PROCEEDINGS OF THE POLYTECHNIC ASSOCIATION. 697 



repeated. The second column contains the serial numbers, by 

 ■which the 808 is successive]}^ multiplied. The third column con- 

 tains the resulting theoretical velocities ; and the fourth column 

 contains the actual velocities. 



• Table 10. 



Theoretical Actual 

 Common Serial velocities. velocities, 



difference. numbers. Miles p. h'r. Miles p. h'r. 



Callisto--. 808 x 22 = 17,776 17,743 



Ganymede 808 ^' 30 " 24,240 24,519 



Europa. 808 " 38 " 30,704 30,716 



lo 808 " 48 " 38,784 38,772 



Serial, relations of the Square Roots of the Mean Distances 

 OF THE Satellites of Jupiter. 

 The mean distance of lo, the nearest satellite to Jupiter, is 

 269,000 miles ; the square root of this number is 518,651, which, 

 if multiplied by the serial number (48), gives a product of 

 24,895,3, the square root of the most distant possible satellite of 

 the series. If we divide 24,853 by the serial number of any 

 satellite in the series, we obtain the square root of the mean dis- 

 tance of that satellite. 



Table 11. 



Most distant Square roots Squares or 



square root Serial of theoretical Actual 



of the series, numbers. distances. distances. distances. 



Callisto.-,. 24,895.3 -h 22 ='1,131.6045 1,280,529 1,152,000 



Ganymede . 24,895.3 " 30 " 819.843 688,639 680,000 



Europa 24,895.3 " 38 " 652.771 415,100 426,500 



lo 24,895.3 " 48 " 518.651 169,000 269,000 



The first,, or left-hand column in table 11, contains 14,895.3 

 repeated. This number was obtained by multiplying 518.651, 

 the square root of the distance of lo, the nearest of Jupiter's satel- 

 lites, by its serial number, 48. The second column contains the 

 serial numbers, by which 24 895.3 is successively divided to pro- 

 • duce the square roots in the third column ; the squares of which 

 are the theoretical mean distances in the fourth column. The fifth 

 column contains the actual mean distances. 



Serial relations of the Orbital Velocities of Saturn's Satel- 

 lites. 

 Explanation of table 12. 

 Let us now examine the system of Saturn's satellites, and apply 



