142 LECTURE ON THE 



live but for a day — the ephemera — may have so many sensations (we 

 cannot call them ideas) during the course of that day that this period 

 may appear on the whole as a long life. Such a measurement of time, 

 varying according to circumstances, is inappropriate; it is evident, 

 therefore, that some other must be sought. 



In a good standard of measure of time there are two or three prop- 

 erties which are indispensable. And first, it should be readily acces- 

 sible: a measure shut up so that it could not be reached would be 

 good for nothing. Second, it should be convenient, both as to size 

 and mode of application. Third, the measure should, if possible, be 

 invariable. Now, there is a standard in nature which embraces these 

 three properties, and that is, the rotation of the earth about its axis. 



It is for some purposes convenient, as regards size and mode of ap- 

 plication, inasmuch as it is nearly the length of the ordinary day. It 

 possesses the third property, invariability. But how do we know that 

 the rotation of the earth is invariable ? This fact may be ascertained 

 by comparing it in the long run, or with something else known to be 

 invariable. To illustrate this, suppose the minute hand of a clock by 

 'some means to go too fast; when it arrives at 12 the hour hand will be 

 some wa}^ behind the position which it would otherwise have occu- 

 pied; and this discrepancy, however small at first, if permitted to go on. 

 will become more and more evident. The moon revolves about the 

 earth in a certain mumber of days, as days now are. Now, if counting 

 ages backward, the day had been changed, the whole number of days, 

 according to our present measurement, would not correspond to the 

 exact number occupied in the moon's revolution, and therefore the 

 position of the moon 'on a ^given day, by this backward reckoning, 

 would be found to be untrue. That this is not so is found by a com- 

 parison of computation with the observation of an eclipse of the 

 moon more than seven centuries before the Christian era, and from it 

 is safely concluded that the rate of the earth's rotation has not changed 

 one three-hundredth part of a second. There are causes which might 

 change this. The most prominent among these is a change of bulk 

 arising from a loss of heat. The loss of heat does not, in every case, 

 produce a shrinking. Cast iron presents a familiar example, as it at 

 first expands in cooling. It may, therefore, happen that within the 

 earth a great deal of expansion and contraction occurs, though there 

 is no sensible shrinking on the whole. Even if the earth actually 

 shrunk, the loss of heat and size would not diminish the force of rota- 

 tion at all, but the time of rotation will diminish with the circuit. If 

 I take a ball with a string attached, and, by means of the string, cause 

 it to revolve around my arm, and then wind up the string, as it pro- 

 ceeds in its revolutions the motion of the ball will become quicker 

 and quicker, until the string is entirely wound up. 



Let me here observe that the earth has more than one motion. It 

 revolves around its axis, and in that revolution pauses not, while it 

 also moves around the sun. Before proceeding to consider this fact, 

 it is desirable to ascertain when a sphere which has two motions has 

 completed a rotation. 



