Parallaxes of fi and e Cassiopeiae. 5 



corresponds to a distance of loo divisions of the scale. It will be 

 seen that this quantity is a measure of the discordance between the 

 scale value for each plate, and the mean scale value for all the plates. 

 Now, by placing these discordances, as derived from pairs of stars 

 difiFering widely in position angle, side by side, we can at once see 

 whether the scale value varies with position angle, or is really a 

 constant for any given plate. To make this comparison quite 

 rigorous, the adopted mean, from which the quantity "mean minus 

 sum" is derived in table IV., ought to be computed from the mea- 

 sures of those plates only, that have impressions of all the stars. 

 Accordingly the "adopted means" of table IV. are computed from 

 the measures of plates 



Except in the case of the pair c, d, which was subsequently added, 

 as already explained. In this case I have used the actual mean of 

 all the values given in table IV., a circumstance which will not 

 materially affect the evidence furnished by this pair of stars. The 

 pair c, e has not been used, since the parallax of e would tend to 

 render its evidence unreliable. Two things become plain from an 

 inspection of the table. In the first place, there is no decisive evi- 

 dence of great variations of scale value with position angle. In 

 fact, if we regard as casual the differences from the mean values 

 contained in the sixth column, we find as the average difference 

 without regard to sign, zbo.0050. This would correspond to about 

 o".o5 per 1000": but it is hardly greater than the necessary uncer- 

 tainty of observation. In the second place, we see that the scale 

 value depends upon temperature. This latter circumstance, it is 

 almost needless to remark, does not influence the parallax determi- 

 nation, though it will be of importance in the general discussion of 

 all the micrometric measures. 



It will therefore be of interest to examine the evidence a little 

 more in detail. In doing this, I have taken into consideration the 

 readings of the focal micrometer, as set down in table I. One 

 revolution of this micrometer is equivalent to 0.05 inches, and the 

 arrangement is such that increasing readings of the micrometer 



