weights; now, as nitrogen under such circumstances weighs 14·06 times as much as hydrogen, we may infer that the atomic weight of nitrogen is about 14·06, or more probably 14·00, that of hydrogen being unity. There is much evidence, again, that the specific heats of elements are inversely as their atomic weights, so that these two classes of quantitative data throw light mutually upon each other. In fact the atomic weight, the atomic volume, and the atomic heat of an element, are quantities so closely connected that the determination of one will lead to that of the others. The chemist has to solve a complicated problem in deciding in the case of each of 60 or 70 elements which mode of determination is most accurate. Modern chemistry presents us with an almost infinitely extensive web of numerical ratios developed out of a few fundamental ratios.
In hygrometry we have a choice among at least four modes of measuring the quantity of aqueous vapour contained in a given bulk of air. We can extract the vapour by absorption in sulphuric acid, and directly weigh its amount; we can place the air in a barometer tube and observe how much the absorption of the vapour alters the elastic force of the air; we can observe the dew-point of the air, that is the temperature at which the vapour becomes saturated; or, lastly, we can insert a dry and wet bulb thermometer and observe the temperature of an evaporating surface. The results of each mode can be connected by theory with those of the other modes, and we can select for each experiment that mode which is most accurate or most convenient. The chemical method of direct measurement is capable of the greatest accuracy, but is troublesome; the dry and wet bulb thermometer is sufficiently exact for meteorological purposes and is most easy to use.
Agreement of Distinct Modes of Measurement.
Many illustrations might be given of the accordance which has been found to exist in some cases between the results of entirely different methods of arriving at the measurement of a physical quantity. While such accordance must, in the absence of information to the contrary, be regarded as the best possible proof of the approximate correctness of the mean result, yet instances have occurred to show that we can never take too much trouble in confirming results of great importance. When three or even more distinct methods have given nearly coincident numbers, a new method has sometimes disclosed a discrepancy which it is yet impossible to explain.
The ellipticity of the earth is known with considerable approach to certainty and accuracy, for it has been estimated in three independent ways. The most direct mode is to measure long arcs extending north and south upon the earth’s surface, by means of trigonometrical surveys, and then to compare the lengths of these arcs with their curvature as determined by observations of the altitude of certain stars at the terminal points. The most probable ellipticity of the earth deduced from all measurements of this kind was estimated by Bessel at 1/300, though subsequent measurements might lead to a slightly different estimate. The divergence from a globular form causes a small variation in the force of gravity at different parts of the earth’s surface, so that exact pendulum observations give the data for an independent estimate of the ellipticity, which is thus found to be 1/320. In the third place the spheroidal protuberance about the earth’s equator leads to a certain inequality in the moon’s motion, as shown by Laplace; and from the amount of that inequality, as given by observations, Laplace was enabled to calculate back to the amount of its cause. He thus inferred that the ellipticity is 1/305, which lies between the two numbers previously given, and was considered by him the most satisfactory determination. In this case the accordance is undisturbed by subsequent results, so that we are obliged to accept Laplace’s result as a highly probable one.