ORIGIN OF ELEMENTARY SUBSTANCES. 121 



member of the solar system an arithmetical mean, or half 

 the sum of the distances of the first and third members. 



3. The atomic weight of the fourth member in each 

 group of elements is equal to the sum of the atomic 

 weights of the second and third ; and the distance of the 

 fourth member of the solar system is also equal, within a 

 unit, to the sum of the distances of the second and third 

 members. 



4. As the smallest planetary distance is a constant 

 function of the distances of the outer planetary bodies, so 

 is the smallest atomic weight in each group a similar 

 function of all the higher members of the series to which 

 it belongs. It will also be observed that the plus and 

 minus signs of these constants are correlated respectively 

 with the interplanetary spaces, and the elementary con- 

 densations. 



5. Each of the atomic weights, after the third in the 

 groups, is an arithmetical mean of aiiy pair of atomic 

 weights at the same distance above and below it ; and the 

 distance of each member of the solar system (minus the 

 constant 4) is a mean proportional of the distances of any 

 two members, externally and internally to it, from the 

 central body. 



6. The geometric ratio of the planetary distances from 

 each other terminates at the two members nearest the 

 central body, and approaches to an arithmetical one ; and 

 a similar departure is also noticeable from the regular 

 arithmetical series of the atomic weights of the first two 

 members of the groups, which renders the third less than 

 an arithmetical mean of the atomic weights of the second 

 and fourth members. 



While most of the atomic weights in Tables II., III., 

 excluding fractions, agree with those generally received 

 by chemists, the remainder, except C8esium=i33, do not 



