PRESIDENT’S ADDRESS. 19 
been utilised by him. Dividing these results into groups we get the 
following comparison :— 
Comparison Groups arranged in order of Proper Motion. 
| Parallax 
ne of Proper Motion | Magnitude Yale—Kapteyn | 
ay Yale Kapteyn | 
: al i : 4 - Md | 
21 0-14 3°8 0:028 0 026 + 0°002 
39 0:49 6:3 "042 “055 — ‘013 
45 0:59 67 068 | 060 + ‘008 
46 0-77 65 “047 ‘O74 — ‘027 
22 1:50 6:2 118 124 — °006 
Groups arranged in order of Magnitude. 
Parallax | 
ae of | Proper Motion | Magnitude || —— | Yale—Kapteyn 
ai Yale Kapteyn | 
é ee Oa eS eee 
10 | 0-61 08 0-103 0°110 | —0:007 
29 53 3° 076 075 ||, +. 001 
33 63 56 064 ‘070 — ‘006 
34 ‘73 6-7 055 00) OTT 
31 68 76 025 061 || = -086 
36 80 83 056 062 | — ‘006 
| / Parall 
No. of Proper | Magni- aed e Yale— 
—— Stars | Motion | tude | Yale Teantend Kapteyn 
— | or al = = a= 
Spectral Type I. iat haa. |s 40 Lit ogra, | Pure 0'000 | 
ss SSL, 81 | 0°67 | 53 0:067 0-074 —0:007 
These results agree in a surprisingly satisfactory way, having regard 
to the comparatively small number of stars in each group and the great 
range of parallax which we know to exist amongst individual stars having 
the same magnitude and proper motion. In the mean perhaps the tabu- 
lar parallaxes are in a minute degree too large, but we have unquestion- 
able proof from this comparison that our knowledge of stellar distances 
now rests on a solid foundation. 
The Distribution of Varieties of Luminosity of Stars. 
But, besides the mean parallax of stars of a particular magnitude and 
proper motion, it is essential that we should know approximately what 
percentage of the stars of such a group have twice, three times, é&c., the 
mean parallax of the group, and what percentage only one-half, one- 
third of that parallax, and soon. In principle, at least, this frequency- 
law may be obtained by means of the directly determined parallaxes. 
For the stars of which we have reliable determinations we can compare 
; c2 
