QUESTIONS ON CHAPTERS I. AND II.

(1) What are the characteristic differences between a Fluid and a Solid?

(2) If a Fluid be a 'material body', according to the Definition, how can Steam be a Fluid?

(3) If a 'material body' be compressible, is it necessarily elastic?

(4) Is Water elastic, or inelastic?

(5) If "Fluids press equally in all directions", does this mean, that a Fluid, acted on only by the Force of Gravity, will press upwards as well as downwards?

(6) In Prop. II. the pressure of the Atmosphere on the surface of the fluid is not taken into account; is the truth of the proposition affected thereby?

(7) Pressure is always the result of force; what then is the force supposed to be acting in Prop. II.?

(8) If the pressure be different at different points of a fluid at rest, how can it be of uniform density'?

(9) Is it assumed in Prop. III. that the fluid is of uniform density? If so, where?

(10) What forces are supposed to act on the fluid in Prop. I.? (11) What is meant by the 'surface' of a fluid in Props. II., and III.?

(12) In Prop. IV., the pressure of the atmosphere on the surface of the fluid is not reckoned; will not that greatly affect the pressure on the bottom of the vessel?

(13) How can the pressure on the bottom of a vessel filled with fluid, and acted on only by the force of gravity, be greater than the whole weight of the fluid?

(14) Bramah's press, used by packers and others, is constructed on the principle explained in Prop. v.; what are the practical limits to its power?

(15) Why is it necessary, that the fluid used in the Hydrostatic Paradox, and in Bramah's press, should be non-elastic?

(16) If the floating body in Prop. vi. were wholly immersed, and at rest when left to itself, would Prop. vI. hold true?

(17) If a vessel be quite filled with fluid, and a solid body be put into it, which floats, and “displaces as much of the fluid as is equal in weight to the weight of itself", will the solid body increaso the pressure on the bottom of the vessel, or not?

CHAPTER III.

SPECIFIC GRAVITIES.

68. THE BULK, or VOLUME, or CONTENT, or MAGNITUDE, of any body is measured by the number of times it contains that of some other body previously fixed upon as a standard of magnitude, or unit.

A cube, whose edge is an inch in length, is called “a cubic inch”. In the following pages a cubic inch will be taken for the unit of solid measurement; so that when it is said, that M is the bulk, volume, content, or magnitude, of a body, it is meant that the number of cubic inches in the body is the number of units in M.

69. Definition of SPECIFIC GRAVITY.

The SPECIFIC GRAVITY of any substance is the weight of a unit of its magnitude, or volume.

If, as stated in the last Article, the magnitude of a body be measured by the number of cubic inches it contains, and the weight of one cubic inch be given in grains, then it will follow, that, S being taken to represent the Specific Gravity of any substance, S is the number of grains that one cubic inch of that substance weighs.

The Tables, which are called "TABLES OF SPECIFIC GRAVITIES", give the Ratios which the weights of bulks of various substances bear to equal bulks of water. In other words, they give the number of times that the weight of any bulk of each of the substances contains the weight of an equal bulk of water.

:

It having been found by experiment that the weight of a piece of Iron the weight of a bulk of Water of the same size :: 7·8 : 1, and that the weight of a piece of Silver: weight of an equal bulk of Water: 105: 1, and so for other substances, Tables have been formed, in which the numbers 1, 78, 105, &c., are placed opposite the words, "Water", "Iron", "Silver", &c. By means of these Tables (as will be shewn), the weight of any bulk of any of the substances so registered can be determined, if the weight be known of some particular bulk of any one of them.

The numbers given in these Tables are generally called the "Specific Gravities" of the several substances registered; but the

enunciation of Prop. vII. Art. 70 will not permit them to be so called here.

The "TABLES OF SPECIFIC GRAVITIES" give

i. The weights of any two substances, are of equal bulk which are in the ratio of the numbers given by the Tables as corresponding to the substances.

For, w, w', w", being the respective weights of equal bulks of Water and of any two substances, as Iron and Silver, since, as explained above,

w': w:: 78: 1, and ww" :: 1 : 105;

therefore, compounding these proportions,

w: w" :: 78: 105.

So that, if it be required, for example,

ii. To find the weight of a cubic foot of Iron, having given that the weight of 10 cubic inches of Silver is 61 ounces nearly—

Weight of a cubic foot (or 12×12×12 cubic inches) of Silver

70. PROP. VII. If M be the Magnitude of a body, S its Specific Gravity, and W its Weight, W= MS.

Suppose the unit of the measurement of magnitude to be a cubic inch; then

M= number of cubic inches in the body.

And the Specific Gravity (S) is the weight of one cubic inch;

..the whole weight of the body = M×S,

or, W= MS.

71. To find the relation which exists between the Weights, Magnitudes, and Specific Gravities, of two substances and of a compound formed of them.

Let W, M,S, W', M',S', W", M", S", be the Weight, Magnitude, and Specific Gravity, of each of the two substances, and of the compound, respectively..

Then, it being supposed that the portions of the substances which are combined together lose neither bulk nor weight by being mixed,

i. M" = M + M',

ii. W" = W +W';

.. by Art. 70, iii. M"S", or (M+M')S" =MS+M'S'.

And it might be shewn, that similar relations exist between the Weights, Magnitudes, and Specific Gravities, of the several substances and the compound formed of them, whatever be the number of the simple substances.

72. COR. Let σ, o', o", be the numbers which are attached to the names of the two simple substances and the compound, respectively, in the "Tables of Specific Gravities", the S. G. (specific gravity) of water being 1.

But S': S: weight of a cubic inch of the second substance

: weight of a cubic inch of the first substance,

COR. In like manner, if W, W', W", be the weights, in pounds, of the two substances and their compound, respectively, it may be proved, that

73. PROP. VIII. When When a body of uniform density floats on a fluid, the part immersed the whole body :: the specific gravity of the body the specific gravity of the fluid.

Let a body of uniform density float on a fluid with M cubic inches of it above, and N cubic inches below, the horizontal plane of the fluid's surface.

Let S S. G. (Specific Gravity) of the solid; S'S. G. of the fluid.

M

N

Then, (M+N)×S= weight of the solid by Prop. VII., fluid displaced.

NxS' =

But because the body floats, these two weights are equal, by Prop. VI.;

.. NS' = (M+N)S; and ..

N S
M+N ‍S'

or N: M+N:: S: S';

that is, the part immersed: the whole body

S. G. of the body: S. G. of the fluid.

74. PROP. IX. When a body is immersed in a fluid, the weight lost whole weight of the body: the specific gravity of the fluid: the specific gravity of the body.

Let M be the number of cubic inches in a body of uniform density, which is wholly immersed in

a fluid; S the S. G. of the body, S' the S. G. of the fluid.

Then the pressure downwards of the solid is its weight; and if the solid be removed, and the space it filled be occupied by an equal

M