Astronomy 587 



of the earth's orbit for every 10,000 years during a period of 

 2,000,000 years is given. The equinoxes perform a revolution 

 in the average interval of 25,694.8 years. The maximum 

 variation of the tropical year is now shorter than in the time 

 of Hipparchus by 11.30 seconds. The mean value of the 

 obliquity is 23° 1 7' i 7'', and the limits are 24° 35' 58" and 

 21° 58' 36". A paragraph on the advantages we derive 

 from a spheroidal earth contains highly interesting conclu- 

 sions too long to be quoted here. 



The duration of the different seasons is also greatly modi- 

 fied by the eccentricities of the earth's orbit. At present the 

 sun is north of the equator scarcely i86>^ days, and south 

 of it 178^ days. 



In the past history of the earth these periods have been 

 changed so as to give a summer, in one hemisphere, of 198% 

 days, and a winter of only i66>^ days. The variations of 

 the sun's distance from the earth in the course of a year, 

 at such times, are also enormous, amounting to almost one- 

 seventh part of its mean distance — a quantity scarcely less 

 than 13,000,000 miles. 



The foregoing illustration of a few of the results of this 

 memoir will show the far-reaching nature of the problems 

 with which it deals, and perhaps of others, of no less im- 

 portance, which it suggests. Its introduction of eighteen 

 pages presents these problems in a clear light. 



HARMONIES OF THE SOLAR SYSTEM 



In this paper,^ which is printed in the "Contributions," Pro- 

 fessor Stephen Alexander seeks to set forth certain numer- 

 ical relations between the distances of the planets and 



1 " Statement and Exposition of Certain Harmonies of the Solar System," 1875 ; in 

 Volume XXI of the "Smithsonian Contributions to Knowledge," first paper. 



