yields the product A. c = 2.13, whilst treble the value, i.e. 55.89, yields 64. The latter number also represents the quantity of iron contained in the molecular weight of ferric chloride (§ 25); this must therefore be regarded as the atomic weight of iron compared with hydrogen as unity. Similar determinations by other chemists yield almost identical results. The mean of the most trustworthy results gives 55.88 as the atomic weight of iron.

The oxides of many elements are difficult to prepare in a state of perfect purity. This is true of many of the light and of some of the noble metals, but the chlorides, bromides, &c. of these elements are admirably adapted for weighing. In such cases the comparison of the atomic weight with that of hydrogen is made by a more indirect method than the preceding. The compounds of silver with chlorine, bromine, and iodine are quite insoluble in water, and are therefore well adapted for analytical determinations. The proportions by weight with which these elements unite with silver have been very carefully estimated. In fact, the most correct of all the stœchiometrical determinations that have ever been made are those which fixed the combining proportions of silver and iodine

This determination was carried out by Stas with the utmost care and skill; the experimental error is about 1 in 100,000. As oxide of silver is too unstable to permit of correct analysis the proportion of silver to oxygen had to be determined by several indirect methods, all of which have yielded similar results.

The analysis of potassium chlorate, KCIO,, gave the relative quantities of potassium chloride, KCl, and oxygen in the salt:

KCI: 04.6616: 1.

By converting weighed quantities of potassium chloride, KCl, into silver chloride, AgCl, the following ratio was obtained:

The same result was obtained in a similar way by the synthesis of silver sulphide, Ag2S, and its oxidation to silver sulphate Ag2SO,. Finally Stas analysed the chlorate, bromate, and iodate of silver, AgCIO,, AgBrO,, and AgIO,. The results of these analyses, and of the syntheses of AgCl, AgBr, and AgI, give the ratio :

Ag: 06-7456 1,

which agrees closely with the former result. Compared with hydrogen, the atomic weight of silver is 107.66,

Ag: H=6·7456 × 15·96: 1–107·66: 1.

Many other methods have been suggested for the indirect determination of the atomic weights of elements in terms of hydrogen. The preceding examples will suffice to illustrate the methods employed.

§ 31. Selection from Different Determinations.-Although no method of determination is free from error, the amount of error is very variable. Consequently the values for the atomic weights obtained by different methods do not coincide absolutely. But as Stas has proved by experiments, specially made for this purpose, that the atomic weights are constant and invariable values, under all known conditions, it follows that only one value can be accepted as correct. It is necessary to select this, the exact value, from the others. This problem is one frequently associated with difficulties, and requires much care and consideration.

The analytical or synthetical methods employed must be submitted to a critical examination for the purpose of ascertaining the extent and the sources of error.

The results of the method which is most free from error are naturally preferred. The magnitude of the error involved in a particular method can often, but not always, be ascertained by making several determinations by the method and comparing the results. This cannot, however, be done when all the determinations contain a common error, a so-called

'constant' error; e.g. if in a case of oxidation the reaction is not quite complete, a definite quantity of the element will always yield too little oxide, and in all such experiments the atomic weight will be found too high.

If the precipitation of an element is accompanied by a certain loss, the total weight of the element will not be obtained, and the atomic weight will be low in all the determinations.

The constant errors are more to be feared than the casual errors, because they lead us to believe in a degree of accuracy which in reality does not exist. This explains why Gauss's method of least squares is seldom used in atomic weight determinations, although, as a rule, it is well adapted for determining the extent of errors of experiment.

A complete analysis or synthesis offers a certain guarantee against constant or occasional errors. If the sum of the constituents is very nearly equal to the weight of the compound, this indicates that no considerable loss has taken place, or that the loss is exactly balanced by a gain of foreign matter taken up during the analysis. The loss of constituents exactly balancing the gain in foreign matter is a very rare occurrence. A partial decomposition may be mistaken for a complete one, and thus occasion serious errors. Berzelius attempted to determine the atomic weight of vanadium by reducing its highest oxide in hydrogen. Roscoe afterwards proved that only of the oxygen in the oxide is removed and that remains in the residue, which Berzelius regarded as the pure element. The true atomic weight of V is 51.1, but Berzelius calculated it to be 137-i.e., according to our present knowledge, V,02.

The best guarantee against error of all kinds is secured when the atomic weight of an element has been determined by several distinct methods, and the results are found to

agree.

§ 32. Accuracy of the Atomic Weights.-An examination of the numerous atomic weight determinations shows that there is an extraordinary difference in their degree of accuracy. The ratio between a small number of the atomic weights has been determined to the T00000 part of their value (e.g.

between iodine and silver), and for a somewhat larger number of elements to the Todo part. The error in the case of other elements amounts to Tooo of their value, and in the case of a few it is not less than one per cent. The relation between the atomic weights of hydrogen and oxygen, which is taken as the standard by which all other atomic weights are measured, may contain an error of one or two thousandths of its value. This possible error affects all the other atomic weights which are referred to this standard. But this uncertainty does not vitiate the accuracy of the stœchiometric calculations, as they are independent of the standard chosen. If we express the other possible errors in terms of this unit, then the error is not greater than 0.1 H for one third of the elements, and does not exceed 0-5 H for a second third. In the case of the remaining elements the error will amount to from 0.5 to 1, and in some cases, which require re-determining, may amount to two or more units.

§ 33. Prout's Hypothesis.-It has already been pointed out in § 31 that our investigations indicate that the atoms of one and the same elements are alike in all respects, but that the atoms of two or more different elements are dissimilar. Up to the present day, it has never been possible to convert one element into another. At the same time, it is improbable that the elements which have been discovered, or are yet to be discovered, are really primal forms of matter. Their large number and other reasons induce us to believe that just as the elements are the basis of the composition of all the compounds derived from them, so they in turn may prove to be combinations of units of a higher order. This idea originated almost at the same time as the atomic theory, but, in spite of much experimental and theoretical effort, it has never advanced beyond the stages of conjecture.

In 1815 an English chemist, Prout, published (at first anonymously) a conjecture of this kind. He observed that the atomic weights of many of the elements appeared to be rational multiples of the atomic weight of hydrogen, and might be represented by whole numbers. Prout's hypothesis is tempting in its simplicity, and for a time was favourably received by chemists, excepting by those who had made exact

and accurate atomic weight determinations. This hypothesis has never received experimental confirmation; on the contrary, many atomic weights may be nearly but not exactly represented by whole numbers, and in all the cases which have been accurately examined the deviations from the whole numbers have proved to be greater than the possible or probable experimental error. This hypothesis has attracted a considerable amount of attention, but is opposed to the best atomic weight determinations of Berzelius, Marignac, Stas, and others.

§ 34. Döbereiner's Triads. Another relation between the atomic weights, discovered by Döbereiner in 1829, has yielded better results. This chemist noticed that in many cases one member of a group of three analogous elements possesses an atomic weight which is approximately the mean of the other two. In other cases, three elements bearing a close resemblance to each other in their properties have nearly the same atomic weights.