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the surface of the cupel, through which it sinks and is lost to view. This fume and the stream of melted matter consist of the lead oxidized by the heat and air, in one case volatilized, in the other vitrified, and in sinking through the cupel it carries down with it the copper or other alloy of the silver. In proportion to the violence of the heat is the density of the fume, the violence with which it is given off, the convexity of the surface of the globule of melted metal, and the rapidity with which the vitrified oxide circulates, (as it is termed,) or falls down the sides of the metal. As the cupellation advances, the melted button becomes rounder, its surface becomes streaky with large bright points of the fused oxide, which move with increased rapidity, till at last the globule, being now freed from all the lead and other alloy, snddenly lightens,-' the last portions of litharge on the surface disappear with great rapidity, showing the melted metal bright with iridescent colours, which directly after becomes opaque, and snddenly appears brilliant, clean, and white, as if a curtain had been withdrawn from it. The operation being now finished, and the silver left pure, the cupel is allowed to cool gradually, till the globule of silver is fixed, after which it is taken out of the cupel while still hot, and when cold accurately weighed. The difference between the globule and the silver at first put in, shows the quantity of alloy, the globule being now perfectly pure silver, if the operation has been well performed."8 Aikin states, that at the Mint two assays are always made of the same mass of metal, and no sensible difference, as ascertained by scales which turn with T^jTjth of a grain troy, between the weight of the two buttons is allowed to pass. If they differ, the assay is repeated. The process is well performed, if the button of silver adheres but slightly to the cupel; if the shape is globular above and below, and not flattened at the margin; if the button be quite clean and brilliant, showing the beautiful white of pure silver, and not in any degree fouled or spotted with any remaining litharge: the surface of the metal must be disposed in scales or lamina?, the effect of sndden crystallization, which gives it a play of light and a striated lustre, very different from that of a perfectly even surface of a white metal, however pure. Examined by a microscope, this striated surface is still more striking; but when any alloy remains in the silver, the surface, although brilliant, appears smooth as if varnished.
In ordinary assays of gold or silver, copper is the alloy usually met with. If the metal be nearly pure, the cupel round the bottom is only stained yellow by the litharge. If copper be present, it leaves a brown grey stain. The other metals except bismuth scarcely penetrate the substance of the cupel, but remain on the edges of its cavity in the form of coloured scoriae, of which iron is black, tin grey, and zinc a dull yellow.
(1) When the whole of the lead separates, the button becms agitated by a rapid movement, by which it is made to turn on its axis. Globules of iron and some other metals under the action of a strong heat behave in a similar manner.
(2) Aikin: ' Chemical Dictionary," our chief authority in this article.
The time required for one assay, from putting the metal into the hot cupel to the lightening or purity of the button, is generally from 15 to 20 minutes, but the time is not of much consequence, as the button is equally pure after a rapid as after a slow cupellation. If the heat be too great, there is danger of error from the volatilization of the silver, but it is desirable to admit as much air into the muffle as possible consistent with a due regard to temperature. It is important also to attend to the gradual cooling of the button, because pure silver in a molten state absorbs oxygen from the air, and in returning to the solid state the whole is again expelled, so that if the cooling be rapid, the silver is spirted out in arborescent shoots, and some minute portions are thus thrown out of the cupel, and the assay is spoilt.
The proportion of lead to the silver to be assayed is also a point of importance. If too little lead be used, the button is very flat, rough at the edges, of a dull colour, with blackish spots, strongly adherent to the cupel and foul with scoria? on and about the button. If an excess of lead be employed, a small portion of the silver will be carried down into the cupel, and thus the sample of silver will be reported a little less pure than it really is. The quantity of lead required for each case of cupellation was formerly estimated by the use of touch-needles, or small slips or bars of metal made with pure silver, alloyed with known proportions of copper in a regularly increasing scries, from the least to the greatest proportion ever required. The silver-to be assayed was then compared with the touch-needles, in colour, tenacity, and other physical characters, and its alloy was estimated by that of the needle which it most resembled. These needles are seldom used now, as an experienced assayer is able to judge of the alloy by the case or difficulty with which it is cut, the colour and grain of a fresh cut surface, the malleability, the change of surface when red-hot, and the general appearance.
The assay of gold is somewhat more complicated than that of silver. If silver be mixed with gold, although the latter be in very small proportion, it becomes a gold assay. Copper or any other base metal mixed with gold may be separated from it by cupellation, but the affinity of copper for gold is so strong as scarcely to be overcome by this method, unless a certain quantity of silver be added. Consequently, a subsequent operation is required to separate the gold from the silver as mixed in the button after cupellation. Gold is frequently alloyed with silver in some foreign coins, and in some kinds of manufacture. The separation of gold from silver is called parting, and is performed with dilute nitric acid, which dissolves the silver and leaves the gold untouched. If, however, the gold be in considerable proportion, it protects the silver from the action of the acid, and the parting is imperfect. In such case it is necessary to add silver, so as to give it a great excess over gold. About 3 parts silver to 1 part gold is the general proportion, and hence the process of parting is also called quartation, the relative proportion of gold being reduced to only one quarter of the mass, but any greater proportion of silver may be parted with equal certainty. As the entire quantity of materials for the assay amounts to only a few grains, and as the intimate mixture of the silver is of great importance, it is usual to cupel them together with lead, so that they may be thoroughly combined into one small neat globule. The process is similar to the cupellation of silver, only a greater heat is required, which may be safely employed, as none of the mixture of gold and silver is lost by volatilization as pure silver is. The copper is worked off along with the litharge, but any minute portion of lead is got rid of by a second fusing. The cold button is then flattened with a hammer, again heated red-hot, and slowly cooled to anneal it and increase its malleability. It is then extended into a small plate, by being passed between rollers of polished steel, and is next rolled up in a loose coil called a cornet. This is put in a glass mattrass called a parting glass, and about twice or thrice its weight of pure dilute nitric acid is poured over it. The whole is slightly warmed, when a portion of the acid begins to decompose, and gives off red fumes of nitrous acid, and in about 15 or 20 minutes the whole of the silver is washed out, leaving the gold still coiled up in a slender brittle mass. The hot acid solution of silver is carefully poured off, and fresh acid, rather stronger, is added and heated for a few minutes, to clear away the remains of the silver. This is decanted off and added to the former solution. The parting glass is then filled with hot distilled water, and as it is of importance, for the sake of accuracy, to get out the cornet without breaking it into fragments, some of which might be lost, this is managed by inverting a small crucible over the top of the parting glass while full of water, snddenly inverting it, when the cornet falls gently down through the water into the crucible. The water is then let off; the crucible is dried and heated to redness in a muffle, when the cornet, which as it left the mattrass was a brown, spongy, brittle mass, shrinks in every direction, becomes firm, regams its metallic lustre, and when fully red-hot has all the appearance of pure gold; it has a beautiful lustre, and is soft and flexible. The gold is accurately weighed, and the process is finished. This weight indicates the absolute quantity of metal in the assayed sample. The difference between the weight of the button after cupellation, (deducting the silver added,) and the finst sample, is the weight of the copper or other base metal in the gold; and the difference between the gold cornet together with the silver added, and the button after cupellation, is the quantity of silver alloyed with the gold. The silver left in solution after parting is usually recovered by immersing in it, when collected in quantity, some bright copper plates, which dissolve, and precipitate the silver in its metallic form.
In the assaying of gold and silver a peculiar set of assay weights is used. The actual quant ity taken for an assay, is from 18 to 36 Troy grains for silver, and from 6 to 12 grains for gold. This is the integer, and whatever its real weight, it is called in England
the assay pound. This imaginary pound is then subdivided into aliquot parts, which differ according to the metal. The silver assay pound is subdivided into 12 ounces, each ounce into 20 pennyweights, and these again into halves. Hence there are 480 reports for silver, this being the number of half pennyweights in the pound, and therefore each nominal half pennyweight weighs ^jth of a troy grain when the entire assay pound is 24 grains.
The report is made according to the proportion of fine metal. Thus the standard silver of the realm is reported by the assayers to be 11 oz. 2 dwt. fine, so that the remainder of the pound consists of 18 dwt. of alloy or copper, or 37 parts silver to 3 of copper. The gold assay pound is subdivided into 24 carats, and each carat into 4 assay grains, and each grain into quarters. Hence there are only 384 separate reports for gold. The standard for gold coin is 22 carats fine, which gives 2 carats alloy. When the gold assay pound or integer is only 6 troy grains, the quarter assay grain only weighs ^th of a troy grain.
Assayers also report gold and silver to be belter or worse than the established standard. Thus gold of 20 carats is reported as worse 2 carats, being that proportion less than the standard of 22 carats. In a mixture of gold and silver, if the quantity of gold exceed that of the silver, it is called gold parting; if the contrary, siher parting. But in silver parting the report is first made on all the fine metal collectively as if for silver alone, so that if 10oz. of fine metal be found, the assaycr reports worse lor. Idict.; that is, 1 oz. 2 dwt. lower than the standard of silver, which is 11 oz. 2 dwt. fine.
When the assay pound is subdivided, as for silver, in the same manner as the troy pound, the lower denominations evidently bear the same relation to caen other, which is useful in transferring the assay reports to real mixtures for use. But the carat subdivision for gold is confined to assaying, but its fractions being aliquot parts of the troy pound, the caleulations for real use are easy. As the troy pound contains 5,760 grs., the carat corresponds to 240 grs. or 10 dwt., the assay grain or fourth of a carat to 60 grs. troy, and the assay quarter grain to 15 grs. troy. To this report the assayer having separated the gold, 4 oz. for example, adds 4 oz. gold in a lb. troy. But in gold parting he takes two equal assay pieces, treats one as a silver assay, and the other as a gold assay, to find the absolute quantity of each metal, after which the report is first made on the gold singly, to which is added the report of the silver separately. Thus if he find 4 oz. of gold, and 3 oz. of silver, he reports worse 14 carats, (2 carats being equivalent to an assay ounce, and consequently the 4oz. of gold equal to 8 carats, which subtracted from 22 carats, the gold standard leaves 14,) to which report he adds fine siher 3 oz. But when the mixed metal contains more than half alloy, it is called metal for gold and siher, and the absolute quantity of each is reported separately.
The assay pound or integer is divided in a different manner in several parts of Europe. Aikin explains the method adopted in France, Germanj and China.
In France a small assay furnace has been invented by Messrs. Aufrye and D'Arcet, which with charcoal fuel can be raised to the proper degree of heat in half an hour.
Assaying now generally inclndes the determination of the quantity of some particular metal in an ore or mixture of the baser metals, such as the determination of the quantity of copper in the ore of that metal, with a view to ascertain the quantity which ought to be produced in smelting, and also, whether it would repay the smelter to work it. An assay may be conducted entirely by the dry way, or merely by heat with the assistance of fluxes; or by the moist way, in which acids or other re-agents are employed. In some cases both methods are used. The best and most elaborate treatise on the subject, is Berlhier's Traile des Essais par la Vote Siche. In two volumes, Paris, 1834. There is also a very good treatise in English, in one volume, partly founded on the above, entitled "Manual of Practical Assaying, intended for the use of Metallurgists, Captains of Mines, and Assayers in General," by Mr. John Mitehell. London, 1846.
ATMOSPHERE. [see Air, Anehometer, &c.]
ATMOSPHERIC RAILWAY. [see Railway.]
ATOM. ATOMIC THEORY. The word atom is derived from the Greek word arof>oi, indivisible. Although matter is capable of being divided to an extent far beyond our powers of conception, yet it is very probable that there is a limit in nature, beyond which it is incapable of further subdivision. Supposing this limit to be attained, the minute particles of matter are then termed atoms; they are incapable of being further divided, and upon this property is founded one of the most beautiful doctrines of moder n chemistry, a doctrine iipon which the precision and consequent advance of this comprehensive science have mainly depended,—namely the Atomic Theory.
In every compound, whether formed artificially or by the hand of nature, the component parts always exist in the same relative quantities. Pure water, at all times and in all places, contains in every 100 parts 11.111 hydrogen, and 88.889 oxygen; marble always contains 56 parts of lime and 44 of carbonic acid, per cent.; common salt always contains 40 parts of sodinm and 60 of chlorine, per cent. If, in forming these substances artificially, any one of the constituents be in excess, combination will still take place, but the excess will bo rejected.
If, instead of considering the composition of the above-named substances by the per centage of their constituents, we take the smaller numbers that will represent their composition, then we say, that 1 atom of hydrogen weighing 1 + 1 atom of oxygen weighing 8 = 1 atom of water weighing 9. Or 1 atom of lime weighing 28 + 1 atom of carbonic acid weighing 22 = 1 atom of carbonate of lime weighing 50. Again, 1 atom of sodinm weighing 24 + 1 atom of chlorine weighing 36 = 1 atom of chloride of sodinm weighing 60. The meaning which is to
be attached to the term weight in these examples, will be explained presently.
Now the atomic theory is based upon the proposition, that matter is capable of being reduced to atoms which do not admit of further division, and that the atoms of one kind of matter, which in the same substance have all the same size and weight, combine with the atoms of a different kind of matter, only in certain invariable ratios. It follows from this, that when two kinds of matter combine to form a compound, they combine atom to atom, for in order to combine chemically, the two bodies must be reduced to their state of greatest division, so that the respective atoms may be free to come within the range of each other's attraction. In such cases, an atom of one kind combines with an atom of the other kind. It cannot combine with half an atom, because no such thing exists, and it cannot combine with two atoms, because its attraction is satisfied with one. The two dissimilar atoms thus combined, now form a single compound atom, which in its turn is incapable of further division, for the very act of division is destruction, as far as the compound is concerned. Hence it will be seen, that, according to this theory, a simple atom is incapable of further division; a compound atom is capable of being divided into two simple atoms, but in such case, the compound ceases to exist. This obvious illustration explains, in a beautiful manner, the immutable nature of compound bodies, as they exist in nature or in art. If, for example, 1 grain weight of one kind of matter, consisting of 100 atoms, were combined with 1 grain weight of another kind of matter, also consisting of 100 atoms, the resulting compound would be homogeneous or of the same nature throughout; a substance would be formed possessing different properties from those of its constituents, and consisting of 100 compound atoms. If, however, to form the same substance, 1 grain or 100 atoms of the one kind of matter were presented to 2 grains or 200 atoms of the other kind of matter, the same compound would be formed, but the excess of 100 grains would be rejected, or be mechanically mixed with the compound.
Now if we suppose matter to be capable of infinite division, that atoms .were in fact divisible, there is no sufficient reason why bodies should not combine in all proportions. The one hundredth of a grain in the above example, ought, in such case, to combine with the half hundredth, or the quarter hundredth, or any other proportional of a grain of the other substance, so as to form an infinite number of compounds, all possessing different properties to each other and to those of their constituents. That bodies do not combine in this indefinite manner, is a strong argument in favour of the atomic theory.
In the above remarks it has been supposed that dissimilar bodies combine only atom to atom. The real fact is, that an atom of one kind of matter may combine not only with 1 atom of another kind of matter, but with 2 atoms, with 3 atoms, or more, producing in each case compounds with distinct properties. Combinations of this kind have been explained on one of two suppositions. 1. Suppose an atom of A to combine with an atom of B, to form a certain compound; in such case, the affinity of A for B may be so far unsatisficd, that an attraction may exist for another atom of B. Should the conditions be favourable for this combination, a second atom will combine with A, producing a compound with new properties; a third atom of B may also combine with A, forming a third distinct compound. 2. Instead of supposing the simple atom A to have a distinct attraction for 1, 2, or 3 atoms of B, we may suppose that the compound atom A + B may exert an attraction for a second atom of B, and form a compound represented by A + 2 B, and that this, in its turn, may attract a third atom of B, forming A + 3 B, and so on.
For example, 32 parts of zinc combine with 8 parts of oxygen, to form 10 parts of oxide of zinc, and the affinity then seems to be satisfied: no further attraction seems to exist between these bodies; but if another portion of oxygen could be absorbed by the zinc, so as to form a second oxide, it would be another 8 parts, neither more nor less, and the deutoxide of zinc would consist of 32 zinc -f- 16 oxygen.
Again, 100 grains of mercury combine with 4 grains of oxygen, so as to form protoxide of mercury. As the combination is atom to atom, it has been supposed, in this, as in other similar cases, that there are as many atoms in 100 grains weight of mercury, as there are atoms in 4 grains weight of oxygen. But in this case, the affinity is not satisfied; an additional quantity of oxygen can be combined with the same quantity of mercury; an atom of mercury nas an attraction for two atoms of oxygen, or 100 grains of mercury will combine with 8 grains of oxygen, and the second oxide contains twice as much oxygen as the first. If a third oxide were to be formed with 100 grains of mercury, it would contain not 9, nor 10, nor 11, but exactly 12 grains of oxygen. Thus molybdenum combines with oxygen in this way, forming three distinct oxides: the first oxide consists of 1 atom of the metal -f- 1 atom of oxygen; the second oxide contains one atom of the metal + 2 atoms of oxygen; and the third consists of 1 atom of the metal + 3 atoms of oxygen.
In these, and all such examples, it is of no consequence which of the combining substances be taken as the constant quantity; 100 of A may unite with 50 of B, or with twice as much, namely 100, or with thrice as much, namely 150; or, what is the same thing, 100 of B, may unite with 200 of A, or with half as much, or one third as much, for it will be observed, that the multiple ratio affects one kind of matter as much as it affects the other.
Gaseous bodies, which have a chemical action on each other, also unite in the same definite manner. For example, the proportions of oxygen that combine with any quantity of nitrogen to form compounds, will be to each other as the numbers 1, 2, 3, i, 5, and never to any intermediate numbers. But instead of taking gases by weight, we may take them by
bulk or volume, and they will be found to combine in the most simple ratios, the ratio being as 1 to 1, 1 to 2, or 1 to 3. Thus 1 volume of oxygen requires exactly 1 volume of hydrogen to form the deutoxide, and 2 volumes to form water. 1 volume of hydrogen requires 3 volumes of nitrogen, to form ammoniacal gas, and so on.
Hence the law of combination may be thus concisely expressed :—When a body A combines with a body B in several proportions, the numbers expressing these proportions are integer multiples of the smallest quantity of B that A can absorb. The law may be also thus expressed:—When two bodies combine in several proportions, the first proportion is either a multiple or a submnltiple of all the rest.
These laws of definite proportions, and of the atomic theory in reference to weights and volumes, are well illustrated by the compounds of nitrogen and oxygen: these bodies unite with each other in 5 proportions, and in the simplest ratios, forming two oxides and three acids.
In the above examples the oxygen combines in regular arithmetical progression. This, however, is not always the case. The law of multiple ratios simply requires, that the proportionals shall all be multiples of the smallest. Thus, in the known compounds of chlorine and oxygen, the oxygen combines by weight or volume, with a weight or volume of chlorine, according to the numbers 1, 3, 4, 5, 7. Should any intermediate compounds be discovered, the oxygen will be in the proportion of 2 and 6; such compounds may, however, be impossible.
It is necessary to attach a precise meaning to the term weight, or combining weights, when speaking of the union of chemical elements. Thus we say, that water is composed of 8 parts by weight of oxygen, and 1 part by weight of hydrogen. In such case, 8 is called the equivalent or combining weight of oxygen, and 1, the equivalent or combining weight of hydrogen, and 8 + 1 = 9, is the equivalent or combining weight of water. But we may also represent hydrogen by 100, or by 1000, or any other number, provided all the numbers be multiplied in an equal ratio; or hydrogen may be represented by y^. or Tttott, if all the other numbers be equally reduced. If hydrogen were represented by 100, oxygen would be 800, and nitric acid 5,400. Or if hydrogen were 0.01, oxygen would be 0.08. It is the ratio that gives value to these numbers. When we say that 40 parts sulphuric acid saturate 48 parts potash, there is nothing in these numbers of any particular value; for 20 and 24, 5 and 6, would do as well, these numbers being in the same ratio as 40 and 48, and this is the ratio between the sulphuric acid and the potassa; but as small numbers arc more easily remembered than large ones, it is an object to reduce the equivalent numbers to the lowest ratio that can be obtained.
Berzelins assumes oxygen as = 100, other chemists have taken oxygen as = 1, in which case the whole scale of equivalent numbers must be reduced to one eighth of what they would be when hydrogen is = 1. Thus sulphuric acid, which in the hydrogen scale = 40, would in the oxygen scale = 5 ; nitric acid, instead of being 54, would be 6.75; lime, instead of being 28, would be 3.5 ; carbonic acid, instead of 22, would be 2.75; and hydrogen would be 0.125. Nearly one half of the ascertained numbers would be fractional. Dr. Thomson gives the following reasons for preferring the oxygen scale: "Hydrogen, so far as we know at present, combines with but few of the other simple bodies; while oxygen unites with them all, and often in various proportions. Consequently, very little advantage is gained by representing the atom of hydrogen by unity; but a very great one by representing the atom of oxygen by unity; for it reduces the number of arithmetical operations respecting these bodies, to the addition of unity; and we see at once, by a glance of the eye, the number of atoms of oxygen which enter into combination with the various bodies."
In the tables of equiealents, as they are called, which have been constructed with great care by firstrate chemists, the quantity, but not the quality, of the weights is given. It is not stated whether these weights are grains, or ounces, or pounds. In the laboratory, or in the chemical manufactory, it may be any one of them, or it may be hundred-weights or tons. In theory, however, a very different denomination is implied. When it is stated, that potash consists of 40 potassinm + 8 oxygen, these numbers are referred to the unit by which all elementary bodies are measured; this unit is hydrogen, and its equivalent number, or combining weight, is 1.
Dr. Dalton was the first who conceived clearly the idea, that from the relative actual weights of the elements in the mass of any compound body, the relative weights of the ultimate atoms of bodies .might be inferred. Water, he conceived, consisted of 1 part by weight of hydrogen, and 8 parts by weight of oxygen, and he supposed that when two combinations of two bodies could be obtained, that the first must be composed of an atom of each, and the second, of 2 atoms of the one, and 1 atom of the other. Applying this reasoning to the compound of oxygen and hydrogen, he supposed that 1 atom of hydrogen + 1 atom of oxygen formed water, and hence that the weights of the atoms must be in the
same ratio as the weights of the total quantities that compose water. In this way he examined a large number of compounds, assuming the weight of hydrogen as unity, and from that determining the weight of the atoms of other elements by representing them as so many times heavier than the atom of hydrogen, the number of times being discovered by comparing the weights of different elements. These weights were determined by the analysis of the compounds formed cither with one part hydrogen, or with a given weight of some other element whose relative atomic weight to that of hydrogen had been ascertained. In this way the weights of the atoms of other bodies were expressed in atoms of hydrogen, each of which was denoted by unity.
The atomic weight of one body being thus arbitrarily fixed, the atomic weights of other bodies were found in the following manner. 100 parts of water contain, according to analysis, 11.111 hydrogen and 88.889 oxygen. Assuming that in the composition of water every atom of hydrogen is combined with 1 atom of oxygen, then the weight of 1 atom of hydrogen = 11.111 : 88.889 = 1:8 and this last number is the atomic weight of oxygen.
100 parts of sulphuretted hydrogen contain 5.9 parts of hydrogen and 94.1 parts of sulphur. Assuming that this compound contains equal numbers of atoms of hydrogen and sulphur, we have the proportion 5.9 : 94.1 = 1 : 16; or the atomic weight of sulphur is 16, if that of hydrogen be assumed as = 1.
On examining the relation of sulphur to oxygen, we find that 100 parts of sulphurous acid contain 50 of sulphur and 50 of oxygen; and 100 parts of sulphuric acid 40 sulphur and 60 oxygen. Now 50 : 50 = 16 : 16, and 40 : 60 = 16 : 24; and since the atomic weight of sulphur is 16, that of oxygen 8, wo may conclude, that in sulphurous acid, 1 atom sulphur = 16, is combined with 2 atoms oxygen = 16, and in sulphuric acid with 3 atoms oxygen = 24.
Carbonic oxide contains 6 parts carbon combined with 8 oxygen; and carbonic acid 6 carbon with 16 oxygen. The atom of carbon is estimated at 6, supposing that in carbonic oxide it is combined with 1, and in carbonic acid with 2 atoms of oxygen.
Sulphuretof carbon contains 6 parts carbon united with 32 sulphur; therefore, 1 atom of carbon with 2 atoms of sulphur.
In ammonia 14 parts of nitrogen are combined with 3 of hydrogen; therefore, 1 atom of nitrogen with 3 atoms of hydrogen.
In the yellow oxide of lead, 103.8 lead are combined with oxygen; the atomic weight of lead may therefore be estimated at 103.8. Galena is a compound of lead and sulphur, in the proportion of 103.8 : 16, and this compound must be regarded as containing equal numbers of atoms of its elements.
In this way the atomic weight of hydrogen being assumed = 1, the following atomic weights have been determined; oxygen 8, sulphur 16, carbon 6, nitrogen 14. lead 103.8. In a similar manner the atomic weights of other elements have been caleulated, as set forth in the following tabic:—