In the preceding chapter we found that facts may be classed under four heads as regards their connection with theory, and our powers of explanation or prediction. The facts hitherto considered were generally of a qualitative rather than a quantitative nature; but when we look exclusively to the quantity of a phenomenon, and the various modes in which we may determine its amount, nearly the same system of classification will hold good. There will, however, be five possible cases:—
(1) We may directly and empirically measure a phenomenon, without being able to explain why it should have any particular quantity, or to connect it by theory with other quantities.
(2) In a considerable number of cases we can theoretically predict the existence of a phenomenon, but are unable to assign its amount, except by direct measurement, or to explain the amount theoretically when thus ascertained.
(3) We may measure a quantity, and afterwards explain it as related to other quantities, or as governed by known quantitative laws.
(4) We may predict the quantity of an effect on theoretical grounds, and afterwards confirm the prediction by direct measurement.
(5) We may indirectly determine the quantity of an effect without being able to verity it by experiment.
These classes of quantitative facts might be illustrated by an immense number of interesting points in the history of physical science. Only a few instances of each class can be given here.
Empirical Measurements.
Under the first head of purely empirical measurements, which have not been brought under any theoretical system, may be placed the great bulk of quantitative facts recorded by scientific observers. The tables of numerical results which abound in books on chemistry and physics, the huge quartos containing the observations of public observatories, the multitudinous tables of meteorological observations, which are continually being published, the more abstruse results concerning terrestrial magnetism—such results of measurement, for the most part, remain empirical, either because theory is defective, or the labour of calculation and comparison is too formidable. In the Greenwich Observatory, indeed, the salutary practice has been maintained by the present Astronomer Royal, of always reducing the observations, and comparing them with the theories of the several bodies. The divergences from theory thus afford material for the discovery of errors or of new phenomena; in short, the observations have been turned to the use for which they were intended. But it is to be feared that other establishments are too often engaged in merely recording numbers of which no real use is made, because the labour of reduction and comparison with theory is too great for private inquirers to undertake. In meteorology, especially, great waste of labour and money is taking place, only a small fraction of the results recorded being ever used for the advancement of the science. For