1879.] "^5 [Chase. 



7. That centripetal energy (/°C - 2 ) varies as the fourth power of tan- 

 gential energy in a circular orbit*( » = -»/ fr oc ■»' — V 



Lockyer has published eightf "basic lines," which furnish illustrations of 

 all these laws, or established harmonies. 



The mean vis viva of the sethereal sphere of which Earth is the centre, tends 

 (law 3) to form a node at .4 of Sun's distance from Earth, or at .6 of the 

 same distance from Sun. Having already seen that the Fraunhofer line A 

 is the exponential correlative of the planet Neptune, we readily find that 

 this node is represented by a wave length of 4215.8 ten millionths of a 

 millimetre. For (Laws 1, 5) : 



Neptune. Earth. A. 



Log. 6442.985 : log. 214.524X.6 : : 7612 : 4215.8 



If we regard this value as a fundamental wave-length for terrestrial 

 chemical elements, we may also (Laws 6, 7), regard (4/) 4 of 4215.8 = 16.468 

 as a fundamental increment, for such harmonic undulations as may be ex- 

 cited in the elastic aether by inertial resistance. 



The "theoretical" column in the following table, is constructed by sim- 

 ple combinations of the fundamental wave length and the fundamental 

 increment. 



Theoretical. " Basic Lines." 



5269.8 -f 3 2 X 16.468 = 5418.0 5416 



4215.8 + 8 2 X 16.468 = 5269.8 5269 



5268 



5170.9 + 2 2 x 16.468 = 5236.8 5235 



5022.7 + 3 2 X 16.468 = 5170.9 b :i b i 



4215.8 + V X 16.468 = 5022.7 5017 



4 4 X 16.468 = 4215.8 4215 



Lockyer does not give the wave lengths of b s and b v (ribbs:): gives 5177 as 

 the wave length of the Mine. Law 2 is illustrated in the third theoretical 

 line (5236.8), which represents § of the interval between 5170.9 and 5269.8. 

 These are both double lines in Lockyer's system. The doubling may, 

 perhaps, be owing to the modification of the other activities by Law 2. 

 Lines 2 and 5 (5269.8 and 5022.7) are directly connected with the funda- 

 mental line. All the incremental multipliers are integral squares. The 

 difference between line 2 and line 5 is 15x16.468. The greatest square in 

 15 is 3 2 , and the greatest square in 15 — 3 2 is 2 2 . These squares are the in- 



*Ib., xiii, 245; 1873. 



t Proc. Roy. Soc. Jan. 1879. 



% Am, Jour. Sci. [2] xliii, 4. 



PROC. AMEB. PHILOS. SOC. XVIII. 103. 2c. PRINTED APRIL 25, 1879. 



