conclusion that the velocity was not really more than 185,172 miles per second. No repetition of the experiment as thus performed would shake this result, and there was accordingly a discrepancy between the two astronomical and the experimental results of about 7000 miles per second demanding explanation.

Now a very little consideration shows that both the astronomical determinations involve the magnitude of the earth's orbit as one datum, because our estimate of the earth's velocity in its orbit depends upon our estimate of the sun's mean distance. Accordingly as regards this quantity the two astronomical results must count only for one. Though the transit of Venus had been considered to give the best data for the calculation of the sun's parallax and distance, yet astronomers had not neglected other less favourable opportunities. Thus Hansen, calculating from certain inequalities in the moon's motion, had estimated it at 8"916; Winneke, from observations of Mars, at 8"964; Leverrier, from the motions of Mars, Venus, and the moon, at 8"-950. Now these independent results agree much better with each other than with that of Bessel (8" 578) previously received, or that of Encke (858) deduced from the transits of Venus in 1761 and 1769, and though each separately might be worthy of less credit, yet their close accordance renders their mean result (8943) probably comparable in probability with that of Bessel. It was further found that if Foucault's value for the velocity of light were assumed to be correct, and the sun's distance were inversely calculated from that and the other requisite data, the sun's parallax would appear to be 8"-960, which closely agreed with the above mean result. This further correspondence of independent results threw the balance of probability strongly against the results of the transit of Venus, and rendered it desirable to reconsider the observations made on that occasion.

Mr. E. J. Stone having re-discussed those observations d found that grave oversights had been made in the calculations, which being corrected would alter the estimate of parallax to 8"-91, a quantity in such comparatively close accordance with the other results that astronomers did not hesitate at once to reduce their estimate of the sun's mean distance from 95,274,000 to 91,771,000 miles, although this alteration involved a corresponding correction in the assumed magnitudes and distances of most of the heavenly bodies. The final decision of this question of the ratio between the earth and the visible universe, so far as it can be decided in the present century, must be made at the approaching transits of Venus in 1874 and 1882.

In this important and interesting question the theoretical relations between the velocity of light, the constant of aberration, the sun's parallax, and the sun's mean distance, are of the simplest character, and can hardly be open to any doubt, so that the only doubt was as to which result of observation was the most reliable. Eventually the chief discrepancy was found to arise from misapprehension in the reduction of observations, but we have a satisfactory example of the value of different methods of estimation in leading to the detection of a serious error. Is it not surprising that Foucault by measuring the velocity of light when passing through the space of a few yards, should lead the way to a change in our estimates of the magnitude of the whole universe?

Selection of the best Mode of Measurement.

When we have once obtained a command over a question of physical science by comprehending the theory of the

d Monthly Notices of the Royal Astronomical Society,' vol. xxviii. p. 264.

subject, we have often a wide choice opened to us as regards the methods of measurement, which may thenceforth be made to give the most accurate results. If we can only measure one fundamental quantity we may often be able by correct theory to assign with accuracy a great many other quantitative results. Thus, if we can once determine satisfactorily the atomic weights of certain elements, we do not need to determine with equal accuracy the composition and atomic weights of their several compounds. When we have once learnt the relative atomic weights of oxygen and sulphur we and sulphur we can calculate the composition by weight of the several oxides of sulphur. Chemists accordingly select with the greatest care that compound of any two elements which seems to allow of the most accurate analysis so as to give the ratio of their atomic weights. It is obvious that we only need to have the ratio of the atomic weight of each element to that of some other common element, in order to calculate with the greatest ease that of each to each. Moreover the atomic weight stands in simple relation to other quantitative facts. The weights of equal volumes of elementary gases at equal temperature and pressure have the same ratio as the atomic weights; now as nitrogen weighs 14'06 times as much as hydrogen, under such circumstances we may infer that the atomic weight of nitrogen is about 14:06 (probably 14'00) that of hydrogen being unity. There is much evidence, again, to show that the specific heats of elements, and even of compounds, 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 any one may lead to that of the others. The chemist accordingly has to solve a most 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 comparatively few fundamental ratios.

In hygrometry we are presented with 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, or 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. Now the results of each such mode can be connected by well-established theory with those of the other modes, and we can select for each experiment that mode which is either most accurate or most convenient. The chemical method of direct measurement is probably capable of the greatest accuracy, but is troublesome; the dry and wet bulb thermometer is sufficiently exact for meteorological purposes.

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 any 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 experimental results of great importance. Even when three or more distinct methods have given nearly

coincident results, a new method has sometimes disclosed a discrepancy which it is yet impossible to explain.

The ellipticity of the earth is known with very 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 the amount of their curvature as determined by the observation 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

1

300'

by Bessel at 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 in different parts of the earth's surface, so that exact pendulum observations give the data for an entirely independent estimate of the ellipticity, which is thus found 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.

to be

320

I

He thus inferred that the ellipticity is which lies be

305'

tween the two numbers previously given, and was considered by him to be the most satisfactory conclusion. In this case the accordance is both close and undisturbed by any other or subsequent results, so that we are obliged to accept Laplace's result as a highly probable and accurate

one.

The mean density of the earth is another constant quantity of the highest importance, because it forms the startingpoint for the determination of the masses of all the other