1881.] 263 [Chase. 



ary velocities, tlie equations of variation, for anj' temporary constancj'- of 



/, t, h or r, can be readily found. In the investigation of spectral lines, 



cliemical atomicities, and general kinetic phenomena, both cosmical and 



molecular, the consideration of / as a maximum often becomes_especiaJ|y 



(r^ d \ ' r II 



important. Then it is evident that/oc I -^- = r d) ; ^ oc -i,' — cc V ; 



the limiting time, therefore, becomes independent of distance, and is merely 

 a function of density. In other words, in a homogeneous medium, all analo- 

 gous motions wMcn are due to the accelerations of a central force, whether 

 of rotation, vibration or translation, are synchronous. In whatever way 

 those motions may be affected by atomic, or molecular rotation, v oc r, with- 

 out any tendency to the production of internal disturbance. All cyclical har- 

 monies and deformations must, therefore, be due to elasticity, or some 

 other form of translatory interaction. In consequence of the proportional- 

 ity of rotating velocity to the distance from the centre of rotation, it be- 

 comes possible to combine chemical elements of the most various densities; 

 foi-, while there is perfect sj'^nchronism in the normal oscillations of each 

 of the elements respectively, the atoms may intersect with radii which give 

 them equal velocities of rotation at the locus of intersection, so as to pro- 

 duce secondary and subordinate synchronisms, such as are indicated by the 

 harmonies of spectral lines, especially in Lockyer's "basic lines"* and in 

 the lines of the widely diffused and important elements, Oxygen and 

 Hydrogen. f As an illustration of the harmonies of independent and com- 

 bined synchronism, we may take the three atoms, H2 O, condensed into 

 two atoms of watery vapor. In rotation, induced, either directly or re- 

 motely, by the fundamental efficient velocity of light, we have seen that 



/T r 



t oc \ -r^^'^ ® "^ -7^ ; therefore dv'^ is constant, in each of the elements, 

 » vd 



and in the compound, e. g. : 



O {d = n; voa J) -f 2 H (<Z = 1 ; fl cc jA = 3 H, O ((? = 9 ; « oc 



and four oscillations of O are synchronous with one of H and three of 

 H,0. 



Such varied evidences of synchronism, both a priori?a\^ a posteriori, may 

 well encourage specialists, in all departments of physical science, to seek 

 for harmonies, under the guidance of the "scientific use of the imagina- 

 tion." We maj'^be assured that such harmonies are abundant everywhere, 

 and we may also be assured that whatever harmonies we find are neither 

 fortuitous nor lawless, although we may, in some cases, be unable to find 

 any other reasons for their existence than the universal canon of nodal ac- 

 tion. The more we study the detailed and coordinated ramifications of 

 such action, the greater will be our appreciation and admiration of the 

 order which is "heaven's first law," and the more confidently we can go 

 on with our researches. 



* Proc, Amer, Phil. Soc, xviii, 225-6. 

 + lb., xix, 25. 



