572 Proceedings of the Royal Irish Academy. 
Column 10 gives the value of A., the angle which the line from the 
principal star to the periastron makes with the line of nodes, measured 
on the real orbit. 
Column 11 contains the value of the semi-axis major of the real 
ellipse, measured in seconds of arc. 
Column 12 gives the name of the computer of the elements given. 
Column 13, the estimated magnitudes of the component stars. 
These are chiefly taken from Struve's estimations. 
Column 14, the colours of the components. 
Column 15 gives the spectrum of the star's light, observed as a 
single star. The numbers given refer to Secchi's types of stellar 
spectra. It will be seen that the observed spectra are of types I. and 
II. only. E"o undoubted binary star has yet been found with a 
spectrum of types III. or IV., types so characteristic of the red and 
variable stars. 
Column 16 contains the ''hypothetical parallax," which I have 
computed for each orbit from the formula p = aP-^. This formula rests 
on the assumption that the combined mass of the components of the 
binary star is equal to the mass of the sun. 
Column 17 gives the most recent parallax found by actual observa- 
tion for those binaries which have been measured for parallax. 
Columns 18 and 19 contain the values of the constants A and B, 
computed from Mr. A. A. Eambaut's formulae {Monthly Notices, 
E. A. S. March, 1890). With the aid of these quantities, the value 
of TT V at any time may be calculated, tt being the star's parallax 
in seconds of arc, and Y the relative orbital velocity in the line of 
sight in miles per second. If Y can be determined with the spectro- 
scope, then the value of tt can be immediately deduced. The maxi- 
mum value which Y can attain is equal to + A + B, and occurs when 
the star is passing through the line of nodes, the position angle of 
which is given in Column 9. Mr. Eambaut's formulae are as fol- 
lows : — 
7rY = 
— COS A + cos {6 - A)] 
TT r=^ + ^cos(^-A), 
lae sin y cos A. 
or 
where 
and 
la sin y 
P\/\-e' 
