planets had moved further from each other, that all objects around us had become larger, that we ourselves had become taller, and that the distance travelled by light in the duration of a vibration had become greater, we should not hesitate to think ourselves the victims of an illusion, that in reality all these distances had remained fixed, and that all these appearances were due to a shortening of the rule which we had used as the standard for measuring the lengths.

From the mathematical point of view, it may be 7 considered that the two hypotheses are equivalent ; all has lengthened around us, or else our standard has become less. But it is no simple question of convenience and simplicity which leads us to reject the one supposition and to accept the other; it is right in this case to listen to the voice of common sense, and those physicists who have an instinctive trust in the notion of an absolute length are perhaps not wrong. It is only by choosing our unit from those which at all times have seemed to all men the most invariable, that we are able in our experiments to note that the same causes acting under identical conditions always produce the same effects. The idea of absolute length is derived from the principle of causality; and our choice is forced upon us by the necessity of obeying this principle, which we cannot reject without declaring by that very act all science to be impossible.

Similar remarks might be made with regard to

the notions of absolute time and absolute movement. They have been put in evidence and set forth very forcibly by a learned and profound mathematician, M. Painlevé.

On the particularly clear example of the measure of length, it is interesting to follow the evolution of the methods employed, and to run through the history of the progress in precision from the time that we have possessed authentic documents relating to this question. This history has been written in a masterly way by one of the physicists who have in our days done the most by their personal labours to add to it glorious pages. M. Benoit, the learned Director of the International Bureau of Weights and Measures, has furnished in various reports very complete details on the subject, from which I here borrow the most interesting.

We know that in France the fundamental standard for measures of length was for a long time the Toise du Châtelet, a kind of callipers formed of a bar of iron which in 1668 was embedded in the outside wall of the Châtelet, at the foot of the staircase. This bar had at its extremities two projections with square faces, and all the toises of commerce had to fit exactly between them. Such a standard, roughly constructed, and exposed to all the injuries of weather and time, offered very slight guarantees either as to the permanence or the correctness of its copies. Nothing, perhaps, can

better convey an idea of the importance of the modifications made in the methods of experimental physics than the easy comparison between SO rudimentary a process and the actual measurements effected at the present time.

The Toise du Châtelet, notwithstanding its evident faults, was employed for nearly a hundred years; in 1766 it was replaced by the Toise du Pérou, so called because it had served for the measurements of the terrestrial arc effected in Peru from 1735 to 1739 by Bouguer, La Condamine, and Godin. At that time, according to the comparisons made between this new toise and the Toise du Nord, which had also been used for the measurement of an arc of the meridian, an error of the tenth part of a millimetre in measuring lengths of the order of a metre was considered quite unimportant. At the end of the eighteenth century, Delambre, in his work Sur la Base du Système métrique décimal, clearly gives us to understand that magnitudes of the order of the hundredth of a millimetre appear to him incapable of observation, even in scientific researches of the highest precision. At the present date the International Bureau of Weights and Measures guarantees, in the determination of a standard of length compared with the metre, an approximation of two or three ten-thousandths of a millimetre, and even a little more under certain circumstances.

This very remarkable progress is due to the

improvements in the method of comparison on the one hand, and in the manufacture of the standard on the other. M. Benoit rightly points out that a kind of competition has been set up between the standard destined to represent the unit with its subdivisions and multiples and the instrument charged with observing it, comparable, up to a certain point, with that which in another order of ideas goes on between the gun and the armour-plate.

The measuring instrument of to-day is an instrument of comparison constructed with meticulous care, which enables us to do away with causes of error formerly ignored, to eliminate the action of external phenomena, and to withdraw the experiment from the influence of even the personality of the observer. This standard is no longer, as formerly, a flat rule, weak and fragile, but a rigid bar, incapable of deformation, in which the material is utilised in the best conditions of resistance. For a standard with ends has been substituted a standard with marks, which permits much more precise definition and can be employed in optical processes of observation alone; that is, in processes which can produce in it no deformation and no alteration. Moreover, the marks are traced on the plane of the neutral fibres 1 exposed, and the invariability of their distance apart

1 The author seems to refer to the fact that in the standard metre, the measurement is taken from the central one of three marks at each end of the bar. The transverse section of the bar is an X, and the reading is made by a microscope.— ED.

is thus assured, even when a change is made in the way the rule is supported.

Thanks to studies thus systematically pursued, we have succeeded in the course of a hundred years in increasing the precision of measures in the proportion of a thousand to one, and we may ask ourselves whether such an increase will continue in the future. No doubt progress will not be stayed; but if we keep to the definition of length by a material standard, it would seem that its precision cannot be considerably increased. We have nearly reached the limit imposed by the necessity of making strokes of such a thickness as to be observable under the microscope.

It may happen, however, that we shall be brought one of these days to a new conception of the measure of length, and that very different processes of determination will be thought of. If we took as unit, for instance, the distance covered by a given radiation during a vibration, the optical processes would at once admit of much greater precision.

Thus Fizeau, the first to have this idea, says: "A ray of light, with its series of undulations of extreme tenuity but perfect regularity, may be considered as a micrometer of the greatest perfection, and particularly suitable for determining length." But in the present state of things, since the legal and customary definition of the unit remains a material standard, it is not enough to measure