By R. Harré
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It is necessary to understand this idea if we are to appreci ate one of Gayley's results in his famous Sixth Memoir on Quantics. We shall therefore introduce it, and at the same time show how the notion of invariance so far discussed in this section is in a sense less general than the so-called projective invariance. The transformation eqns. (19) represent a special case of what is known as an affine transformation. The equations of the general affine transformation for a three-dimensional space (we can always drop the Z- and z-coordinates if we wish to come down to two dimensions) may be written : X = a±x + bxy + cxz + dl9 Ί Y = a2x + b2y + c2z + d2} γ Z = a3x + b3y + czz +
Sylvester was unable to find another post in America and returned to London, this time as an actuary for a life insurance company. Amongst a handful of pupils we find the name of Florence Nightingale, only a few years before beginning her work in the Crimea. At last, in 1846, Sylvester entered the Inner Temple to read for the Bar, and in this way he and Cayley came together. Sylvester could never suppress his feelings of gratitude to Cayley for, as he put it, "restoration to the enjoyment of mathematical life".
In March 1914 M u r r a y was killed in a motoring accident in Edinburgh. An original and suggestive thinker with a strong forceful character, he h a d devoted the whole of his life to the study of the sea. His ability a n d devotion were duly rewarded. B. in 1898. Characteristically he always claimed that these honours were conferred on the Challenger expedition rather than on himself. H e held a number of important offices in various scientific societies in Edinburgh a n d for almost 2 years, from 1896 to 1898, he was Scientific Member of the Scottish Fishery Board.