362 L iterary and Philosophical Society. 



mences at the second and corresponding member of each 

 group. 



' 2. As the atomic weight of the second element in each 

 group is half the sum of the atomic weights of the first and 

 third elements, so is the distance of the second 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 the 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 func- 

 tion 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 condensations. 



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

 groups is an arithmetical mean of any 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 arith- 

 metical series of the atomic weights of the first two mem- 

 bers of the groups, which renders the third less than an 



