Pin placed upon the Ballance towards the backfide, will regulate the Motion exceeding well.. For the Regulating the inequality of a Swing, when it may rise sometimes high, fometimes lower: There are two ways, either by making the Line play betwixt two Cheeks of a Cycloid, as Monieur Hugens hath directed, which may easily be effected to any Length of the Pendulum: Or elfe, by not fuffering the Pendulum to Vibrate above an Inch from its fettlement. Monfieur Hugens in his Book of Pendulum Clocks, proposeth aVVatch about a Mans height to go 30 Hours, and to have thefe Numbers. D B 6―――72 a 30-30 a. a 80-8-(10 E 48 8-(6 The Great Wheel 80, &c. which turns about in an Hour, and fhews Minutes; therefore for an Hour, Multiply the Quotients 10, 6, 2, 15, 2, and they will produce 3600, the Seconds in an Hour (60 in 60) is equal to 3600, or Beats. Now the Third Wheel I turn about in one Minute, for 10 in 6 is equal to 60, and carries a Plate divided into 60 Seconds, and fhews the Seconds: And upon the Arbor of the Great Wheel, is fixed a Wheel, a, turning another Wheel, both of 30 Teeth; and both turning about in an Hour; the latter has on it a Pinion of 6 Teeth, turning B 72 in 12 Hours. This Watch bath a Pully tyed to its Weight, by which you may pull it up, and not ftop the Watch. The Pendulum plays between two Cheeks, part of a Cycloid. The next Queftion (fuppofing there be a Screw below, or above the Pendulum, to lift it up, or let it down upon a Square Brafs Rule, divided into Inches and Tenth Parts) to know how many Minutes and Seconds every Tenth Part of an Inch will make the Watch go fafter or flower in a Day. I take the Pendulum which fwings Seconds, whofe length is 39.2, And then by the Logarithms I make the following Table. The first Column in the Table, has in the Middle the Length of the Pendulum 39.2 Inches: Upwards it diminisheth one Tenth, and downwards increaseth one Tenth. The Second Column, are the Logarithms of the First. The Third Column, are half of the Logarithms of the difference of the II. taken out of the Logarithm 5.149588, which is, of the standing Number 141120 aforesaid. The Fourth Column are the Numbers anfwering to the Logarithms in the III. The Fifth Column are the Minutes and Seconds that those Augmentations or Diminishings will caufe in a Day; and are obtained by Multiplying 24 in 60, which makes 1920 equal to the Minutes in one Day, by the Decimals above or under 60". which work may be easily done, any length of a Pendulum. for RULE IV. of finding out fit Numbers for the Wheels and Pinions. 1. ANY two Fractions whofe Terms are proportional perform the fame Motion; The upper for the Wheel, The lower for the Pinion. 2. If it be, As one Wheel, to one Pinion, So is the Product of many Wheels, 1 To the Product of many Pinions: And both will perform the fame Motion. 1 Example |