Time Measurement

Return now to the question of a possible free oscillation of the axis of rotation of the earth, with respect to axes fixed in its body. We have so far supposed the earth rigid; but the earth, though very stiff in its main body, is not rigid. If it were rigid and if we suppose the actual axis of rotation to depart slightly from the principal axis of greatest inertia, it follows from the foregoing equations of motion that the axis of rotation would de scribe in the body a circle about the axis of inertia in a period 2 r A days, which the ascertained period of the precession n(C— A) shows to be about 305 days. No such motion exists, whence for a long time it was falsely concluded that the two axes coincided so closely that observation could not separate them. This is not the case. Observations by F. Kiistner, extended by S. C. Chandler, and now conducted internationally at a number of suitably placed observatories, show that the axis about which the earth rotates moves around its mean position, at a distance of some Soft. or less (o".3), in a complicated curve, which can be analysed into two main components, one with a period of about 432 days, and the other one year. Both are therefore greater than the period for a rigid earth. It was pointed out by S. Newcomb that the proper interpretation is found in a slight yielding of the body under rota tional stress, such as would accord with the estimated rigidity, viz., a little greater than that of steel. The longer period probably refers to this cause. A period of a year might easily be furnished by some seasonal effect.

Change of Length of the Day.

The foregoing has assumed that the couple N, the resolved part of the whole couple about the polar axis, is zero, or say that its mean value is zero ; which implies that the rotation period for the earth must be constant. But reasons are known to be in operation that may change it. Thus if the body of the earth had gradually shrunk, as pretty certainly it must have done, the coefficient c would have dimin ished, and the angular momentum remaining unaltered, the angular velocity would have increased. On the other side, the tides which in their phases generally follow the moon by a time that is fixed at any place, move in the same sense as the earth rotates, but much more slowly, so that they furnish a species of friction clutch or brake upon the earth and must slow down its rotation. A more general consideration of the earth-moon system and their secular changes of relative distance and relative motion shows that the slowing effect is divided between the earth's rotation and the moon's mean motion, but does not alter this consideration. Hence it is very unlikely that the day, which we have used as a standard, is really constant. The only tests we can apply to it are the other circulating bodies, the moon, Jupiter's satellites, the sun, the planets. Of these the moon is the most favourable. It moves much more slowly than the inner satellites of Jupiter, but its theory though complicated accords much more closely with observation. Now there is another theoretical cause for secular acceleration in the moon's motion, but the theoretical value does not accord with the observational value. That the difference is really to be ascribed to a lengthening of the day is indicated by tracing a proportion ately smaller unexplained secular movement in the sun and residuals from the planets Venus and Mercury, all of which are in general agreement with the unexplained residues from the moon.

The two causes of tidal friction and bodily changes in the earth affect in different degree the apparent accelerations of the moon, and the sun and planets. This permits us to determine separately the two effects by fitting their joint outcome to the observed residues requiring explanation in both cases. These residues are remarkable. In place of a smooth curve of regular progression, they correspond very closely to a broken series of straight lines, which would mean sudden changes of increase or decrease of the length of the day at definite dates. Thus in 1897 there was a sharp increase of the length by about .004sec. and in 1918 an equally sharp decrease by the same amount. The portion of these changes that must be attributed to tidal friction seems to accord numerically with what can be calculated. The loss of energy takes place almost entirely in the shallow seas, such as the Irish Sea, where turbulent motion ensues and, so to speak, the energy of the tide is trapped. As regards the other constituent, it is a different matter. If the whole earth contracted proportionately, a decrease in the length of the day of the amounts mentioned above, would entail a shrinkage of half a foot in the radius over all the surface. This seems very improbable, and still more is the change that would account for the increase of the day in 1897.

The outcome of this criticism is that as far as astronomy is concerned, uniform duration is an abstraction, an idea; we can not find any standard time-keeper that can be called absolute or even uniform. It is perhaps improbable that one should be found. The atom is a more likely place to look for an invariable standard. But this, too, may be a delusion. Atomic motions are certainly not less complicated than planetary motions. In any case, their periods, of the order of are too small a standard.

Practical Determination of Time.

Coming to the actual determination of time, we have a similar sequence of a direct method, simple and at first sight complete in theory, but requir ing to be overlaid in practice with very numerous corrections in order to bring execution near to the idea. As already pointed out, the clock is a secondary standard, which must be adjusted in subordination to observations of the earth's rotation. The astro

nomical observation is thus often described as "finding the error of the clock." The astronomical observation, where any accuracy is aimed at, is always that of sidereal time. The beginning of the day at any place is the transit of the true equinox across the meridian. Hence, as already remarked, it is affected by nutation. The equinox itself cannot be observed, being merely the intersec tion of two abstract lines upon the sky ; but by a very long chain of observations, going back continuously to Hipparchus i so B.C., and earlier, the relative spacing on the sky of all the lucid stars, and a great many more, has been determined with continually increasing accuracy, together with the "proper motion" belonging to each. Relative to this mass of material the position of the equator and ecliptic are assigned, or what comes to the same thing, the coordinates of each star are given relative to the equinox and equator. A collection of this kind is called a star catalogue. Star catalogues are of various grades. As far as measurement of time goes we need only consider the fundamental catalogues, which are based on an elaborate critique of all the material, and of which the latest example is Boss's Preliminary General Catalogue of 6,188 Stars; Epoch 1900. The places of the stars given in such a catalogue cannot be used directly. They are "mean places at the epoch," and require correction for ( ) proper motion in the interval, (2) precession, (3) nutation, (4) aberration, (5) parallax where sensible, (6) refraction, be fore the data will accord with the true or apparent place on the day and at the place considered. As a rule these numerous and troublesome corrections (excepting the last) are computed and applied in the Nautical Almanac or other national ephemeris. Imagining then the whole heavens to rotate in a piece about the polar axis, if we could observe correctly the passage of a single star across the meridian of the place and compare it with the time registered by the clock, we should have determined the error of the latter. This, however, again requires several precautions. In the first place, the meridian must be marked, by an instrument that can survey all parts of it. Such an instrument must turn (I) at right angles to an axis that is set, (2) horizontally, and (3) due east and west. We must define what line in the instru ment is to be perpendicular to the axis. In a telescope this can be done with great precision. But the three geometrical conditions can only be achieved imperfectly, and the only way to find whether they are achieved or not, is to study the way that faults in respect to them would affect the observation, and then to make a set of observations expressly to find the faults. Further, no matter with what care and solidity the instrument is built, it cannot be trusted to keep the same values for its faults or errors from one night to the next, nor even, with changing tem perature, throughout a single night. This complicates the question very much, for these observations are themselves fallible in very much the same degree as the direct determinations of the time of transit of a star. In particular, the determination of the level of the axis has proved the source of erratic variations in "clock error" which have certainly nothing to do with the clocks. Yet reference to the level in some form is indispensable. In the transit circle at an observatory, level error is usually found by turning the telescope downwards to a bath of mercury, which supplies a mirror that is a fiducial level, and viewing the reflection in it of the webs in the focal plane of the object glass. The distance from the web to its image involves the fault of level in the axis, which can thus be measured and applied to the observa tions. For field work a smaller reversible instrument is used, in which the axis is first levelled with the help of a spirit level and half-way through the observation the pivots are lifted from their bearings and reversed east and west. This seems to give more consistent results than the other method, allowance being made for the lower telescopic power of the portable instrument. But the matter is obscure. Further sources of error arise in registering the apparent time of transit. (See CHRONOGRAPH.) In the end the best determinations of clock error are much less consistent than the going of the best clocks. Yet the former must be treated as primary sources and the latter subordinated to them. This is a matter of considerable delicacy, for the primary data, besides hav ing erratic features, are also irregularly spaced owing to weather conditions. We must take a considerable body of primary determi nations, and use the going of the clock to detect and reject their erratic features, before we use the mean run so found in order to assign the error of the clock. This work cannot be done without the exercise of judgment, and, according to their experience, dif ferent persons exercise their judgment differently. The result is seen in the comparison of time as determined at different observa tories, a comparison that has been made possible with accuracy and simplicity by means of wireless time signals. If the times differed by constant amounts it could be ascribed to an error in the re puted longitudes. But they do not. They vary rather irregularly by quantities of the order of o.i sec., even o.2sec., which are perhaps not very large, but are much larger than is tolerated in any other region of astronomy, and much larger than the methods would lead one to expect.