1878. ] 345 (Chase. 
rangements among spectral lines of chemical elements. M is the common 
dividend ; the combinations of various powers of z and 7 are divisors. 
~ — ratio of circumference to diameter, and, as I have also shown, ratio 
between incipient and complete centrifugal dissociative force. 
n = Gummere’s criterion = 11.6569 Saas I give it this designa- 
tion, because I obtained it from a calculation which was suggested by a criti- 
cism of Samuel J. Gummere, late President of Haverford College, on En- 
nis’s theory. The criticism, together with Ennis’s rejoinder, may be found 
in Appendix II, to ‘‘ Origin of the Stars.’? Gummere says, of the relation 
1: //2; ‘‘ This relation being essential to stability, must exist, whatever 
be the origin of the velocity. Hence it proves nothing as to the source of 
the orbital velocity, except that it is entirely compatible with the assump- 
tion that it is due to gravity.’’ This cautiousness of statement is like that 
which has enabled Herschel’s presentation of the nebular hypothesis to adapt 
itself to all the astronomical discoveries which have hitherto been made. 
f. — Sun’s present nebular radius, or the distance at which planetary 
r~' olution and solar rotation would be synchronous. 
The subscript figures denote apsidal positions: 1, secular perihelion ; 
2, Mean perihelion ; 3, mean ; 4, mean aphelion ; 5, secular aphelion. 
The multiple, 2, denotes the primitive nebular radius which would give 
the vis viva of circular-orbital revolution, by simple condensation to the 
present planetary radius-vector. 
It should be noted that critical positions of all the planets, together with 
some asteroidal positions, are represented in the table; that all the sym- 
metrical combinations of z and m, which are embraced in the table, have 
planetary representatives ; that both rupturing factors seem to have been 
simultaneously operative ; that, after the first conversion of linear into cir 
cular motion, the exponential increments of z are figurate ; and that: ° 
relations have all been found, not by happy guessing, but by following indi- 
cations which are mathematically deducible from the necessary action of 
central forces. 
The following table shows the character of the accordances : 
Theoretical. Observed. Manian Meainem 
M =~ xn 60.210 2w, 60.668 4 1142 +. .142 
eee 19.165 { Ge 19.184 == (i) — .019 
2h, 19.078 + .087 +. .087 
20) 5.168 — ,003 — .003 
M — zn? 1.644 a 1.644 .000 = 1230) 
Min 1.942 2D, —«*1.932 + .010 — .058 
iste § on 3) 2.408 Eiht 132 
20, 1.396 — .004 find 
bigho ae 9, 723 + .007 + 097 
28, 114 = hou Lig 
M = x‘n? .167 Op LB? .000 .000 
*See ante, p. 99. 
