the quantities of the two ingredients H and L, in the compound c. And so for any other demand.

PROPOSITION LVIII.

To find the Specific Gravity of a Body.

288. CASE 1.-When the body is heavier than water: weigh it both in water and out of water, and take the difference, which will be the weight lost in water. Then, by corol. 6, prop. 57, s= where B is the weight of the body

B

BW

out of water, b its weight in water, s its specific gravity, and w the specific gravity of water. That is,

As the weight lost in water,

Is to the whole or absolute weight,
So is the specific gravity of water,
To the specific gravity of the body.

EXAMPLE. If a piece of stone weigh 10lb, but in water only 631b, required its specific gravity, that of water being 1000?

Ans. 3077..

289. CASE II.-When the body is lighter than water, so that it will not sink: annex to it a piece of another body, heavier than water, so that the mass compounded of the two may sink together. Weigh the denser body and the compound mass, separately, both in water, and out of it; then find how much each loses in water, by subtracting its weight in water from its weight in air; and substract the less of these remainders from the greater. Then say, by proportion,

As the last remainder,

Is to the weight of the light body in air,
So is the specific gravity of water,

To the specific gravity of the body.

That is, the specific gravity is = by cor. 6, prop. 57.

(c

LW

c) (H - b)'

EXAMPLE. Suppose a piece of elm weighs 15lb in air; and that a piece of copper, which weighs 181b in air and 16lb in water, is affixed to it, and that the compound weighs 6lb in water; required the specific gravity of the elm?

Ans. 600.

290. CASE III.-For a fluid of any sort.-Take a piece of a body of known specific gravity; weigh it both in and out

of

of the fluid, finding the loss of weight by taking the difference of the two; then say,

As the whole or absolute weight,

Is to the loss of weight,

So is the specific gravity of the solid,
To the specific gravity of the fluid.

That is, the spec. grav. w =

EXAMPLE.

A piece of cast iron weighed 35, ounces in a fluid, and 40 ounces out of it; of what specific gravity is that fluid?

Ans. 1000.

PROPOSITION LIX."

291. To find the Quantities of Tavo Ingredients in a Given

Compound.

TAKE the three differences of every pair of the three specific gravities, namely, the specific gravities of the compound and each ingredient; and multiply each specific gravity by the difference of the other two. Then say, by proportion,

As the greatest product,

Is to the whole weight of the compound,
So is each of the other two products,
To the weights of the two ingredients.

EXAMPLE. A composition of 112lb being made of tin and copper, whose specific gravity is found to be $784; required the quantity of each ingredient, the specific gravity of tin being 7320, and that of copper 9000?

Answer, there is 100lb of copper, in the composition. and consequently 12lb of tin,

SCHOLIUM.

292. The specific gravities of several sorts of matter, as found from experiments, are expressed by the numbers annexed to their names in the following Table :

A Table

293. Note. The several sorts of wood are supposed to be dry. Also, as a cubic foot of water weighs just 1000 ounces avoirdupois, the numbers in this table express, not only the specific gravities of the several bodies, but also the weight of a cubic foot of each, in avoirdupois ounces; and therefore, by proportion, the weight of any other quantity, or the quantity of any other weight, may be known, as in the next two propositions.

PROPOSITION LX.

294. To find the Magnitude of any Body, from its Weight.

As the tabular specific gravity of the body,
Is to its weight in avoirdupois ounces,
So is one cubic foot, or 1728 cubic inches,
To its content in feet, or inches, respectively.

Example 1. Required the content of an irregular block of

common stone, which weighs lcwt, or 112lb?

Ans. 12282016 cubic inches.

Example 2. How many cubic inches of gunpowder are

there in 1 lb. weight?

Ans. 29 cubic inches nearly.
Example 3.

Example 3. How many cubic feet are there in a ton weight Ans. 381 cubic feet.

of dry oak?

PROPOSITION LXI,

295. To find the Weight of a Body from its Magnitude.

As one cubic foot, or 1728 cubic inches,

Is to the content of the body,

So is its tabular specific gravity,

To the weight of the body.

Example 1. Required the weight of a block of marble, whose length is 63 feet, and breadth and thickness each 12 feet; being the dimensions of one of the stones in the walls of Balbeck?

Ans. 683 ton, which is nearly equal to the burden of an East-India ship.

Example 2. What is the weight of 1 pint, ale measure, of gunpowder ? Ans. 19 oz. nearly. Example 3. What is the weight of a block of dry oak, which measures 10 feet in length, 3 feet broad, and 21⁄2 feet deep or thick? Ans. 43351 lb.

OF HYDRAULICS.

296. HYDRAULICS is the science which treats of the motion of fluids, and the forces with which they act upon bodies.

PROPOSITION LXII.

297. If a Fluid Run through a Canal or River, or Pipe of various Widths, always filling it; the Velocity of the Fuid in different Parts of it, AB, CD, will be reciprocally as the Transverse Sections in those Parts.

THAT is, veloc. at A: veloc. at C: CD AB; where AB and CD denote, not the diameters at A and B, but the areas or sections there.

B

D

For, as the channel is always equally full, the quantity of water running through AB is equal to the quantity running through CD, in the same time; that is, the column through

AB

AB is equal to the column through CD, in the same time; or AB X length of its column = CD x length of its column; therefore AB CD :: length of column through CD length of column through AB. But the uniform ve

locity of the water, is as the space run over, or length of the columns; therefore AB CD :: velocity through CD: velocity through AB.

298. Corol. Hence, by observing the velocity at any place AB, the quantity of water discharged in a second, or any other time, will be found, namely, by multiplying the section AB by the velocity there.

But if the channel be not a close pipe or tunnel, kept always full, but an open canal or river; then the velocity in all parts of the section will not be the same, because the velocity towards the bottom and sides will be diminished by the friction against the bed or channel; and therefore a medium among the three ought to be taken. So, if the velocity at the top be 100 feet per minute, that at the bottom

and that at the sides

60

50

3) 210 sum;

dividing their sum by 3, gives 70 for the mean velocity, which is to be multiplied by the section, to give the quantity discharged in a minutę.

PROPOSITION LXIII.

299. The Velocity with which a Fluid Runs out by a Hole in the Bottom or Side of a Vessel, is Equal to that which is Generated by Gravity through the Height of the Water above the Hole; that is, the Velocity of a Heavy Body acquired by Falling freely through the Height AB.

DIVIDE the altitude AB into a great number of very small parts, each being 1, their number a, or a the altitude AB,

AL

B

Now, by prop. 54, the pressure of the fluid against the hole B, by which the. motion is generated, is equal to the weight of the column of fluid above it, that is the column whose height is AB or a, and base the area of the hole B. pressure on the hole, or small part of the fluid 1, is to its weight, or the natural force of gravity, as a to 1. But, by art. 28, the velocities generated in the same body in any

Therefore the