1895. ] NEW YORK ACADEMY OF SCIENCES. 37 
we shall have the position of the fixed point in the apparent 
orbit, referred to the principal star, given by the following co- 
ordinates : 
—mp’ for the distance, 
6 for the position angle. 
It follows that if we let: 
o, p= the distance and position angle of any star on the plate 
from Eta, fully corrected of course for refraction and aberration. 
o/= the distance of the fixed point from the same star, 
we shall have: : 
; o—o’/==—m pp’ cos (9—>p). 
In Eotanlishing equations from whose solution by least 
squares we are to determine the quantity m, we cannot consider 
either the parallax or proper motion known, These three quan- 
tities are entangled together in such a way that it is impossible 
to work out either one of them by itself. The first step in the 
proposed investigation will be to free the measured distances, 
as given by Dr. Davis, from the effects of variation of scale 
value. It is almost needless to remark that I propose to use 
only the distances, and not the position angles measured by 
Rutherfurd in the present research. To get rid of the variation 
of scale value, it would seem best to apply such a correction to 
the scale value of each plate as will make the sum of the dis- 
tances of the three stars numbered 19, 41 and 62 in Dr. Davis’ 
list, a constant. These stars are on all the plates, and they are 
favorably situated. The sum of their distances from Eta is 
7141’, or 254.9215 divisions of the scale, and their distribution 
‘in position angle is such that : 
sin p = — 0.13, = cos p = — 0.20. 
They are therefore admirably adapted for correcting the varia- 
tion of scale value. To do this, let us put: 
019) x1) %2, = the distances of stars 19, 41 and 62 from Eta on 
any given plate, expressed in divisions of the scale. 
Then we must add to every distance on that plate the quantity : 
o 
254.92 92 (254. 9215 — OF ed OA ie oe) 
where © is the distance of the star from Eta, as given by Dr. 
Davis, and expressed in divisions of the scale. 
The next step is the correction of the distances for proper 
motion. This is to be done by adding to them the quantity : 
S, P, + Sy Pe 
where the symbols have the same signification as in Dr. Davis’ 
paper on the Parallax of Eta, p. 301. 
