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Notes on Book III. 3 POSTSCRIPT by way of Notes on Book III. re. lating to the Rifing of Water in Pumps. T O compleat this Colledion of Hy- draulicks, I add, by way of Poft- fcript, an Obfervation which I have long made concerning the Practitio ners in the Art of Pump-work, who dif fer very largely from each other in their Opinion, relating to the proper Length or Fall of Piftons in Pumps ; thofe who are for making the Stroke long, viz. 3, 4, or 5 Foot, or fometimes more, urge the Ne- cefiity there is to force up large Quantities of Water to great Heights, and fay, that if there is not fuch a Thruft, the Water will recede backwards again, and not rife up with that Uniformity which is requifite in Works that go continually; but others are of a different Opinion, and, amongft them, Mr. New/ham of Cloth-Fair tells us in his printed Propofals, That what is got in Purchafe is loft in Timt; and indeed I cannot but be of the fame Opinion as this laborious Engineer is of, and think, that where there are 3 or 4 Leavers con- ffantlyat Work, there is no Occalion for long Strokes, unlefs it be where there is only a fingle Pifton, as is in the York~ Buildings Engine; and there indeed a 6 Foot Stroke is neceffary, in order to the giving the Water in the Pipes its full Force. Mariotte, Page 105. of his Hy draft a- ticks (Englifh Edition) makes ufe of an Algebraical Calculation for the railing of Water in the following Manner. Sup- pofe, (fays he) the Barrel to be 11 Foot above the Surface of the Water, that you would raife ; and fuppofe that you have a mind to raife it to this Height of 12 Foot by one Stroke of the Pifton, you mull make this Analogy : As 10, the Complement of 12 Foot, is to 32 ; fo is 12 Foot of common Air to a 4th Proportional; this 4th Proportio nal will be 19 y, which lhews that the Barrel of the Pump mult be pretty long to raife the Pifton 19 Foot -< above the 12 Foot, in order to raife the Water 12 Foot, by only one Stroke of the Pifton; but if the Play or Stroke of the Pifton were li mited to 2 Foot, you muft fay; As 32—A, is to 32, fo is 12—-A to 14—-A. The lirftTerm is the Complement of the un known Height to which the Water will rife, to 32 Foot of Water ; which is the Weight of the Atmofphcre : The third Term is the 12 Foot minus that Height,, and the Fourth is the 2 Foot that the Pifton rifes, join’d to 12 Foot minus the fame Height. Now the ProduCt of 14— A,, by 3 2 — A, is 448 — 45 A -}- A A, and the Product of the two middle Terms is 584. —. 32 A ; the Equation being reduc’d,, there will be an Equality betwixt A A and 14 A — <?4; and becaufe 64 cannot be taken fron 49 the Square of 7, which is half the Roots, ’tis a Sign, that in con tinuing to pump, at feveral times you may raife the Water up to the Pifton ; and to know how far it will rife the firft Stroke, you muft fttppofe that the Pifton is rifen 2 Foot; there will be an uniform Barrel of 14 Foot; and according to the Rules laid down in his Eflay upon Logick, and his Treatife of the Nature of Air, which makes this Calculation. The enclos’d Air was 12 Foot; 12 Foot -f- A is to A, as 3 2 to 2 — A; the Equation being reduc’d, you will rind that A A will be equal to 24 — 42 A; and at laft, that the Value of the Root will be a little lefs than f which being taken from 2, there will re main 1 f and a little more; and confe- quently the Water will by the firft Stroke of the Pifton rife but one Foot f, and a little more. If you had fuppos’d the Play of the Pifton to be one Foot, you might know by the fame Calculation how high the Wa ter would rife by the firft Stroke of the Pifton ; and if you would know to what "Height it may rife after feveral Strokes, you muft fay, As 32 — A is to 32,. fo ia —. A is to 13 — A; the Equation being reduc’d, you will find 13 3* e( )ual 4 to A