98 
MR. GALLOWAY ON THE PROPER 
appears to move in a direction nearly opposite to that of the parallactic motion 
resulting from the assumed hypothesis, the difference of the angles ^ and 4 >l being in 
this case 173° 4 f, 9. If we reject this star also, on account of the great probability 
there is that the apparent motion is here due to the excess of the true proper motion 
of the star above the parallactic motion, we shall have from the remaining seventy- 
eight stars, 
(nn) = 120332*5, (aa) =36*4473, (bb)=2&6875, 
(ab) = ~ 5-8285, (an) = +2-308, (bn) = — 49*213, 
whence the following results, 
dA=+0° 14'-4+4° 31'-4, 
dD= + ]° 53'-8±5° 17'-2, 
e(¥)= 26°49'-8. 
Applying these corrections to the assumed values of A and D, the position of the 
point Q, for 1790, is found as follows : — 
A = 260° 0'-6±4° 31'*4, D=-f 34° 23'*4±5° 17''2. 
These values of A and D are almost identical with those which were deduced by 
Otto Struve from the combination of his own result with those of Argelander and 
Lundahl. 
From the near agreement of these results with the hypothesis, it is manifest that it 
would be an entirely useless labour to recompute values of from slightly altered 
values of the right ascension and declination of Q, the corrections of the assumed 
values being so far within the limits of the probable errors. So close a coincidence, 
whether accidental or otherwise, is not a little remarkable. In fact the southern 
stars would seem to accord with the hypothesis even better than those in the other 
hemisphere ; for the mean value of (•^—.4/) sin%, or g(T), in respect of the whole of 
the stars, is less than the mean found by Argelander from his second and third 
classes ; and if we leave out the two stars above mentioned near the pole, it is less 
even than that given by his first class, the values for his three classes being respec- 
tively 31° 3l'*0, 32° 36'*6, 35° 41'-6. 
It is difficult to form a satisfactory estimate of the probable accuracy of the result 
of this calculation, as compared with the results of Argelander and Otto Struve. 
The number of stars, though not large, might perhaps be regarded as sufficient to 
render the result worthy of confidence if the proper motions in right ascension and 
declination indicated by the comparison of the catalogues could be safely relied on ; 
but, unfortunately, in the present case, the probable errors of observation are hardly 
susceptible of exact appreciation, and the result is of course affected by the uncer- 
tainty of the data. With respect to the two recent catalogues, there is, indeed, no 
difficulty, inasmuch as the probable errors can be estimated with sufficient precision. 
Mr. Johnson considers the probable error in right ascension of a position given by 
the mean of five observations to be 0 s ‘034xsec £ in time (£ being the declination of 
