Abstract
THE principal novelties in Dr. Macfarlane's calculus are that a distinction is made between linear and cyclic successions of vectors, and that the commutative law of addition, as well as that of multiplication, is abandoned. To express what most vectorists write β + α=α + β, Dr. Macfarlane writes Σ(β+ α)=Σ>(α + β). Thus α + β — α is not the same as β, but either three sides of a parallelogram, or three coinitial vectors, according as we take linear or cyclical succession. By introducing some subsidiary and rather artificial rules, the author is able to get formula? that are, in appearance, analogous to the binomial and exponential theorems, and so on.
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M., G. An Algebra for Physicists 1 . Nature 91, 595–596 (1913). https://doi.org/10.1038/091595b0
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DOI: https://doi.org/10.1038/091595b0