190 



POPULAR SCIENCE MONTHLY 



so competent and critical an authority 

 as Biitschli accepts Dar'wan's explana- 

 tion, 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 COOL- 

 ING AND METEORIC DUST ON 



THE LENGTH OF THE DAY. 

 It is well known that the day, or in- 

 terval required for one complete rota- 

 tion of the earth, is the time unit by 

 M^hich 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 cer- 

 tain 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 impor- 

 tance, especially in those branches of 

 astronomy which deal with long inter- 

 vals of time, to understand the effects 

 of such secular causes as may tend to 

 modify the length of the day. In a re- 

 cent number of the 'Astronomical Jour- 

 nal' Professor R. S. Woodward has pub- 

 lished a mathematical investigation of 

 the effects of secular cooling and of 

 accumulations of meteoric dust. The 

 cooling, and consequent cubical contrac- 

 tion, 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 La- 

 place in his 'Mecanique celeste.' As- 

 suming that the earth is in the last 

 stages of cooling he reached the con- 

 clusion 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 his- 



tory 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 

 tlie 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 3x10—^, 

 it follows that the day will be ulti- 

 mately shortened by about six per cent, 

 of its initial length, or by an hour and 

 a half nearly. Tlie length of time re- 

 quired by the earth to cool down sen- 

 sibly 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 prog- 

 ress 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 

 tbat the accumulation of such dust goes 

 on so slowly that its effect will not be- 

 come perceptible imtil the total effect 

 from secular cooling is nearly complete. 

 In round numbers, the latter effect 

 goes on two hundred thousand times as 



