The mechanism of the ossicles of the ear and membrana tympani / by H. Helmholtz ; translated from the German, with the author's permission, by Albert H. Buck and Normand Smith.

Hermann von Helmholtz

Date:: 1873

Credit: The mechanism of the ossicles of the ear and membrana tympani / by H. Helmholtz ; translated from the German, with the author's permission, by Albert H. Buck and Normand Smith. Source: Wellcome Collection.

Provider: This material has been provided by The Royal College of Surgeons of England. The original may be consulted at The Royal College of Surgeons of England.

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$2. For its surface, dz where C is understood to represent a constant. In the cen- tral point of the membrane r — o, and -^-= cot. a, a repre- senting the angle so designated in Fig. 10. For this point therefore equation No. 2 becomes reduced to 0= — X cos a and the equation ]STo. 1 gives for the same point *L® + -kp A cos a = 0. d z When we, on the other hand, represent the amount r at the border of the membrane by H, and let ~ — tang 0, as in Fig. 10, then according to equation No. 2 „ if — X cos (3 = G = — A cos a consequently if = A (cos /3 — cos a) and the force g _ dG _ 7r p B2 cos a ' dz ~ cos (3 — cos a as given in the previous section. Again, from equation JSTo. 2 follows: /dz\ or r3 + 7. cos a a5 — (r3 + A cos af dz dr This is an elliptical integral which we restore to the normal form when we make Y2 sin ~.co8u dr = \ / 2 i in^- . tin u d u$