REPORT OF THE SECRETARY. 15 



The author discusses anew the expressed values of the distances in 

 question, in view of the fact that Kepler's third law is itself slightly 

 modified by the consideration due to the masses of the revolving bodies. 

 After an exhibition and discussion of the appropriate formula, the 

 author arranges the results iu the form of a table; in which the results 

 thus shown are respectively consistent with two values of the solar 

 parallax, viz. Professor Newcomb's value, - = 8".848, and that which 

 others prefer, tt = 8".78. 



Section II exhibits the laws of arrangement of the distances, both of 

 planets and their satellites, from their resijective centers of attraction, 

 without the introduction in the same connection of any physical hy- 

 I)othesis on which those laws seem to be founded or of which they are 

 the exponents. 



From a comparison of the several distances of the planets, taking five- 

 ninths of the distance of jSTeptuue from the center of attraction and five- 

 ninths of this product, &c., he finds among the several terms of the 

 geometrical series thus formed, those which represent the relative dis- 

 tance of Saturn and Jupiter, also a position among the asteroids and 

 those which represent the distance of Mars, and of Mercury in aphelion. 

 There are, however, in the geometrical series just mentioned, terms 

 which do not find their correspondences in the series of distances of the 

 planets, but which the author very ingeniously supplies by attributing 

 to certain of the planets the characteristic of half planets, the term 

 pertaining to them being indicative of the distance between the two 

 planets at which their masses would be united. 



Section III exhibits an explanation of the phenomena founded on the 

 nebular hypothesis of La Place, which seems to reconcile and account 

 for the laws in question as well as a number of other phenomena. 



Approximation to these laws have, from time to time, been exhibited 

 by the author of this paper to the American Association for the Advance- 

 ment of Science at several of its meetings, beginning with that at 

 New Haven, iu 1850 ; but it is only within the past few months that the 

 entire form and consistency of the results have been quite fully made out. 

 The principal part of the memoir was read before the National Acad- 

 emy of Sciences at its meeting in Ajiril, 1873, and some additional por- 

 tions of the same at the meeting in April, 1874. In accordance with 

 usage in such cases, the work was accepted for publication iu the. 

 Smithsonian Contributions to Knowledge. 



3. The Winds of the Globe, by the late Prof. J. H. CofSn, prepared at 

 the expense of the Institution, relative to which further information will 

 be given under the head of meteorology. Of this, 250 quarto pages 

 have been stereotyped, and the whole work, which will form an entire 

 volume of the Smithsonian Contributions to Knowledge, will be published 

 during the year 1875. 



4. The Temperature-Tables of the North American Continent, prepared 



