188 ANNUAL REPORT SMITHSONIAN INSTITUTION, 193 3 



Observations of the moon at the present time are accumulating at 

 a rapid rate — in 1931 over a thousand were compared with their 

 theoretical values. There are probably some 10,000 available in 

 the 20 years elapsed since the present theory was finished, and the 

 constants of that theory were determined from nearly 30,000. 



Up to this point I have dealt only with those bodies in the solar 

 system for which the calculated theories have a degree of accuracy 

 similar to that of the observations. To complete the list one must 

 mention certain of the satellites which have been under observation 

 for long periods of years. Of the large numbers of small planets 

 with diameters ranging from 300 miles down which have been dis- 

 covered and kept in view since the beginning of the nineteenth 

 century, only one, Vesta, has had its orbit calculated with an accu- 

 racy similar to that of the orbits of the great planets. In addition 

 we have some scores of comets which belong to the system, and come 

 into the range of observation at regular intervals. 



To sum up the results of this immense amount of calculation and 

 observation, it may be stated that no deviation from the Newtonian 

 or the extended relativistic laws of motion and gravitation has yet 

 been established in the motions of the solar system. Such apparent 

 deviations as have been confirmed have hi'therto been found to be due 

 to other sources of disturbance, either in the method of observation 

 or in the calculations, or can be ascribed to a lack of knowledge of 

 the distribution of the matter which may cause the deviation. But 

 the desire for accuracy has done more than merely to give a verifi- 

 cation of the laws, for through it remote effects of these laws have 

 been found which could hardly have been discovered in any other 

 way. The amount of the tidal friction, which has played an impor- 

 tant part in the past history of the system, the verification of the 

 relativity laws, the changes in the rate of rotation of the earth, may 

 be cited as modern examples. Other cases of more technical interest 

 will occur to the astronomer. 



Perhaps the most useful service this work is performing at the 

 present time is the more accurate determination of the motion of the 

 earth relatively to the stars, or what is the same thing mathemati- 

 cally, the motion of the stars relatively to the earth. We can only 

 observe from our moving platform, and to get exact results it is 

 necessary to know how the platform moves. Thus the emphasis 

 shifts from time to time, but the work goes on, and ultimately most 

 of it is found to have value for one purpose or another. This is 

 desirable, for there is no way of recalling the past, and we must 

 capture the present with the hope of benefits in the future. 



