15 
If we combine these results with those contained in my 
former paper, we obtain an indirect comparison of Sir John 
Herschel’s scale with that of Professor Struve. The results 
thus obtained present but a moderate accordance with those 
of Sir John Herschel’s direct comparison, as given in Vol. iii. 
of the Memoirs of the Royal Astronomical Society. This is 
perhaps owing, apart from the indirectness of the method, to 
the fact that I have not confined myself to the list of stars 
employed by Sir J. Herschel, and that my comparison was 
made with the magnitudes of the Mensurce Micrometricce , 
and not with those of the Dorpat Catalogue . 
“ Note on the Combined Magnitude of two Stars in close 
proximity,” by George Knott, F.R.A.S. Communicated 
by Mr. Baxendell. 
It is sometimes convenient to know the magnitude resulting 
from the combined effect of two stars in such close proximity 
as to appear as one star , either to the naked eye, or in a tele- 
scope of insufficient power to separate them. 
If m and m-\- Am be the magnitudes of two stars so circum- 
stanced, and p the decreasing ‘ light-ratio,’ then if g be the 
combined magnitude required, it may easily be shown that*: — 
,t=m+ (l + P M 
log. p 
It thus appears that if we tabulate the values of the 
function A j“ _. P (the sign of which it will be 
log. p 
observed is essentially negative,) for certain definite values 
of Am, we can obtain, by inspection, the value of the correc- 
tion to be applied to the numerical magnitude of the greater 
of two stars closely juxtaposed, in order to obtain the magni- 
tude resulting from their combination. 
* I have adopted the symbols of the formula as kindly communicated to 
me by Lieut. Tupman, R.M.A., F.R.A.S., as being more symmetrical than 
those of my own independent investigation. 
