By A. E. H. LOVE
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Extra resources for A TREATISE ON THE MATHEMATICAL THEORY OF ELASTICITY
Ar Mr (f>rOC But since the sides 3r, (3r+ Mr. Ar 1), is ^ vertical Mr 1 a^_i is through Ar are a and 4 and the breadth Ar Ar+i we have (l>rCC Hence centroid. ^r+i- and the triangle of forces for the intersection of 3 of this triangle its OC Ar Sr/Ar Ar+i. Ar Sr/Ar A^'r+i . Vi = ^n-ifi'n- THE ELASTICA. 227] 47 on which the lines are drawn and the extensions of the method to cases where the extremities are built in, or the supports are not all on the same level, the reader is referred to M. Levy's Statique A paper by Professors Perry and Ayrton in Graphique, t.
Voigf*, wh-en worked out, led to little better agreement, by and it appears that the attempt to trace the phenomena of impact Much more successful was the to vibrations must be abandoned. theory of Prof. Hertz ^ He suggested that the phenomena may depend on a local statical effect gradually produced and gradually The problem becomes a particular case of that solved by M. Boussinesq and Signor Cerruti which we have discussed in I. ch. IX. Prof Hertz made an independent investigation of the subsiding.
Xx. to have been first correctly See also Vorlesungen Uber mathematische Physik^ HISTORICAL INTRODUCTION. 19 given in the Natural Philosophy of Lord Kelvin and Professor Tait. These authors make little use of the theory of Elasticity, but deduce the values of the stress-couples by a method similar to that which they employed in the case of thin rods. More recent expositions of the same theory have been given by Saint- Venant^, and by Mr Basset^ and Prof Lamb^ The two latter were led thereto by the difficulty in the subject of thin shells to be referred to presently.