Chase.] 602 ^-^^^^ 4^ 



piter's orbit. If we suppose the length of each -wave to be increased in 



1 

 the ratio r = (1901.355 ~ 1900.355)*, we get the following approximations : 



Sehellen. 

 760.09 

 718.50 

 686.68 

 656.18 

 589.50 

 526.89 

 517.20 

 486.06 

 430.72 

 410.12 

 396.80 

 393.28 



The lines can be grouped in three sets : — 1. A, a, B, D^ ; 2. C, b.,, 

 F, 7i ; 3. E, G, Hj, H^. All members of the first and third groups are con- 

 nected Mith the other members of their own groups hj some power of r* ; 

 those of the second group, by some power of r^ ; the memliers of the third 

 group being connected with those of the first by some odd power of r"^ ; 

 those of the second with those of either of the other groups, by odd powers 

 of r. Three lines of the middle group, C, F, /i, are hydrogen lines. The 

 boundaries of the group are phyllotactic ; 5 C = 8 A. 



153. Interpretation and Mass-Belations. 

 The considerations involved in the foregoing notes were orbital velocity 



I r^ cc \~^ /> gravitatmg velocity, | «j = (/OC 7^ I, the constant velocity 

 of light, (v.^) and inertia, or mass. Orbital velocity varies as the fourth 



root of gravitating velocity, [Vg oc i\* ) ; hence the ratio of increase varies 

 as the fourth root of the relative disturbance of inertia, r = (1901.355 h- 

 1900.355)4. 



If we take the constant relation between gravitating and photodynamic 

 action at Earth's surface as a unit, (2h = !)> there should be some har- 

 monic relation between p^ and Jupiter's incipient perturbation, {p^ = 

 ■?■* — 1), dependent on the masses of Earth, (m.^), and Jupiter, (m^). Earth's 

 reaction upon its linear centre of oscillation, relative to the centre of the 

 "line of force " which connects it with Jupiter, is exerted at (^ of |) = ^ of 

 the distance of Jupiter's action upon Earth, consequently with a six-fold 

 relative efficiency. Accordingly we find : 



m, 6 7)- 6 1 



«i3 ^ 1^ ~ 1900.355 — 316T26 



--" = 316.726 X 1047.879 = 331890 

 P3 =92,796,300 miles. 



