. The London, Edinburgh and Dublin philosophical magazine and journal of science . from which, or directly, we see that if c = l, corresponding tothe transition case between real and imaginary values, 2>(i)=o. (59) If, as we shall now suppose, ©2, ®3 • • • vanish, (59) may bewritten in the form =0, . (60) where. ar ©o-l©! ; ©0-9 ©! «3 = ©o-25 ©! (61) The first approximation, equivalent to (26), is found byconsidering merely the central determinant of the secondorder involving only % ; thus, af-l^O. ...... (62) The second approximation is (63) 156 Lord Rayleigh on the Maintenance of The thir
. The London, Edinburgh and Dublin philosophical magazine and journal of science . from which, or directly, we see that if c = l, corresponding tothe transition case between real and imaginary values, 2>(i)=o. (59) If, as we shall now suppose, ©2, ®3 • • • vanish, (59) may bewritten in the form =0, . (60) where. ar ©o-l©! ; ©0-9 ©! «3 = ©o-25 ©! (61) The first approximation, equivalent to (26), is found byconsidering merely the central determinant of the secondorder involving only % ; thus, af-l^O. ...... (62) The second approximation is (63) 156 Lord Rayleigh on the Maintenance of The third is {a°-iY{(a>—^-)2-l}=0, • • • (64) the second approximation to the equa-tion discriminating the real and imaginary values of c is (eo-lXeo-9)-©^ ±6,(80-9). . (67) One of the most interesting applications of the foregoinganalysis is to the case of a laminated medium in which themechanical properties are periodic functions of one of thecoordinates. I was led to the consideration of this problemin connexion with the theory o
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