134 TRANSACTIONS OF THE [APR. 11, 



varies inversely as the cube of their distance, and directly as the 

 sine of their declination. 



It requires about nineteen years for the moon to go through a 

 cycle of such changes. There is an increase of its effective pull 

 for about nine and a half years, and a decrease for as many more. 

 The former, by the first law, causes tilting towards the ecliptic ; 

 and the latter, by the second law, causes tilting from the ecliptic. 

 This is nutation in latitude ; that in longitude is effected in the 

 same way. 



The same reasoning applies to solar nutation, but its cycle is 

 only a year. 



There is a secular variation in the eccentricity of the earth's 

 orbit, and this generates a secular change in that of the moon. 

 Hence there must be a secular change in nutation. This I 

 pointed out more than two years ago in a paper before Vassar 

 Brothers Institute, of Poughkeepsie. 



It is an interesting fact that last summer it was announced 

 in Nature, and also, I believe, in Science, that M. Folic had dis- 

 covered a secular change in nutation, and that approximately its 

 period is 30,000 years. It is confirmatory of the view taken in 

 this paper of the physical cause of such variation, that what 

 may be called the present cycle in the earth's orbital eccen- 

 tricity occupies about the same time. Some past cycles have 

 been much greater. Hence, the secular change in nutation is 

 itself subject to changes; all, however, obedient to one grand 

 law, viz. : 



Increase of the '' second force " increases the depth of the 

 nutation, while decrease of that force increases its height. 



The above laws and their application to nutation are, I be- 

 lieve, new, and, as at present informed, I claim them as such. 



Whether they account for all the nutation is a question out- 

 side of my present purpose. That change of distance is a real 

 cause seems to me beyond doubt. 



Note. — A series of experiments on all forms of gyrating bodies per- 

 formed in my laboratory give the same testimony. A large number of 

 these, with drawings " from life," are published in my Studies on Gy- 

 rating Bodies. See Proceedings of Vassar Brothers Institute, 1885. The 

 "Studies," 204 pp., can be had of the writer. 



