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Published online by Cambridge University Press: 24 October 2008
The two previous papers of this series dealt with the determination of the complete system of combinantal covariants and contravariants of a pencil of quadric surfaces. The present paper is concerned with combinantal forms involving line-complexes, and with certain syzygies which exist between these forms. It is essentially a preparation for the determination of the complete system of combinantal line-complexes of the pencil, which will be carried out explicitly in the next paper of the series.
* Todd, , Proc. Cambridge Phil. Soc. 43 (1947), 475, 488.CrossRefGoogle Scholar We shall refer to these papers as (I) and (II).
† Turnbull, , Proc. London Math. Soc. (2), 18 (1919), 69.Google Scholar
‡ Todd, , Proc. Cambridge Phil. Soc. 41 (1945), 127.CrossRefGoogle Scholar
* See § 4 of (I).
* The notation is as in (I). It is hoped that no confusion will occur between the α of (26) and αλ.
* The formulae are given in (47), (48), (49) of T.
* Compare Salmon, , Analytical Geometry of Three Dimensions (6th ed., Dublin, 1914), 248,Google Scholar and also § 9 of the paper T cited above [where, in (51), a term −γ23 γ31 γ12 has been omitted].