of the Satellites from their Primaries. 177 



6. The mean values of r, all obtained by a like process, 

 have been found as follows: — for Jupiter 2.42, for Saturn 1.87 

 and 3.12, for Uranus 1.53, and for the planets 1.96. It will 

 perhaps be remarked that these numbers are near the very simple 

 quantities i^, 2, 2^, 3. 



1.53 - 1.50 =+ .03 



1.87 — 2.00 = - .13 



3.12 - 3.00 = + .12 I 



2.42 - 2.50 = - .08 



1.96 - 2.00 = — .04 



The differences are most considerable for Saturn's .satellites, the 

 distances of which appear to be most disturbed. The smallness 

 of the differences tempts us to suspect that they indicate deviations 

 from a law which would make the ratios be exactly ij, 3, 

 2^, 3. Suppose r = 2^ for Jupiter's satellites: we shall then' have 

 four equations for determining a and b. Consequently six different 

 values of each of these two quantities may be found by combining 

 the equations two and two. 



Equations. Values of a. Values of 6. 



1, 2 60485 35750 



1, 3 60485 37206 



1, 4 60485 40197 



2, 3 58057 38178 



2, 4 63141 33094 



3,4 75850 31061 



6)378503 6)215486 



Mean 63084 35914 



Empirical Values. True Values. Differences. 



Hence a = 63084 6o485 - 2599 



a + b = 98998 96235 -2763 



a + rb = 152869 153502 + 633 



a + r^6= 287546 269983 -17563 



Vol. III. Part I. Z 



