952 REPORT—1905. 
a. If the two components of a binary system are so far apart that 
they can be readily discerned in a telescope as two points, or even as 
an elongated point of light, then visual observations, when carefully made 
and correctly treated, will yield 1, 3, 4, and 5. 
This method of inquiry will not furnish any information regarding 
2, 6, 7, 8, and 9 unless the distance of the system is known, as in the 
case of a Centauri and Striws, and then forthwith 2 and 7 are also 
known. 
The relation which exists between the visual observations of wide 
binary systems and the elements of the system have been set forth by 
many astronomers. The writer has found the formule given by Asaph 
Hall! the most convenient in practice. 
It must be remembered that as yet no close binary system has been 
separated, or even elongated, by any telescope, however powerful. I am 
not without hope, however, that one day, and that not remote, this may 
be accomplished, especially in the case of vast systems like V Puppis. 
b. If the system is bright enough to come within spectroscopic range, 
as in the case of many wide and close binary systems, then this examina- 
tion yields J, 2, 3, and 7. Spectroscopic observations yield no clue to 3, 
6, 8, and 9. 
The equations connecting line of sight observation with the elements 
of a binary system have been set forth with great fulness by Lehmann- 
Filhes.2, I have found, however, the simpler relations established by 
Rambaut? quite as convenient in practice. 
c. If two stars of a close binary system revolve in a plane so situated 
that they mutually eclipse cach other, it is evideut that the regular ebb 
and flow of light thus brought about will be a measure of the brightness, 
size, position, and figure of the component stars. If, accordingly, we 
determine from observation the variation of a close binary system we have 
the means of ascertaining 1, 3, 5, 6, 8, and 9. The relation existing 
between these elements and the light-curve of an apioidal binary system 
has been set forth by the writer in a paper recently published in the 
‘Monthly Notices’ of the Royal Astronomical Society.‘ 
The value of this method of investigation when available, as against 
a and db, is at once evident. We know six elements out of the nine, only 
2, 4, and 7 remaining unknown. Indeed, with our present limitations, it 
is only through the avenue of stellar variation that we can arrive at any 
knowledge whatever of the size and shape of a star. 
We may group the preceding statements in a table, thus :— 
ee | ‘8 | 4 | 5 | 6 | ae eer i ba. eae 
CCS eer Pee ee ee ee ae a ie 2 = = 
1 oye linet Onl o ream B18) ~ ak eal oe B = = 
Cc | — o — C C — C af | 
It is clear from this table that B and C alone will determine all the 
elements of an apioidal binary system, with the exception of 4, the position 
of the line of nodes. 
1 Astronomical Journal, No. 324, p. 89. 
2 Astronomische Nachrichten, No. 3242. 
3 Monthly Notices R A.S., vol. li. p. 316. 
4 Thid., vol, \xiii, p. 527. 
