one meteorologist like Quetelet, Dove, or Baxendell, who devotes himself to the truly useful labour of reducing other people’s observations, there are hundreds who labour under the delusion that they are advancing science by loading our book-shelves with numerical tables. It is to be feared, in like manner, that almost the whole bulk of statistical numbers, whether commercial, vital, or moral, is of little scientific value. Purely empirical measurements may have a direct practical value, as when tables of the specific gravity, or strength of materials, assist the engineer; the specific gravities of mixtures of water with acids, alcohols, salts, &c., are useful in chemical manufactories, custom-house gauging, &c.; observations of rainfall are requisite for questions of water supply; the refractive index of various kinds of glass must be known in making achromatic lenses; but in all such cases the use made of the measurements is not scientific but practical. It may be asserted, that no number which remains isolated, and uncompared by theory with other numbers, is of scientific value. Having tried the tensile strength of a piece of iron in a particular condition, we know what will be the strength of the same kind of iron in a similar condition, provided we can ever meet with that exact kind of iron again; but we cannot argue from piece to piece, nor lay down any laws exactly connecting the strength of iron with the quantity of its impurities.
Quantities indicated by Theory, but Empirically Measured.
In many cases we are able to foresee the existence of a quantitative effect, on the ground of general principles, but are unable, either from the want of numerical data, or from the entire absence of any mathematical theory, to assign the amount of such effect. We then have recourse to direct experiment to determine its amount. Whether we argued from the oceanic tides by analogy, or deductively from the theory of gravitation, there could be no doubt that atmospheric tides of some amount must occur in the atmosphere. Theory, however, even in the hands of Laplace, was not able to overcome the complicated mechanical conditions of the atmosphere, and predict the amounts of such tides; and, on the other hand, these amounts were so small, and were so masked by far larger undulations arising from the heating power of the sun, and from other meteorological disturbances, that they would probably have never been discovered by purely empirical observations. Theory having, however, indicated their existence and their periods, it was easy to make series of barometrical observations in places selected so as to be as free as possible from casual fluctuations, and then, by the suitable application of the method of means, to detect the small effects in question. The principal lunar atmospheric tide was thus proved to amount to between ·003 and ·004 inch.1
Theory yields the greatest possible assistance in applying the method of means. For if we have a great number of empirical measurements, each representing the joint effect of a number of causes, our object will be to take the mean of all those in which the effect to be measured is present, and compare it with the mean of the remainder in which the effect is absent, or acts in the opposite direction. The difference will then represent the amount of the effect, or double the amount respectively. Thus, in the case of the atmospheric tides, we take the mean of all the observations when the moon was on the meridian, and compare it with the mean of all observations when she was on the horizon. In this case we trust to chance that all other effects will lie about as often in one direction as the other, and will neutralise themselves in the drawing of each mean. It is a great advantage, however, to be able to decide by theory when each principal disturbing effect is present or absent; for the means may then be drawn so as to separate each such effect, leaving only minor and casual divergences to the law of error. Thus, if there be three principal effects, and we draw means giving respectively the sum of all three, the sum of the first two, and the sum of the last two, then we gain three simple equations, by the solution of which each quantity is determined.