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Published online by Cambridge University Press: 14 March 2016
(I.) It is proposed to consider determinants of the form

and of the same form as this with the top horizontal and last vertical rows removed, in connection with the two series of quantities

(II.) From the two given sets of quantities

two new sets are deduced

by means of the auxiliary quantities

viz.,

Then in like manner from the sets (c, d) two new sets

by means of the auxiliary quantities

page 625 note * I have to express my best thanks to Professor Catley for his kind revision of this paper, and for his advice in accordance with which it was re-written and the forms of §§ II. and IV. entirely-altered.