Parallaxes of fi and 9 Cassiopeise. 9 



inclined to regard (a) as the best scale value formula deducible from 

 the evidence made available up to the present time. In the case 

 of the ^ Cygni plates, whose mean focal reading is 7.68, and mean 

 temperature 68°. o, this formula gives 28". 01 25, which agrees almost 

 exactly with the scale value (28".oi24) actually employed in the 

 ^ C3"gni reductions. 



Returnins' now to the results arising from the solution of the 

 equations in table Y. (p. 20) we find the following values for Tt, 

 the parallax, and y, the correction of the annual proper motion 

 effect. The quantity x, which is merely the eri'or of the value 

 arbitrarily assumed for the "corrected difference," is here omitted. 



Comp. Stars. a* 



a and h -\- 0.249 =^ 0.045 



c and fZ -|~ 0.266 ± 0.035 



(? and/' -)- 0.324 ± 0.050 



c and (J -f- 0.15 1 ± 0.026 



It will be seen at once that the values of n deduced from the first 

 three pairs agree with each other fully as well as might be expected 

 from their probable errors. The parallax depending on c and 9, on 

 the other hand, differs widely. We may conclude that this is due 

 to the existence of a sensible parallax belonging to 9. If we then 

 depend upon the first three pairs for the parallax of ^ we shall have, 

 taking the mean bv weight : 



Parallax of ^ Cassiopeife = -)- o".2 75 ± o".o24. 



But if we consider the three determinations as having equal weight, 

 Ave get for the arithmetical mean, and probable error from the three 

 residuals, 7t ^= -\- o".28o ± o".o26. Now if we admit the existence 

 of a sensible parallax for 9, the result obtained above from the com- 

 parison stars c and 9 is not the parallax of (i, but a quantity which 

 is very nearly equal to : 



where : ji and Ttg are the parallaxes of ^ and 9, 



S and Sa are the distances of c and 9 from (i . 



* This is the probable error of the difference of two distances as measured 

 on one plate. But as there are two impressions on each plate, it may also be 

 regarded as the probable error of one complete measure of distance from a 

 single impression. 



