By A. E. H. LOVE

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**Example text**

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