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keil, L believe, by J. IIoi'Kinsos '). Il will be coiivcuient to repeat in u somewhat different notation bis formulation of tlu* general tlieory, and aftenvards to apply it to some special problems to which the optical metliod of exaniination is applicable.

In the usual notation-) if 1', >1, li, S, T, Ij be tbc component* ol' stress; tt, v, w the displacements at the point .c, //, ,« the elastic

constants; we have siich equations as

111

s=K|+S <»

These liold «hen the materin' is :it the standard temperature. 11'we suppose tliat the teiaperature is raised b\ (i and tbat no stresses are applied,

dit dv tlic .

dje dj) tlz " '

uhile tl te tl t/ kv. vanisli. The stresses tliat would be needed to ])roduce tbc sanie displacenicuts without change of temperature are

/' =U = 11 — (:3a + ïy.) y.ó,

S= T= U = 0.

Ifence, so far as the principle of superposition bolds good, we niay u rite in general

+!+!)+'*£- «•»+•»« <»>

'-"(*+»> «

witli similar equations for Q, 11, T, U.

II' there be no bodih forces the equution of equilibrium is

dP dU dT

Js + di (5>

') Mess. of' Math. vol. viii. p. 108 (1879).

') See, for exaniple, Love's 'Tlieory of Elasticity,' Cambridge l'niversitx Press, 1892.

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