332 Mutherfurd Photographic Measures. 



The corrections for precession, etc., have been obtained by means 

 of the usual formulae,* which for the present plates become : 



ajb=[i.324]^+ [» 9-6i5] B+ [n 9.283] (7 + T9-689] A ^ position angles. 

 as = J [n 4.480] C -\- [>4. 195] D\s, for distances. 



These corrections are additive to the observed quantities, and will 

 reduce them to 1875.0. The numerical values are given in table III. 

 The "zero corrections" (table IY.) have been computed by the 

 aid of the formula — f 



v = ^ k z tan 8 — y -\- x, 



in which v is the zero correction which must be added to all the 

 observed position angles of any plate. The significance of the 

 other quantities entering into the formula may be found by refer- 

 ring to my paper on the Pleiades. The special corrections required 

 by the position angles Of the Western impressions in consequence 

 of using the same zero point in measuring both impressions,^ are 

 also given in table IY. The last column of the table contains the 

 final correction, as actually applied in the reductions. The scale 

 value employed for all the observations is 28". 01 24, which is the 

 mean of the scale values determined from all the Pleiades plates. § 

 The "tangent correction"|| has been applied to the distances ex- 

 pressed in divisions of, the scale: for the distances were not trans- 

 formed into arc, until after the final means had been taken. This 

 was made possible by the use of a constant scale value instead of 

 a separate value for each plate. The tangent corrections are con- 

 tained in table IY. A. 



It is customary in reducing micrometric observations, to elimi- 

 nate partly the effect of casual variations of scale value, by assuming 

 the distances of certain standard stars, and then using such a scale 

 value for each plate as will make the sum of the standard distances 

 come out equal to the assumed constant value. I adopted this 

 method in reducing the Pleiades observations, using six standard 

 stars.^f Similar methods have been used by Pritchard and Gill 

 in stellar parallax work,** and by Elkin in the heliometric triangu- 

 lation of the Pleiades. ff But in the case of the present j3 Cygni 



* Ann. N. Y. Acad, vi, p. 267. f Ibid., p. 272. $ Ibid., p. 278. 



§ Ibid., p. 270. || Ibid., p. 276. ^[ Ibid., p. 270. 



** See Gill in Monthly Notices, Royal Astron. Soc, xlix, 3, p. 117. 

 ff Trans. Astr. Obs. of Yale University, vol. i, part i, p. 18. 



