PENDING PROBLEMS OF ASTRONOMY. 49 



fication of the elements of this spheroid in order to take account of 

 the new data. It will be better to assume some closely approximate 

 spheroid as a finality ; its elements to be forever retained unchanged, 

 while the deviations of the actual surface from this ideal standard will 

 be the subject of continued investigation and measurement. 



A more important and anxious question of the modern astronomer 

 is, Is the earth's rotation uniform, and, if not, in what way and to 

 what extent does it vary ? The importance, of course, lies in the fact 

 that this rotation furnishes our fundamental measure and unit of time. 

 Up to a comparatively recent date there has not been reason to sus- 

 pect this unit of any variation sufficient to be detected by human ob- 

 servation. It has long been perceived, of course, that any changes in 

 the earth's form or dimensions must alter the length of the day. The 

 displacement of the surface or strata by earthquakes or by more 

 gradual elevation and subsidence, the transportation of matter toward 

 or from the equator by rivers or ocean-currents, the accumulation or 

 removal of ice in the polar regions or on mountain-tops — any such 

 causes must necessarily produce a real effect. So, also, must the fric- 

 tion of tides and trade-winds. But it has been supposed that these 

 effects were so minute, and to such an extent mutually compensatory, 

 as to be quite beyond the reach of observation ; nor is it yet certain 

 that they are not. All that can be said is, that it is now beginning to 

 be questionable whether they are, or are not. 



The reason for suspecting perceptible variation in the earth's revo- 

 lution lies mainly in certain unexplained irregularities in the apparent 

 motions of the Moon. She alone, of all the heavenly bodies, changes 

 her place in the sky so rapidly that minute inaccuracies of a second 

 or two in the time of observation would lead to sensible discrepancies 

 in the observed position ; an error of one second in the time, corre- 

 sponding to about half a second in her place — a quantity minute, cer- 

 tainly, but perfectly observable. No other heavenly body has an 

 apparent movement anywhere nearly as rapid, excepting only the 

 inner satellite of Mars ; and this body is so miuute that its accurate 

 observation is impracticable, except with the largest telescopes, and 

 at the times when Mars is unusually near the Earth. 



Kow, of late, the motions of the Moon have been very carefully 

 investigated, both theoretically and observationally ; and, in spite of 

 everything, there remain discrepancies which defy explanation. "SYe 

 are compelled to admit one of three things : either the lunar theory is 

 in some degree mathematically incomplete, and fails to represent accu- 

 rately the gravitational action of the earth and sun and other known 

 heavenly bodies, upon her movements ; or some unknown force other 

 than the gravitational attractions of these bodies is operating in the 

 case ; or else, finally, the earth's rotational motion is more or less ir- 

 regular, and so affects the time-reckoning and confounds prediction. 

 If the last is really the case, it is in some sense a most discouraging 



VOL. XXTI.- 



