Of the mensuration of running waters an excellent piece written in Italian by Don Benedetto Castelli ... ; Englished from the third and best edition ; with the addition of a second book not before extant / by Thomas Salusbury.

PROPOS. III. PROBLEME II.

A Chanel of Water being given whose breadth exceeds not twenty Palms, or thereabouts, and whose quick height is less than five Palms, to measure the quantity of the Water that runneth thorow the Chanel in a time given.

PLace in the Chanel a Regulator, and observe the quick height in the said Regulator; then let the water be turned away from the Chanel by a Chanellet of three or four Palms in breadth, or thereabouts: And that being done, measure the quantity of the water which passeth thorow the said Chanellet, as hath been taught in the second Proposition; and at the same time observe exactly how much the quick height shall be abated in the greater Chanel, by means of the diversion of the Chanel∣let; and all these particulars being performed, multiply the quick height of the greater Chanel into it self, and likewise multiply into it self the lesser height of the said bigger Chanel, and the lesser square being taken, from the greater, the remainder shall have the same proportion to the whole greater square, as the wa∣ter of the Chanellet diverted, hath to the water of the bigger Chanel: And because the water of the Chanellet is known by the Method laid down in the first Theorem, and the terms of the Theorem being also known, the quantity of the water which run∣neth thorow the bigger Chanel, shall be also known by the Gol∣den Rule, which was that that was desired to be known. We will explain the whole business by an example.

Let a Chanel be, for example, 15 Palms broad, its quick height before its diversion by the Chanellet shall be supposed to be 24 inches; but after the diversion, let the quick height of the Chanel be onely 22 inches. Therefore the greater height to the lesser, is as the number 11. to 12. But the square of 11. is 121, and the square of 12. is 144, the difference between the said lesser

square and the greater is 23. Therefore the diverted water, is to the whole water, as 23. to 144: which is well near as 1 to 6 6/23: and that is the proportion that the quantity of the water which runneth through the Chanellet shall have, to all the water that runneth thorow the great Chanel. Now if we should finde by the Rule mentioned above in the first Proposition, that the quantity of the water that runneth through the Chanellet, is v. g. an hundred Barrels, in the space of 15 second minutes of an hour, it is manifest, that the water which runneth through the great Chanel in the said time of 35 min. sec. shall be about 600 Barrels.

The same operation performed another way.

ANd because very often in applying the Theory to Practice it happeneth, that all the necessary particulars in the The∣ory cannot so easily be put in execution; therefore we will here add another way of performing the same Problem, if it should chance to happen that the Chanellet could not commodiously be diverted from the great Chanel, but that it were easier for the water of another smaller Chanel to be brought into the greater Chanel; which water of the smaller Chanel might be easily mea∣sured, as hath been shewen in the first Probleme; or in case that there did fall into a greater Chanel, a lesser Chanel that might be diverted and measured. Therefore I say in the first case, If we would measure the quantity of the water that runneth in a certain time thorow the greater Chanel, into which another lesser Chanel that is measurable may be brought, we must first exactly measure the Chanellet, and then observe the quick height of the greater Chanel, before the introduction of the lesser; and having brought in the said Chanellet, we must agnin find the propor∣tion that the water of the Chanellet hath to all the water of the great Chanel; for these terms of the proportion being known, as also the quantity of the water of the Chanellet, we shall also come to know the quantity of the water that runneth thorow the great Chanel. It is likewise manifest, that we shall obtain our intent, if the case were that there entered into the great Chanel, another lesser Chanel that was measurable, and that might be diverted.