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.

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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 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 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 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.

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The mean density of the earth is a constant of high importance, because it is necessary for the determination of the masses of all the other heavenly bodies. Astronomers and physicists accordingly have bestowed a great Ideal of labour upon the exact estimation of this constant. The method of procedure consists in comparing the

gravitation of the globe with that of some body of matter of which the mass is known in terms of the assumed unit of mass. This body of matter, serving as an intermediate term of comparison, may be variously chosen; it may consist of a mountain, or a portion of the earth's crust, or a heavy ball of metal. The method of experiment varies so much according as we select one body or the other, that we may be said to have three independent modes of arriving at the desired result.

The mutual gravitation of two balls is so exceedingly small compared with their gravitation towards the immense mass of the earth, that it is usually quite imperceptible, and although asserted by Newton to exist, on the ground of theory, was never observed until the end of the 18th century. Michell attached two small balls to the extremities of a delicately suspended torsion balance, and then bringing heavy balls of lead alternately to either side of these small balls was able to detect a slight deflection of the torsion balance. He thus furnished a new verification of the theory of gravitation. Cavendish carried out the experiment with more care, and estimated the gravitation of the balls by treating the torsion balance as a pendulum; then taking into account the respective distances of the balls from each other and from the centre of the earth, he was able to assign 548 (or as re-computed by Baily, 5'448) as the probable mean density of the earth. Newton's sagacious guess to the effect that the density of the earth was between five and six times that of water, was thus remarkably confirmed. The same kind of experiment repeated by Reich gave 5'438. Baily having again performed the experiment with every possible refinement obtained a slightly higher number, 5.660.

A different method of procedure consisted in ascertaining the effect of a mountain mass in deflecting the plumb-line; for, assuming that we can determine the dimensions and mean density of the mountain, the plumb-line enables us to compare its mass with that of the whole earth. The mountain Schehallien was selected for the experiment, and observations and calculations performed by Maskelyne, Hutton, and Playfair, gave as the most probable result 4713. The difference from the experimental results already mentioned is considerable and is important, because the instrumental

operations are of an entirely different character from those. of Cavendish and Baily's experiments. Sir Henry James' similar determination from the attraction of Arthur's Seat gave 5'14.

A third distinct method consists in determining the force of gravity at points elevated above the surface of the earth on mountain ranges, or sunk below it in mines. Carlini experimented with a pendulum at the hospice of Mont Cenis, 6,375 feet above the sea, and by comparing the attractive forces of the earth and the Alps, found the density to be still smaller, namely, 4'39, or as corrected by Giulio, 4950. Lastly, the Astronomer Royal has on two occasions adopted the opposite method of observing a pendulum at the bottom of a deep mine, so as to compare the density of the strata penetrated with the density of the whole earth. On the second occasion he carried his method into effect at the Harton Colliery, 1,260 feet deep; all that could be done by skill in measurement and careful consideration of all the causes of errror, was accomplished in this elaborate series of observations (p. 291). No doubt Sir George Airy was much perplexed when he found that his new result considerably exceeded that obtained by any other method, being no less than 6.566, or 6·623 as finally corrected. In this case we learn an impressive lesson concerning the value of repeated determinations by distinct methods in disabusing our minds of the reliance which we are only too apt to place in results which show a certain degree of coincidence.

1

In 1844 Herschel remarked in his memoir of Francis Baily,2" that the mean specific gravity of this our planet is. in all human probability, quite as well determined as that of an ordinary hand-specimen in a mineralogical cabinet, -a marvellous result, which should teach us to despair of nothing which lies within the compass of number, weight and measure." But at the same time he pointed out that Baily's final result, of which the probable error was only 0'0032, was the highest of all determinations then known, and Airy's investigation has since given a much higher result, quite beyond the limits of probable error of any of

1 Philosophical Transactions (1856), vol. cxlvi. p. 342.

2 Monthly Notices of the Royal Astronomical Society, for 8th Nov 1844, No. X. vol. vi. p. 89.

the previous experiments. If we treat all determinations yet made as of equal weight, the simple mean is about 5:45, the mean error nearly 05, and the probable error almost 0'2, so that it is as likely as not that the truth lies between 565 and 5.25 on this view of the matter. But it is remarkable that the two most recent and careful series of observations by Baily and Airy,' lie beyond these limits, and as with the increase of care the estimate rises, it seems requisite to reject the earlier results, and look upon the question as still requiring further investigation. Physicists often take 5 or 567 as the best guess at the truth, but it is evident that new experiments are much required. I cannot help thinking that a portion of the great sums of money which many governments and private individuals spent upon the transit of Venus expeditions in 1874, and which they will probably spend again in 1882 (p. 562), would be better appropriated to new determinations of the earth's density. It seems desirable to repeat Baily's experiment in a vacuous case, and with the greater mechanical refinements which the progress of the last forty years places at the disposal of the experimentalist. It would be desirable, also, to renew the pendulum experiments of Airy in some other deep mine. It might even be well to repeat upon some suitable mountain the observations performed at Schehallien. All these operations might be carried out for the cost of one of the superfluous transit expeditions.

Since the establishment of the dynamical theory of heat it has become a matter of the greatest importance to determine with accuracy the mechanical equivalent of heat, or the quantity of energy whieh must be given, or received, in a definite change of temperature effected in a definite quantity of a standard substance, such as water. No less than seven almost entirely distinct modes of determining this constant have been tried. Dr. Joule first ascertained by the friction of water that to raise the temperature of one kilogram of water through one degree centigrade, we must employ energy sufficient to raise 424 kilograms through the height of one metre against the force of gravity at the earth's surface. Joule, Mayer,

1 Philosophical Magazine, 2nd Series, vol. xxvi. p. 61.

Clausius,1 Favre and other experimentalists have made determinations by less direct methods. Experiments on the mechanical properties of gases give 426 kilogrammetres as the constant; the work done by a steam-engine gives 413; from the beat evolved in electrical experiments several determinations have been obtained; thus from induced electric currents we get 452; from the electromagnetic engine 443; from the circuit of a battery 420; and, from an electric current, the lowest result of all, namely, 400.2

Considering the diverse and in many cases difficult methods of observation, these results exhibit satisfactory accordance, and their mean (4239) comes very close to the number derived by Dr. Joule from the apparently most accurate method. The constant generally assumed as the most probable result is 423.55 kilogrammetres.

Residual Phenomena.

Even when the experimental data employed in the verification of a theory are sufficiently accurate, and the theory itself is sound, there may exist discrepancies. demanding further investigation. Herschel pointed out the importance of such outstanding quantities, and called them residual phenomena. Now if the observations and the theory be really correct, such discrepancies must be due to the incompleteness of our knowledge of the causes in action, and the ultimate explanation must consist in showing that there is in action, either

(1) Some agent of known nature whose presence was not suspected;

Or (2) Some new agent of unknown nature.

In the first case we can hardly be said to make a new discovery, for our ultimate success consists merely in reconciling the theory with known facts when our investigation is more comprehensive. But in the second case we meet with a totally new fact, which may lead us

1 Clausius in Philosophical Magazine, 4th Series, vol ii. p. 119. 2 Watts' Dictionary of Chemistry, vol. iii. p. 129.

3 Preliminary Discourse, §§ 158, 174. Outlines of Astronomy, 4th edit. § 856.