April 20, 2017

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By A. E. H. LOVE

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Journ. de VEcole Proc. Lond. Math. HISTORICAL INTRODUCTION. 21 From a quadratic function of the changes of principal curvature. he easily deduced the form of the normal functions and the this frequencies of the component tones. ^ By an adaptation of Gehring's theory of plates I found that Lord Rayleigh's solutions fail to satisfy the boundaryconditions which hold at the edges of a shell vibrating freely, and I proposed to adopt for bells M. Mathieu's theory that the extension is the governing circumstance.

1886. 33 is a function BENDING OF RODS IN ONE PLANE. 40 AB wq In the span have, measuring [223 x towards B, since as in equation (42) of the last article we may express the shearing force to the right of by taking moments about B. A Now we multiplying this equation by xj^ and integrating, find dy Since y = and dy/dx o . ^, x towards ,, ,,,, A B and G and pc' (Oc that there is fixed point in 54 for this case and we [^5(7]. a weight TT at a point A and B, we have in BQ ; and in ^^2-^c+Go(OG-x) G and <^a; {x-OB){00 - x) dx moments member by no load between by moments about aj2 from a fixed point da; the equation of three X being measured from a Q (53), GQ = (54).

The two cases will be distinguished as the inflexional elastica corresponding to the oscillating pendulum, and the 7ioninfleccional elastica corresponding to the revolving pendulum. The line of action of R is called the line of thrust. In both cases we have a first integral of the equation (61) in the form ^B(^\ = Rcos + const and the two cases are distinguished according by the constant. 228. (62), to the value taken Inflexional Elastica. Suppose first that the pendulum of the kinetic analogue through an angle 2a.

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