CERTAIN HARMONIES OF THE SOLAR SYSTEM. 79 



is approximately equal to that distance which corresponds to the period of rotation 

 of the central body of that system,' or say" 



a=1680ifiPf, 



where M — mass of central body, in terms of the mass of the earth, P the period 

 of the axial rotation in hours, /I in miles as before. 



It thus appears that dividing the value of X for any system by the value of 

 ilfiPI for the central body of the system, the quotient should be 1580. For the 

 Solar, Jovian, and Saturnian the quotients are 1790, 1340, 1720, mean 1620. For 

 the Earth ;i = 13100 ; so that regarding tife Moon as a fourth satellite (the three 

 interior ones missing) the theoretical distance is 210,000 miles.^ 



The paper concludes with some considerations as to M. Lescarbault's planet 

 Vulcan. 



[Sir J. Herschel, in a Note to Article (505) of the 11th edition of his Ouilines 

 of Astronomy, makes the following statement : — 



" Another law has been proposed (in a letter to the writer, dated March 1, 1869), 



by Mr. J. Jones, of Brynhyfryd, Wrexham. If the planets' mean distances from 



the sun be arranged in the following orders : Mercury, Venus, Jupiter, Saturn ; 



the Earth, Mars, Uranus, Neptune ; the product of the means in each group is 



nearly equal to the product of the extremes. 



Venus X Jiwiter Earth x Neptune . ^ n j- ■ 



-^Tf fT-, = -^ Yf = 1- ill point 01 tact the first traction 



Mercury x oaturn Mars x Uranus '■ 



= 1.02, and the last = ^3, so that the approach to verification of the law is really 



very near." 



Now the first fraction 



Venus X Jupiter 



may be resolved into 



Mercury x Saturn'' 



Venus Jupiter 



X 



Mercury Saturn 



An inspection of the ratios exhibited in our Table (B), in fl4), will show that 

 the first of these component fractions expresses a whole planet ratio r ; and the 



second component the inversion of that, - . So that the value of the whole 



r 



expression 



Venus X Jupiter ij-i.Vi. ^.i, -^j ^li 



^f— -;— -, resolved into its two components here specified = - X = 1- 



Mercury x oaturn 1 r 



rr-u ii, i-i, f 4.- Earth x Neptune , ^ ^ ■ ^ HJarth Neptune 



ihen the other traction, —-: ± , may be resolved into x tt^ '■> 



Mars X Uranus Mars Uranus 



' The error is here nearly \ of the quantity to be determined ; whereas in our Tables (B) to (E), 

 and even (F), inclusive, the greatest difference between veritable Law and Fact is that in the 

 instance of Uranus, in which the discrepancy is not Jg- of the quantity to be measured, and even for 

 that [5 of (43)] a special reason is assigned. In almost every other instance the discrepancy is far 

 less than that; indeed, all but incomparably small. The greater differences specified in Mr. Hall's 

 paper are such as are characteristic of " Bode'a Law." 



