(341.) The determination of the atomic weights of the chemical elements, like that of other standard physical data, with the utmost exactness, is in itself a branch of enquiry not only of the greatest importance, but of extreme difficulty. Independent of the general reasons for desiring accuracy in this respect, there is one peculiar to the subject. It has been suggested (by Dr. Prout), and strongly insisted on (by Dr. Thomson), that all the numbers representing these weights, constituting a scale of great extent, in which the extremes already known are in proportion to each other, as 1 to upwards of 200, are simple even multiples of the least of them. If this be really the case, it opens views of such importance as to justify any degree of labour and pains in the verification of the law as a purely inductive one. But in the actual state of chemical analysis, with all deference to such high authority, we confess it appears to us to stand in great need of further confirmation, since it seems doubtful whether such accuracy has yet been attained as to enable us to answer positively for a fraction not exceeding the three or four hundredth part of the whole quantity to be determined: at least the results of the first experimenters, obtained with the greatest care, differ often by a greater amount; and this degree of exactness, at least, would be required to verify the law satisfactorily in the higher parts of the scale. (342.) The mere agitation of such a question, however, points out a class of phenomena in physical science of a remote and singular kind, and of a very high and refined order, which could never become known but in an advanced state of science, not only practical, but theoretical,--we mean, such as consist in observed relations among the _data_ of physics, which show them to be quantities not _arbitrarily_ assumed, but depending on laws and causes which they may be the means of at length disclosing. A remarkable instance of such a relation is the curious law which Bode observed to obtain in the progression of the magnitudes of the several planetary orbits. This law was interrupted between Mars and Jupiter, so as to induce him to consider a planet as wanting in that interval;--a deficiency long afterwards strangely supplied by the discovery of _four_ new planets in that very interval, all of whose orbits conform in dimension to the law in question, within such moderate limits of error as may be due to causes independent of those on which the law itself ultimately rests.[54]