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 too 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 mistakes. 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 V is 51.1, but Berzelius calculated it to be 137i.e. V2O2.

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 T00006 part of their value (e.g. between iodine and silver), and for a somewhat larger number of elements to the Too part. The error in the case of other elements amounts to Too of their value, and in the case of a few it is not less than one per cent. The relation between the

PROUT'S HYPOTHESIS

51

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 acccuracy of the stochiometric 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 element 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 will 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 led to better results. This chemist noticed that it frequently happens that 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.

Döbereiner believed that in these relations might be found the basis of a systematic classification of the elements, but it was long before this idea received development. It was impossible for the attempts which were made in this direction by Pettenkofer (1851), Dumas (1859), and others to be successful, as at this time the atomic weights had not been systematically deduced from the analytical results. When this had once been accomplished, it was found possible to arrange all the elements in groups of 3, 4, or 5 members, in all of which groups the differences were approximately the same. In these groups of elements, arranged in the order of the atomic weights of their members, is to be found the realisation of the systematic classification of the elements which Döbereiner had striven to accomplish.

The development of this system was brought about by the labours of Newlands, Mendeléeff, Lothar Meyer, and others. The following tables contain some of the elements arranged in groups of four and five members each. The corresponding members of the different groups form a continuous series of elements arranged in the order of their atomic weights.

In the four last groups the second member is nearly the arithmetical mean of the first and third; the fourth is the mean of the third and fifth. In the first three groups, the elements corresponding to the first members are missing. The differences are nearly the same as in the other families.

The second table embraces a number of similar groups, in which the difference between the first and second members is only half the difference between the second and third members. The first and last groups of this second table occur at the beginning and end of the first one, so that both tables may be united into a continuous one.

§ 35. Arrangement of the Elements in the Order of their Atomic Weights.—Most of the groups in the second table are related to one of the groups in the first table by analogies in the properties of their members, and especially by the isomorphism of their compounds. Vanadium, V, is associated with phosphorus, P, and arsenic, As, by isomorphism; in the same way chromium, Cr, and molybdenum, Mo, are related to sulphur, S, and selenium, Se; by the isomorphism of the permanganates with the perchlorates, manganese, Mn, is associated with chlorine, Cl. The first table does not contain any elements analogous to iron, nickel, cobalt, and the six platinum metals; but copper, Cu, and silver, Ag, are related to sodium, Na; and zinc, Zn, to magnesium, Mg, and calcium, Ca; indium, In, to aluminium, Al; and tin, Sn, is isomorphous with silicon, Si, and titanium, Ti. We are therefore not only justified in joining these two tables together, but in uniting them to form the following table. The perpendicular columns contain not only closely-allied elements, but also others which only bear an analogy to them in certain respects, but differ from them widely in other points.