CHANGES IN LENGTH OF DAY— BROWN 171 



Much more startling are changes which seem to be irregular and 

 which take place in a much shorter time. Our knowledge of them 

 arose originally from a discovery by Simon Newcomb that there was 

 an apparent oscillation in the motion of the moon which was not 

 accounted for by theory. I have said above that the theory of the 

 motion of the moon is the most accurate amongst those of all astro- 

 nomical bodies. But this has been acliieved only at the cost of great 

 labor. Starting with Isaac Newton who formulated the laws of motion 

 and gravitation from which the theory is developed, a host of workers 

 have toiled to improve it — Euler, Laplace, Hansen, Delaunay, New- 

 comb, and G. W. Hill, to mention only a few of the most famous great 

 mathematicians and great astronomers who have added successively 

 to it. Finally, the writer, building on the work of liis predecessors 

 and especially on that of G. W. Hill, gave the results of a calculation 

 which, if free from mistakes, had an accuracy at least comparable with 

 that of observation. This last work had to be done by old-fashioned 

 methods since macliines were not then available and the human factor 

 entered largely. To make assurance doubly sure, the work is being 

 repeated almost wholly by machinery so that little doubt will remain 

 as to the accuracy of the results. 



At the time of Newcomb 's discovery, however, the best theory was 

 that of Hansen, and it was by no means certain that some important 

 term had not been omitted which could account for the deviation. 

 The completion of the writer's theory showed that such a solution 

 of the difficulty was highly improbable since the deviation was much 

 larger than any probable mistake in the theory. 



The question of the source of the deviation was reopened by Innes, 

 who, in examining the deviations of the planet Mercury, found char- 

 acteristics which with some stretching of the imagination could be 

 compared with those given by the moon. But the observational 

 material was too poor to carry conviction. However, it suggested to 

 the writer the thought that perhaps another body, the sun, might 

 show changes more certainly than Mercury. The sun moves much 

 more slowly around the earth than Mercury does around the sun and 

 on that account is a much poorer testing body. On the other hand, 

 it has been continuously and carefully observed at every fine noon 

 for 170 years and perhaps the mass of observations could make up 

 for the slow motion. 



The material was gathered and the curves of deviations from its 

 theoretical orbit drawn, and it was immediately seen that the ques- 

 tion had been solved — the deviation was not in the motion of the 

 moon but in our measure of time. Newcomb had suggested this as a 

 possibility, and Innes had adopted it to explain his deviations. 



I must go into some further details in order to show what the 

 evidence is worth. Newcomb had represented the deviations of the 



