Abstract
American Journal of Mathematics, vol. xix. 3.—Development of the A-process in quaternions, with a geometrical application, by Dr. J. B. Shaw, gives several interesting results.—On the analytic theory of circular functions, by A. S. Chessin. The writer points out that the similarity between simply and doubly periodic functions ceases to exist when the behaviour of the function at infinity comes to be investigated. He refers to M. Méray's “Leçons nouvelles sur l' Analyse infinitésimale et ses applications Géométriques,” wherein is given a classification of simply periodic functions into polarised and non-polarised functions. He then states that the character and rôle of the polar values of a circular function have not been clearly set forth, and that the object of his paper (pp. 216–258) is to supply the deficiency.—Sur un probléme concernant deux Courbes Gauches, by Prof G. Kœnigs. The problem, of which a direct solution is given, is “une Courbe C étant donnée. en trouver une autre C, qui lui corresponde point par point de sorte que le plan osculateur à chaque courbe aille passer par le point qui correspond sur l'autre au point de contact.”—The object of a second paper, by Dr. Shaw, entitled “The Linear Vector Operator of Quaternions,” is the development of the linear vector operator, entirely from a quaternion point of view, which amounts, the author writes, to an extension or development of nonions; reference is made to a paper by Dr. H. Taber in vol. xii. of the journal.—On certain applications of the theory of probability to physical phenomena, by Dr. G. H. Bryan. This is a subject to which much has been contributed in our columns. Dr. Bryan arrives at the conclusion that even the theory of probability does not furnish us with a conclusive proof of the Boltzmann-Maxwell law. That the law in question represents accurately the state of the molecules in a perfect gas, and approximately their state in an ordinary gas, cannot be doubted; but directly we attempt to generalise the law by applying it to assemblages of densely crowded molecules, we are confronted with the necessity of making some assumption or other, and the above treatment (i.e. employed in Dr. Bryan's note) shows that even probability considerations do not afford a sure way out of the difficulty.
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Scientific Serials. Nature 56, 260 (1897). https://doi.org/10.1038/056260b0
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DOI: https://doi.org/10.1038/056260b0