1881.] ^'«^ [Chase. 



centres of nebulosity and of nebular planetarj' inertia, | of Jupiter, the 

 mean distance of asteroids 167 and 168, asteroid 85 and asteroid 149. The 

 four roots between 893.6 and 464.1 are all asteroidal, the centre of asteroidal 

 density being represented by 569.1. Newcomb gives the mean distances of 

 172 asteroids, of which 104 are at mean distances ranging between 506 and 

 594. The curve of frequency has a maximum at 566 ; the mean distance of 

 the four chief asteroids in point of magnitude, Ceres, Juno, Pallas and 

 Vesta, is 567 ; the mean, distance of the five which include the maximum 

 and are limited by equal ordinates of frequency, is 5(j9.1. The mean dis- 

 tance of Mars is an arithmetical mean between 383.3 and 270.3, which cor- 

 respond very nearly with the secular apsides. 



38. Nodes in the Dense Belt. 



In my harmonic anticipation of intra-Mercurial planets,* I showed 

 that the controlling influence of Jupiter is modified by the nodal influences 

 at the centre of the dense belt. This modification is also shown, and per- 

 haps more strikingly, in the relations between the sethereal and cosmical 

 nodes within the belt. If we begin with Mars, at the outer limit of the 

 dense belt, and take successive increments of -V- x -0153, we find the follow- 

 ing accordances : 



The infra-Telluric loci which represent the harmonic roots are Yenus's 

 mean perihelion ; Yenus's linear centre of oscillation of incipient subsi- 

 dence, or of secular aphelion ; Mercury, semi-axis major ; Mercury, peri- 

 helion ; Mercury, linear centre of oscillation. All of the harmonic roots, 

 both supra-asteroidal and infra-asteroidal, correspond ^recj-^eZy with plane- 

 tary loci, and very nearly with apsidal or mean positions. All the harmonic 

 quotients represent regions of spectral interference, and correspond very 

 nearly with the mean positions of important spectral lines. The numer- 

 ous evidences which have been adduced of the influence of planetary dis- 

 turbances upon Sun spots, together with Lockyer"s explanation of the spots 

 by "the approach or retreat of vapor," seem to justify a careful and sys- 

 tematic study of the variations in the position and breadth of spectral 

 lines, such as I recommended in my note of August 23, 1877. f By obser- 

 vations at diff"erent hours of the day, it would soon be found whether there 

 is any systematic daily variation ; three months would suffice for approxi- 



*Proc. Am. Phil. Soc, xiii, 2>7-y. 

 tib. xvii, 112. 



