[Footnote 1: Jevons: Principles of Science, p. 270.]
The history of science exhibits a constant progress from rude guesses to precise measurement of quantities. In the earliest history of astronomy there were attempts at quantitative determinations, very crude, of course, in comparison with the exactness of present-day scientific methods.
Every branch of knowledge commences with quantitative notions of a very rude character. After we have far progressed, it is often amusing to look back into the infancy of the science, and contrast present with past methods. At Greenwich Observatory in the present day, the hundredth part of a second is not thought an inconsiderable portion of time. The ancient Chaldreans recorded an eclipse to the nearest hour, and the early Alexandrian astronomers thought it superfluous to distinguish between the edge and center of the sun. By the introduction of the astrolabe, Ptolemy, and the later Alexandrian astronomers could determine the places of the heavenly bodies within about ten minutes of arc. Little progress then ensued for thirteen centuries, until Tycho Brahe made the first great step toward accuracy, not only by employing better instruments, but even more by ceasing to regard an instrument as correct.... He also took notice of the effects of atmospheric refraction, and succeeded in attaining an accuracy often sixty times as great as that of Ptolemy. Yet Tycho and Hevelius often erred several minutes in the determination of a star's place, and it was a great achievement of Roemer and Flamsteed to reduce this error to seconds. Bradley, the modern Hipparchus, carried on the improvement, his errors in right ascension, according to Bessel, being under one second of time, and those of declination under four seconds of arc. In the present day the average error of a single observation is probably reduced to the half or the quarter of what it was in Bradley's time; and further extreme accuracy is attained by the multiplication of observations, and their skillful combination according to the theory of error. Some of the more important constants... have been determined within a tenth part of a second of space.[2]
[Footnote 2: Ibid., pp. 271-72.]
The precise measurement of quantities is important because we can, in the first place, only through quantitative determinations be sure we have made accurate observations, observations uncolored by personal idiosyncrasies. Both errors of observation and errors of judgment are checked up and averted by exact quantitative measurements. The relations of phenomena, moreover, are so complex that specific causes and effects can only be understood when they are given precise quantitative determination. In investigating the solubility of salts, for example, we find variability depending on differences in temperature, pressure, the presence of other salts already dissolved, and the like. The solubility of salt in water differs again from its solubility in alcohol, ether, carbon, bisulphide. Generalization about the solubility of salt, therefore, depends on the exact measurement of the phenomenon under all these conditions.[1]
[Footnote 1: See Jevons, p, 279 ff.]
The importance of exact measurement in scientific discovery and generalization may be illustrated briefly from one instance in the history of chemistry. The discovery of the chemical element argon came about through some exact measurements by Lord Rayleigh and Sir William Ramsay of the nitrogen and the oxygen in a glass flask. It was found that the nitrogen derived from air was not altogether pure; that is, there were very minute differences in the weighings of nitrogen made from certain of its compounds and the weight obtained by removing oxygen, water, traces of carbonic acid, and other impurities from the atmospheric air. It was found that the very slightly heavier weight in one case was caused by the presence of argon (about one and one third times as heavy as nitrogen) and some other elementary gases. The discovery was here clearly due to the accurate measurement which made possible the discovery of this minute discrepancy.
It must be noted in general that accuracy in measurement is immediately dependent on the instruments of precision available. It has frequently been pointed out that the Greeks, although incomparably fresh, fertile, and direct in their thinking, yet made such a comparatively slender contribution to scientific knowledge precisely because they had no instruments for exact measurement. The thermometer made possible the science of heat. The use of the balance has been in large part responsible for advances in chemistry.
The degree to which sciences have attained quantitative accuracy varies among the physical sciences. The phenomena of light are not yet subject to accurate measurement; many natural phenomena have not yet been made the subject of measurement at all. Such are the intensity of sound, the phenomena of taste and smell, the magnitude of atoms, the temperature of the electric spark or of the sun's atmosphere.[1]
[Footnote 1: See Jevons, p. 273.]