1. Cayley commences his third paper on Skew Determinants (May, 1854) by recalling his development of them in terms of Pfaffians, and then goes on to say:—“J'ai trouve recemment une formule analogue pour le developpement d'un déterminant gauche borde, tel queCette formule est:and he explains that the expressions 12, 1234, etc., are Pfaffians, whose law of formation is—12 = 12,1234 = 12·34 + 13·42 + 14·23,123456 = 12·34·56 + 13·45·62 + 14·56·23 + 15·62·34 + 16·23·45 + 12·35·64 + 13·46·25 +14·52·36 +15·63·42 + 16·24·53 + 12·36·45 + 13·42·56 + 14·53·62 + 15·64·23 + 16·25·34.No proof is given, and the law of formation of the development itself is not explained.