so competent and critical an authority as Bütschli accepts Darwin's explanation, as amplified by later workers, not only as a possible one, but also as the most probable one thus far advanced.
THE EFFECT OF SECULAR COOLING AND METEORIC DUST ON THE LENGTH OF THE DAY.
It is well known that the day, or interval required for one complete rotation of the earth, is the time unit by which the succession of terrestrial and celestial events is measured. The earth revolves with a regularity which far surpasses that of the best clocks and chronometers except for short intervals of time, such as a few minutes, or a few hours at most. But it is not certain that the day has been of the same length in the remote past as at present, or that it will remain of the same length in the distant future. It is therefore a matter of prime importance, especially in those branches of astronomy which deal with long intervals of time, to understand the effects of such secular causes as may tend to modify the length of the day. In a recent number of the 'Astronomical Journal' Professor R. S. Woodward has published a mathematical investigation of the effects of secular cooling and of accumulations of meteoric dust. The cooling, and consequent cubical contraction, of the earth tends to shorten the day; while the increment to the earth's mass from meteorites, of which not less than twenty millions daily fall into the atmosphere, tends to lengthen the day. The effect of secular cooling was considered to a limited extent by Laplace in his 'Mécanique céleste.' Assuming that the earth is in the last stages of cooling he reached the conclusion that the length of the day has not changed appreciably in the past two thousand years. Without making any assumption as to the present stage in the history of cooling, Woodward shows that during no interval so short as twenty centuries in the entire history of cooling can the length of the day change by so much as a thousandth of a second from the cause in question. In fact, so slowly does the effect of secular cooling accumulate that the day will not change, or has not changed, as the case may be, by so much as a half second in the first ten million years after the earth began to solidify and to lose heat by conduction through its crust. On the other hand, the shortening of the day which must come with the end of the process of cooling is a very sensible fraction of its present length. For this total effect Woodward gives a remarkably simple expression, namely: the ratio of the change in length of the day to its initial length is equal to two-thirds of the product of the fall in temperature of the earth by its cubical contraction. Supposing the earth to have been initially at a temperature of 3000°C., and that its cubical contraction is the same as that of iron, or about 3 x 10—5, it follows that the day will be ultimately shortened by about six per cent, of its initial length, or by an hour and a half nearly. The length of time required by the earth to cool down sensibly to the temperature of surrounding space is very great. Nothing short of a million years is suitable as a time unit for measuring the historical progress of such events. Thus Woodward shows that it will require about three hundred thousand million years for the earth to accomplish ninety-five per cent, of its contraction, and that after a million million years its contraction would no longer sensibly affect the length of the day.
To what extent is this shortening of the day due to contraction offset by the lengthening due to accessions of meteoric dust? The calculation shows that the accumulation of such dust goes on so slowly that its effect will not become perceptible until the total effect from secular cooling is nearly complete. In round numbers, the latter effect goes on two hundred thousand times as
