In the above examples, illustrating the determination of chemical equivalents, the elements named combine with each other in one proportion only. We have, however, frequently mentioned, that two elements are often capable of combining with each other in more than one proportion, and it is in the study of such compounds, that the third law of combination is developed.

7. Law 3rd.— When one body combines with another in several proportions, the quantities of the second body, contained in the different compounds, bear to each other a very simple ratio.

In a very large number of cases, the proportions of the second body are simple multiples of the quantity contained in the first compound: thus, in the compounds of nitrogen with oxygen it is found that

Here the quantities of oxygen in combination with nitrogen are to each other as 1, 2, 3, 4, &c. In other cases, the ratio is as 1, 1, 2, &c. Thus the combinations of manganese with oxygen take place according to

this ratio:

protoxide.
sesquioxide.
peroxide.

manganic acid.

permanganic acid. affects not only

binary, but also secondary, ternary, and quarternary

compounds, thus: —

:

8. The combining proportions of secondary, ternary, and quarternary compounds are expressed in the fourth law of combination, which may be thus announced :Law 4th. The equivalent number of a compound is equal to the sum of the equivalent numbers of its constituents.

Thus the combining proportion of water, which is 9, is found by adding together the equivalents of its elements, 1 and 8. The equivalent of quicklime is 28, because it consists of 1 equivalent of calcium (20), and 1 equivalent of oxygen (8). And, for the same reason, the combining proportion of hydrate of lime is 37, which is the sum of the equivalents of its constituents, lime 28 and water 9.

9. The remarkable facts, expressed by the third and fourth laws of combination, have received a very simple and beautiful explanation in the so-called atomic theory, which, together with the laws of combination, was developed principally by the intellectual genius of Dalton. According to this theory, all bodies are made up of a number of exceedingly small particles, termed atoms, which are absolutely indivisible by any force we can apply to them; the particles of different kinds of matter possess different weights, and probably also different sizes, and it is the relative weights of these atoms which express the combining proportions of the substances they compose. The atoms of hydrogen are, therefore, the lightest of all known atoms, inasmuch as hydrogen has the smallest equivalent number; those of oxygen are eight times heavier; those of nitrogen fourteen times heavier, &c. Taking this view of the constitution of matter, it is easy to see why substances unite chemically in definite proportions only, and also why, when more compounds than one are formed by the same element, such compounds must stand in a very simple relation to each other. Thus, when nitrogen unites with oxygen, the first compound consists of fourteen parts or one atom of nitrogen, and eight parts or one atom of oxygen; the second compound contains one atom or fourteen parts of nitrogen, and two atoms or sixteen parts of oxygen; the third contains three atoms or twenty-four parts, by weight, of oxygen, and so on. In the compounds of manganese with oxygen this theory also clearly illustrates the cause of the numerical relations of the two elements: thus, the first oxide of manganese contains one atom of manganese, and one atom of oxygen; the second, two atoms of manganese and

three atoms of oxygen; the third, one atom of manganese and two atoms of oxygen; the fourth, one atom of manganese and three atoms of oxygen; and the fifth, two atoms of manganese and seven atoms of oxygen. It must therefore follow that, in the first oxide, 27.72 parts, by weight, of manganese are united with 8 parts of oxygen; in the second, twice 27.72 = 55·44 parts of manganese, with three times 8 = 24 parts of oxygen; in the third, 27.72 parts of manganese, with twice 8 = 16 parts of oxygen; in the fourth, 27-72 parts of manganese, with three times 8 = 24 parts of oxygen; and in the fifth, twice 27.7255.44 parts of manganese are combined with seven times 856 parts of oxygen. Thus the laws of combination are beautifully elucidated by this theory, the very simplicity of which is strong evidence of its truth; nevertheless, it must be borne in mind, that the laws of combination rest upon incontrovertible facts, and, as regards their soundness, are altogether unconnected with any theoretical considerations whatever.

10. We have hitherto considered only the relative weights in which bodies combine chemically, but if we also examine into the volumes in which those substances unite, which either exist as gases, or can be converted into vapours, we find even a still more simple relation amongst these combining volumes. If we take equivalent quantities by weight of hydrogen, nitrogen, chlorine, iodine, and bromine, and compare the volumes which these elements occupy in the gaseous condition, underthe same temperature and pressure, we find that such equivalent weights of these elements occupy exactly the same volume: thus 1 grain of hydrogen, 14 grains of nitrogen, and 35-47 grains of chlorine, occupy precisely the same space. Again, equal volumes of oxygen and the vapours of phosphorus and arsenic, contain equivalent weights of these elements; although the volumes are only one-half of those just given: if, for instance, a certain volume of oxygen weighs 8 grains, then the same volume of phosphorus and arsenic vapour will weigh, respectively, 32 and 75 grains. It hence follows that when these bodies unite chemically, they do

so in volumes which bear a very simple relation to each other thus two volumes of hydrogen and one volume of oxygen unite to form water; two volumes of nitrogen and one volume of oxygen form nitrous oxide; two volumes of nitrogen and two volumes of oxygen form binoxide of nitrogen; two volumes of nitrogen and three of oxygen hyponitrous acid; two of nitrogen and four of oxygen, nitrous acid; and two of nitrogen and five of oxygen form nitric acid. The same simple relation of combining volumes also holds good in the union of compounds.

11. These laws, relative to the atomic combination of substances, render still more evident the great advantages of symbolical nomenclature, which is made the means of conveying to the mind, not only the qualitative composition of chemical compounds, but also their quantitative constitution. Thus the symbol HO, not only signifies a compound of hydrogen and oxygen, but it likewise indicates, that that compound consists of one part by weight of hydrogen and eight parts by weight of oxygen; whilst HO,, in the same manner, signifies a compound of one part of hydrogen and sixteen parts of oxygen. Symbolical nomenclature, therefore, furnishes an exact and simple mode of expressing the law of multiple proportions.-EDWARD FRANKLAND,

DIRECTION AND AMOUNT OF FORCES.

1. WE have already seen that the whole purpose of machinery is to regulate the action of a force, by altering either its direction or the velocity it produces. The object of the present chapter is to show how this end is accomplished in a number of simple machines, in order that we may be better able to trace hereafter the mode of action of more complicated contrivances. Previous to

this, however, we must make a few remarks upon the direction and amount of forces, and the manner in which these can be represented.

2. The tendency of any single force acting upon a body is to produce motion in a straight line; and the line of direction in which the motion would result if allowed to take place is called the direction of the force.

It is true that we scarcely ever see a body in motion under the influence of only a single force, because the natural forces, and particularly gravitation, are in incessant operation, in addition to any force that man may apply; we have, therefore, few opportunities for observing what the effect of one force would be. Still in the descent of a falling body under the exhausted receiver of an air-pump, we have a perfect instance of rectilinear motion; and a round ball rolled over a smooth even surface, though acted upon by gravity, the resistance of the air and friction, in addition to the impulse given to it by the hand, moves in the direction of the impelling force. The shape, size, and weight of the body acted upon also materially influence its motion, so that, for greater simplicity, we shall at present suppose the body to be represented by its centre of gravity alone, or by a material point, and afterwards consider how its mass and form are to be taken into account.

3. The straight line which indicates the direction of a force may be made to represent its relative amount, compared with any standard we assume as a unit. Thus, suppose we agree that a length, equal to one-tenth of an inch, shall stand as an arbitrary symbol for the force able to raise one pound to a height of one foot, then two-tenths of an inch will stand for a force of double this amount, three-tenths for one three times as great, &c. We thus find that by means of a scale forces can be geometrically exhibited, in direction and general amount, by straight lines. This fact we shall find of the greatest use in our inquiries.

Further, having our line of direction, we may mark off the length representing the amount of force, anywhere in this line that suits our convenience in considering a problem. The length of a rope, for instance, can make