Summary: (1) DR. SILBERSTEIN'S “Vectorial Mechanics” is an able exposition of the power of vector analysis in attacking certain types of physical problems. Heaviside's modification of Hamilton's original vector and scalar notations is adopted throughout. So far as the simpler applications of vector analysis go, the question of notation is apparently of little consequence. Almost every vector analyst who writes a book on the subject has his own pet notation; and there is a tendency for these authors to fail to recognise that their best creations are usually Hamilton's originals disguised. Even Dr. Silberstein, who knows and works quaternions, ascribes to Heavi-side a formula given long ago by Hamilton, assigns to Clifford (1878) a problem which is completely solved in the first edition (1867) of Tait's “Quaternions,” and refers to Henrici and Turner as authorities in connection with a simple geometrical problem given in Kelland and Tait's “Introduction to Quaternions.” One might with as much historic truth ascribe the proposition Euclid i. 47 to the first English examiner who set it in an examination paper. Indeed, the historic references throughout the book are not all that might be desired. For example, it is incorrect to speak of Willard Gibbs as the one to whom, after Hamilton, the discovery of the fundamental properties of the linear vector function is due. What of Tait's powerful paper of 1868 on the rotation of a rigid body about a fixed point? It positively bristles with new-found properties and applications of the linear vector function. Dr. Silberstein's own chapter v. is simply a reproduction of part of this memoir. Then in the second edition (1873) treatise on “Quaternions,” Tait for the first time develops the application of the linear vector function to strains; and in the last chapter of Kelland and Tait's “Introduction to Quaternions” (1873) presents the theory in a different form. Willard Gibbs's “Vector Analysis” (not published) was printed for the use of his students in 1881 and 1884. Apart from new names and a new and extremely interesting presentation, it is doubtful if Gibbs gave in that pamphlet any important property of the linear vector function which was not to be found in the pages of either Hamilton or Tait.