TABLE OF contents; 



ARTICLE I. 



ARTICLE IL 



Introduction. Pp. 16. 



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List of Officers of the Sr 



ithsonian Institution 



(No. 280.) Statement and Exposition of Certain Harmonies op the 

 Solar System. By Stephen Alexander, LL.D., Professor of Astro- 

 nomy in the College of New Jersey, 1874-1875. 4to. pp. 104. 



Section I. Introductory statement ...... 



Correction of data ....... 



Table (A) of periodic times, distances, and masses of planets, respectively 



Section II. First approximation to a Law of planetary distances, with an 

 approximate tabular arrangement of the system 

 Half-planet characteristics of the Earth and Venus 



Half- planet characteristics of Uranus . . . . . 



Ratios for half-planet terms ; viz. : — 



^!P!^\ ^^] and also Mercury in aphelion , ^y^h, with r for 

 Uranus Mars Mercury in perihelion 



the leading ratio of the system, all approximate to r ; also ratio 



Earth 



t7 , approximating to r'. Symbolical arrangement represent 



ing planetary ratios ..... 



Mode of computation of terms ..... 



Laws op planetary distances, involving leading ratio r, also r , and r' 

 2d Approximate Arrangement of the system 



Question of regular variation of ratio r considered 



Subsidiary Induction in the region from Saturn to Mars inclusive 



SpeciBc values of r in the Planetary System 



Completed Arrangement of the Planetary System; exhibiting the corres 

 pondence of Law with Fact, in Table (B) ... 



System of Saturn . . . . ■ . 



Centre of gyration of a thin homogeneous ring is in the circumference oi 

 a circle bisecting the area of the ring .... 



A formula for the centre of gyration of any two equal masses similar to the 

 reduced formula for the homogeneous ring 



Definite Arrangement of the Saturn System in Table (C) ; the rings {re- 

 ferred to their centres of gyration) claiming their places as satellites 



Other relations in Saturn's System .... 



Definite Arrangement of Jiqnter's System, in Table (D) . 



Apjoroximate Arrangemeiit of the System of Uranus, in Table (E) 



10 

 II 

 12 

 13 



14 

 15 



16 



17 



18 

 19 

 20 

 21 



Each memoir is separately paged and indexed. 



