698 



TRANSACTIONS OF THE AMERICAN INSTITUTE. 



the foregoing principles to them. The orbital velocity of Mimas, 

 the satellite nearest to Saturn, is 34,986 miles per hour. This 

 number, divided by 714, the common difierence, gives a quotient 

 of 49, which is therefore assumed as the serial number of Mimas. 

 The most distant possjble satellite of this series has a theoretical 

 velocity of 714 miles per hour, which is the same as the common 

 difierence. Japetus, the most distant known satellite of Saturn, 

 has 11 for his serial number, because his velocity is 11 times 714 

 miles per hour. The following table (12) will, now be understood. 



Serial Relations of the Square Roots of the Distances of 

 Saturn's Satellites. 



Ex])lanaion of Table 13. 

 We will next examine table 13 of the square roots of the dis- 

 tances of Saturn's satellites. The mean distance of Mimas, the 

 nearest satellite, is 126,000 miles. The square root of this num- 

 ber is 35.5, which, if multiplied by the serial number 49, gives a 

 product of 1,740, which is the square root of the distance of the most 

 distant possible satellite of this series. 1,740 being divided by 



