GRAVITATION — BROWN 187 



positions during the years 1926-30 have scarcely exceeded two-tenths 

 of a second of time, and the majority of them are smaller. But the 

 problem of accounting for such dillerences as exist has become more 

 diilicidt, mainly because they are so much smaller than those to be 

 dealt with in the past. Effects that could previously be laid aside as 

 too small for consideration must now be taken into account. Changes 

 in our measure of time, for example, must be considered, at least 

 in dealing with the inner planets. A3 far as the outer planets, 

 Uranus and Neptune, are concerned, there is some evidence that 

 the agreement with observation could be unproved by a new deter- 

 mination of their theoretical orbits. Althougli a new planet, Pluto, 

 has been discovered in their neighborhood, the weight of the evi- 

 dence at present available indicates that its mass is too small to 

 affect their motions to an extent sensibly greater than the errors 

 of observation within the interval during which the planets have 

 been followed. 



The latest theory of the moon's motion appears to satisfy the 

 observations when we take account of the changes in our measure 

 of time. It must be stated, however, that as the moon is the chief 

 30urce for the exact detennination of these changes, the argument 

 is not conclusive ; it depends as much on the nature of these changes 

 and on the evidence that can be gathered from other sources. There 

 is some difference between the calculated and observed motions of 

 its perigee. 



The present theory of the sun's action should be taken to another 

 place of decimals before it can be asserted that this difference is 

 real, but the amount of calculation needed to obtain this increased 

 accuracy is so great that it will hardly be undertaken as long as other 

 influences on its motion are in doubt. The chief of these is the effect 

 produced by the distribution of the moon's mass; the constants 

 adopted for this effect are very doubtful, and a redetermination of 

 them from accurate observations of the librations extending over a 

 long period of years is the first step. 



I have mentioned several times the fact that large numbers of 

 observations have contributed mainly to our knowledge of the accu- 

 racy of the laws which govern the motions of the bodies in the solar 

 system. Some statistics may be of interest. In his Astronomical 

 Constants (1895) Newcomb gives the following numbers used in his 

 discussion : 



Sun 40, 176 



Mercury 5, 421 



Venus 12, 319 



Mars 4, 114 



A similar discussion taken up at tlie present time would probably 

 require the consideration of an additional 10,000 to 15,000. 



