Masterpieces of Science 



be too sanguine of any immediate success. Still, 

 mathematical science has of late been making 

 such great advances that it cannot be unreason- 

 able to expect new and decisive conquests in this 

 region. Until we have some such new methods 

 and appliances, progress in dealing with the 

 motions of star-clusters and of the great stellar 

 system must be slow and painful; indeed, the 

 full completion of the theory of our own little 

 planetary system cannot apparently be reached 

 by our present resources, though it is true that 

 the discrepancies between calculation and ob- 

 servation are now, for the most part, so slight 

 that until our instruments and methods of ob- 

 serving are much improved they are of small 

 practical account. It is only rarely that these 

 outstanding discordances are such as to make 

 it certain that the theory itself is distinctly in- 

 adequate. 



At present it is only in certain rather infrequent 

 cases, and with considerable difficulty, that we 

 can reach the precision of a "tenth of a second of 

 arc" in the determination of the absolute direc- 

 tion of a planet or of a star; and in measuring the 

 slight annual change of direction of a star (upon 

 which our determination of its distance depends) 

 the limit of error is at least a third as great. 

 From many points of view even such precision 

 is wonderful; one-thirtieth of a second is only 

 half an inch seen at a distance of fifty miles. 

 But the stars are so remote that from most of 

 them the great orbit of the earth around the sun 

 62 



