. The Astrophysical journal. f the brighter star is{k = ) o. 54 that of the fainter. In the following, Russells methodsand notation are used.^ With this value of k no values of ^ = . ^ , „, sin^02—sin^^3 , ,, , ^ ^ - ^ • r • sm^2 and B = —^^^ ^-z- could be found which gave a satisfymg I 2C COS C/^ representation of the mean of the two branches of primary mini-mum. ^ = , ^=, 5 = represents the ascendingbranch fairly well, but the whole echpse calls for a value of k in theneighborhood of This value of k requires a depth of sec-ondary minimum exceeding the observed by 0^^01
. The Astrophysical journal. f the brighter star is{k = ) o. 54 that of the fainter. In the following, Russells methodsand notation are used.^ With this value of k no values of ^ = . ^ , „, sin^02—sin^^3 , ,, , ^ ^ - ^ • r • sm^2 and B = —^^^ ^-z- could be found which gave a satisfymg I 2C COS C/^ representation of the mean of the two branches of primary mini-mum. ^ = , ^=, 5 = represents the ascendingbranch fairly well, but the whole echpse calls for a value of k in theneighborhood of This value of k requires a depth of sec-ondary minimum exceeding the observed by 0^^012. Any assump-tion of darkening calls for a still deeper secondary. The amount ofellipticity, which was well determined by the least-squares solution,is unexpectedly large.^ Representations of primary minimum were Russell, Astrophysical Journal, 39, 407, 1914. ^ Astro physical Journal, 35, 36, and 39. 3 See Shapleys table, Contributions of Princeton Observatory, Xo. 3, p. 115. 138 RAYMOND S. DUGAN * 8 ili ;-^——. ! T •1 •-1 r3 • 1 T —• • in; ^ ;^ J- 1 ~ J u • m-o X 1 ^^—i— • u •l 1 a -if ] ^ ^ 1~ 1 V (? ? ?] ^ 1 , yf • \ •0- i . S^; J\ ^^ n J ! 1 1 _^ - 1 • K) b aO > u oO THE ECLIPSING VARIABLE RV OPHIUCHI 139 attempted, assuming the amount of ellipticity anticipated fromexperience, and assuming no ellipticity at all. In neither case wasthere much improvement. At this point the discussion of syste-matic residuals was undertaken, and still the representation wasnot satisfactory. The thought comes to one that it may be futileto attempt to find elements to represent the mean of the twobranches of such an asymmetrical curve as the one under the value of k is affected by the elements of rectification,it seemed best to attempt a least-squares solution of the entire curvein 7 unknowns, A, B,k, a, b, c, and \ the observed intensity duringtotality. The intensity during the annular phase of secondaryminimum is expressed as
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