. The London, Edinburgh and Dublin philosophical magazine and journal of science. In fig. 5we have the section of the surface by the ZOXplane. The curves of section are the circle and the ellipse a2x2 + c2z2 = a2c2. The radius of the circle is 3. * From the ease with which this relationship follows from the equationto the surface it is improhable that it has not been noticed previously ;but it is not, perhaps, well known. Writing the equation to the surface in the form :— (x2+f+z2){a2x2+bY^c2z2)-a2(b2+c2)x2-b2(c2 + a2)f — c2(cr + b2)z2-\-a2b2c2 = 0and substituting values z=b, and .r=0 we obtai
. The London, Edinburgh and Dublin philosophical magazine and journal of science. In fig. 5we have the section of the surface by the ZOXplane. The curves of section are the circle and the ellipse a2x2 + c2z2 = a2c2. The radius of the circle is 3. * From the ease with which this relationship follows from the equationto the surface it is improhable that it has not been noticed previously ;but it is not, perhaps, well known. Writing the equation to the surface in the form :— (x2+f+z2){a2x2+bY^c2z2)-a2(b2+c2)x2-b2(c2 + a2)f — c2(cr + b2)z2-\-a2b2c2 = 0and substituting values z=b, and .r=0 we obtain {y2+h2)(b2y2+c2b2) -b\c2-\-ir)tf - b2c2(a2 + b2) + a2b2c2 = 0,or i/2-\-b2 — a2 = 0, whence y— + Va2 — b2, which proves the proposition. From the symmetry of the equation to the surface, it follows that thetwo other analogous propositions are also true. 324 Mr. J. H. Vincent on Models and Diagrams to The ellipse may be set out from the table given above forthe section of ellipsoid of elasticity by the ZOX plane byreducing the figures in the ratio of 3 : 2. Fig. The foci of the ellipse are indicated by crosses. The curvemarked 2 is the section of the outer surface by the plane?/ = 2. This plane touches the inner sheet on the axis of y andthus (see footnote above) curve 2 goes through the foci ofthe ellipse. Illustrate the Propagation of Ligld in Biaxals, 325 Section of Surface by Plane y = 2. Inner section a point, the , x. y. 0-00 3-46 1-09 3-00 1-50 2-60 1-53 2-58 1-96 2-00 2-44 1-00 2-60 0-00 Tbe projection of the curve appears to go through thesingular points, but does not actually do so. It cuts thecircle in the point «=150, z = 260 and not in the singularpoint. The line OMis an optic axis, the angle MOX=tan-l!845 = 40° 10; the angle ZOM, the semi-angle between the optic axes, = 4l>° 50 as we saw before from the ellipsoid of elasticity. The line OP is an axis of single-ray velocity, the angle XOP=tan-1l-69 = 59° 20. The circle NM is the cir
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