smaller towards the poles; the meridians, on the contrary, are all of equal size. The circle NES W N represents a meridian or circle of longitude. The fourth part of this circle, or, what is the same thing, the fourth part of the circumference of our earth, as N E, is the basis of the French system. This quaddrant was divided into ten million parts, one of which was taken as the unit, under the name of metre. A metre is about 393 inches in length. The smaller measures are produced by dividing by ten, and are designated by Latin prefixes ; Fig. 3. the larger ones by multiplying by ten, and are designated by Greek prefixes. The system of weights was derived from the measure of length, in the following manner. A cubical box was taken, measuring exactly one centimetre in each direction, and this was filled with water at its greatest density (at the temperature 40° F.) (4° C.); the weight of this quantity of water was called a gramme. This is taken as the unit of the decimal weights, and is multiplied or divided by ten. Centigramme = '01 or Hectogramme Myriagramme = 10,000 One gramme is equal to 15.432349 grs. Troy. It is well enough known that the body whose weight is to be ascertained must be put into one scale, and in the other, weights sufficient to restore the index to its original perpendicular position. The weight of a body thus determined is, in scientific language, called its absolute weight. Thus, a piece of sugar weighing two ounces has an absolute weight of two ounces; or, if a vessel be filled with two pounds and one ounce of water, this water has an absolute weight of two pounds and one ounce. Measuring of Liquids and Gases.-The English system for liquids is as follows: 1 gallon of water at 60° Fah. = 277-276 cubic inches, weighs 10 lbs. 70,000 grains. Av. = 1 fluid ounce of water weighs 1 ounce Av. = 437.5 grains. Grains of water are likewise frequently employed as a measure for liquids. 1,000 grain measures = of a gallon. Gases are generally measured in cubic inches. The standard of measure in the French system is the litre, which is the same as one cubic decimetre, or a cube of nearly 4 inches on each side. The same prefixes are used for the fractions and multiples as for the metre and gramme, but it will be seen that the litre is also equal to 1000 cubic centimetres. Cubic centimetres are generally used in chemistry for the measurement both of liquids and gases. As one cubic centimetre of water weighs one gramme, a litre of water weighs 1 kilogramme. It is almost exactly equal to 13 pint. SPECIFIC GRAVITY. Ice floats in water, iron sinks in it, because the former is lighter, the latter heavier, than water. But if we put a piece of ice in spirit it sinks, or if we put a piece of iron upon mercury (quicksilver), it floats; consequently, ice is heavier than spirit, iron lighter than mercury. It also follows that spirit is lighter than water, since it can support less weight, and mercury heavier than water, as it can bear a greater weight. The terms heavier and lighter, in this sense, correspond to what in scientific language is called specifically heavier or specifically lighter, and equal bulks are always to be understood in speaking of the comparative weights of bodies. The expression, ice is lighter than iron, means, therefore, that, taking equal bulks of each, the former weighs less than the latter; and when we say that mercury is heavier than water, we mean that in equal volumes, as a pint, for instance, the mercury has a greater weight than the water. But in absolute weight, no regard is paid to the volume of subtances. In order to ascertain how many times heavier mercury is than water, or iron than ice, it is only necessary to weigh equal volumes or portions of each, and to compare their weights. If, for example, we take five vessels, each of which would contain exactly 100 grains of water, and fill them respectively with spirit, ice, water, iron, and mercury, the following differences in weight will be found: the vessel with spirit would weigh 80 grains; with ice, 90 grains; with water, 100 grains; with iron (if quite pure),780 grains; with mercury, 1350 grains. To facilitate the comparison of the numbers which denote how much greater the specific gravity of one body is than that of another, water has been fixed upon as the standard or unit. Therefore, in the above case, the question is, how much lighter than water are spirit and ice, and how much heavier are iron and mercury? or, in other words, how many times is 100 contained in 80, 90, 780, and 1350? The other numbers, then, are to be divided by 100, the weight of water, and there is found for Spirit,, or, in decimals, 0·80; it is therefore than water. Ice, 90, or, in decimals, 0·90; it is therefore water. 780 lighter lighter than Iron, 188, or, in decimals, 7.80; it is therefore 7 times heavier than water. Mercury, 1350, or, in decimals, 13.50; it is therefore 13 times heavier than water. These numbers represent the specific weights (sp. gr.). Thus, according to calculation, spirit having a specific gravity of 0.80, 80 parts of it would occupy the same space as 100 parts of water; therefore it is only four-fifths as heavy as water, or, what is the same thing, one-fifth lighter than water. The specific gravity of mercury being 13.5, that is, 13 parts of mercury do not take up more space than one part of water; since it is 13 times heavier than water. Determination of Specific Gravity.-Experiment.-To deter mine the specific gravity (the density) of a fluid, a vial is weighed, then filled with water, and again weighed. This gives the weight of the water. Now pour out the water, and refill the vial either with spirit, syrup, lye, beer, or some other liquid, and ascertain by the balance the weight of each. Then divide the weight of each of these fluids by the weight of the water, and the quotient indicates the specific weight. It is very convenient to use a vial made to contain exactly 1000 grains of water, as then, without any calculation, the number of grains which such a vial contains of any liquid expresses its specific weight. Experiment. Weigh a bottle filled with water; then place a half-ounce weight (apothecaries' scale) on the pan which holds the weights, and by the side of the bottle nails enough to adjust the beam. Remove both the nails and the bottle from the pan, and put the nails into the bottle. A bulk of water will be displaced equal to that of the nails; to determine its amount, replace the bottle, after it has been thoroughly wiped on the outside, upon the pan, and remove weights from the other pan until the equipoise is restored. The weights taken away (about 32 grains) form the divisor, and the half-ounce, or 240 grains, the dividend; the quotient, 240 7.5, is the specific gravity of iron, of which the nails were made. 32 The specific gravity of gases is determined by a process which is similar in principle to the above, but is much more difficult. The standard of specific gravity for gases now generally used is hydrogen, which is the lightest gas known. When we say that the specific gravity of oxygen is 16, we mean that it is 16 times heavier than hydrogen. Air is sometimes taken as the standard. It is 14.4 times heavier than hydrogen, so that, knowing the specific gravity of a gas in relation to hydrogen, it is easy to find it in relation to air by dividing by 14.4. Thus the specific gravity of oxygen as compared with air is = 1.1. Experiment. If we have to determine the specific gravity of a piece of iron, or of any other body which cannot be put into a bottle, it must be fastened by a piece of fine thread to the pan of a common balance (Fig. 4, b), the cords of this pan having been previously shortened. Weigh the body first in air, and then in water, immersing it an inch deep. When it is immersed, the opposite pan falls; consequently iron Fig. 4. must be lighter in the water than in the air. If the iron in the air weighed half an ounce, then, in order to restore the equilibrium, it will be necessary, as in the former experiment, to remove from the pan a 32 grains, equal to the weight of the bulk of water displaced by the iron. The loss of weight is the same, whether the water be removed from the vessel or merely displaced within it. This forms the divisor, and 240, the weight of the = iron in the air, the dividend, giving the quotient 240 7.5. Every substance becomes as much lighter in water as the quantity of water displaced weighs; this is a law of nature. If it displaces less water than its weight in the air, it sinks; if more, it floats. Even very heavy bodies can be made to float by increasing their volume; ships are constructed of iron, although it is eight times heavier than water; a tumbler floats upon water, and yet the specific gravity of glass is from three to four times greater than that of water. A thick piece of iron, weighing half an ounce, loses in water nearly one-eighth of its weight; but if it is hammered out into a plate or vessel of such a size that it occupies eight times as much space as before, it then loses its whole weight in water, and will float, sinking just to the brim. If made twice as large, it will displace one ounce of water-consequently twice its own weight; it will then sink to the middle, and can be loaded with half an ounce weight before sinking entirely. Hydrometer or Areometer. The same floating body will sink to a greater or less depth in different liquids-deeper in the lighter ones, and not so deep in those which are denser. This has suggested a very convenient instrument for determining the specific gravity of liquids-the hydrometer, or areometer. This instrument consists of a hollow glass tube, made as represented in Fig. 5. The interior is hollow, and |