the weight of a cubical block of stone, one of whose edges is 4 feet, its specific gravity being 2.5. Ans. 10000 lbs.

2. Required the number of cubic feet in a body whose weight is 1000 lbs., its specific gravity being 1.25.

Ans. 12.8.

3. Two lumps of metal weigh respectively 3 lbs., and 1 lb., and their specific gravities are 5 and 9. What will be the specific gravity of an alloy formed by melting them together, supposing no contraction of volume to take place.

Ans. 7.3 4. A body weighing 20 grains has a specific gravity of 2.5. Required its loss of weight in water. Ans. 8 grains.

5. A body weighs 25 grains in water, and 40 grains in a liquid whose specific gravity is .7. What is the weight of the body in vacuum? Ans. 75 grains.

6. A NICHOLSON's hydrometer weighs 250 grains, and it requires an additional weight of 726 grains to sink it to the notch in the stem, in a mixture of alcohol and water. What is the specific gravity of the mixture? Ans. .781.

7. A block of wood is found to sink in distilled water till of its volume is submerged. What is its specific gravity? Ans. .8825.

weight of

8. The weight of a piece of cork in air, is oz.; the weight of a piece of lead in water, is 64 oz.; the the cork and lead together in water, is 4 oz. the specific gravity of the cork?

What is Ans. 0.24.

9. A solid, whose weight is 250 grains, weighs in water,

147 grains, and, in another fluid, 120 grains. specific gravity of the latter fluid?

What is the

Ans. 1.262.

10. A solid weighs 60 grains in air, 40 in water, and 30 in an acid. What is the specific gravity of the acid?

Ans. 15.

The following table of the specific gravity of some of the most important solid and fluid bodies, is compiled from a table given in the Ordnance Manual.

172. A thermometer is an instrument used for measuring the temperatures of bodies. It is found, by observation, that almost all bodies expand when heated, and contract when cooled, so that, other things being equal, they always occupy the same volumes at the same temperatures. It is also found that different bodies expand and contract in a different ratio for the same increments of temperature. As a general rule, liquids expand much more rapidly than solids, and gases much more rapidly than liquids. The construction of the thermometer depends upon this principle of unequal expansibility of different bodies. A great variety of combinations have been used in the construction of ther

mometers, only one of which, the common mercurial thermometer, will be described.

1212

The mercurial thermometer consists of a cylindrical or spherical bulb A, at the upper extremity of which, is a narrow tube of uniform bore, hermetically sealed at its upper end. The bulb and tube are nearly filled with mercury, and the whole is attached to a frame, on which is a scale for determining the temperature, which is indicated by the rise and fall of the mercury in the tube.

0 32

Fig. 151.

The tube should be of uniform bore throughout, and, when this is the case, it is found that the relative expansion of the mercury and glass is very nearly uniform for constant increments of temperature. A thermometer may be constructed and graduated as follows: A tube of uniform bore is selected, and upon one extremity a bulb is blown, which may be cylindrical or spherical; the former shape is, on many accounts, the preferable one. At the other extremity, a conical-shaped funnel is blown open at the top. The funnel is filled with mercury, which should be of the purest quality, and the whole being held vertical, the heat of a spirit-lamp is applied to the bulb, which expanding the air contained in it, forces a portion in bubbles up through the mercury in the funnel. The instrument is next allowed to cool, when a portion of mercury is forced down the capillary tube into the bulb. By a repetition of this process, the entire bulb may be filled with mercury, as well as the tube itself. Heat is then applied to the bulb, until the mercury is made to boil; and, on being cooled down to a little above the highest temperature which it is desired to measure, the top of the tube is melted off by means of a jet of flame, urged by a blow-pipe, and the whole is hermetically sealed. The instrument, thus prepared, is attached to a frame, and graduated as follows:

The instrument is plunged into a bath of melting ice, and, after being allowed to remain a sufficient time for the

parts of the instrument to take the uniform temperature of the melting ice, the height of the mercury in the tube is marked on the scale. This gives the freezing point of the scale. The instrument is next plunged into a bath of boiling water, and allowed to remain long enough for all of the parts to acquire the temperature of the water and steam. The height of the mercury is then marked on the scale. This gives the boiling point of the scale. The freezing and boiling points having been determined, the intermediate. space is divided into a certain number of equal parts, according to the scale adopted, and the graduation is then continued, both upwards and downwards, to any desired extent. Three principal scales are used. FAHRENHEIT'S scale, in which the space between the freezing and boiling point is divided into 180 equal parts, called degrees, the freezing point being marked 32°, and the boiling point 212°. In this scale, the 0 point is 32 degrees below the freezing point. The Centigrade scale,i n which the space between the fixed points is divided into 100 equal parts, called degrees. The 0 of this scale is at the freezing point. REAUMUR'S scale, in which the same space is divided into 80 equal parts, called degrees. The 0 of this scale also is at the freezing point.

If we denote the number of degrees on the Fahrenheit, Centigrade, and Reaumur scales, by F, C, and R respectively, the following formula will enable us to pass from any one of these scales to any other:

The scale most in use in this country is FAHRENHEIT'S The other two are much used in Europe, particularly the Centigrade scale.

Velocity of a liquid flowing through a small orifice.

173.

Let ABD represent a vessel, having a very small orifice at its bottom, and filled with any liquid.

B

Denote the area of the orifice, by a, and its depth below the upper surface, by h. Let D represent an infinitely small layer of the liquid situated at the orifice, and denote its height, by h'. This layer is (Art. 155) urged downwards by a force equal to the weight of a column of the liquid whose base is equal to the orifice, and whose height is h; denoting this pressure, by p, and the weight of a unit of volume of the liquid, by w, we shall have,

p=wah.

Fig. 152.

If the element is pressed downwards by its own weight alone, this pressure being denoted by p', we have,

p' = wah'.

Dividing the former equation by the latter, member by member, we have,

that is, the pressures are to each other as the heights h and h'.

Were the element to fall through the small height h', under the action of the pressure p', or its own weight, the velocity generated would (Art. 115) be given by the equation,

v' = √2gh'.

Denoting the velocity actually generated whilst the element is falling throught the height h', by v, and recol lecting that the velocities generated in falling through a