The London, Edinburgh and Dublin philosophical magazine and journal of science . G, the graspor numerical aperture of an objective, the direction of which is immaterial,and of which, therefore, the scalar part is the only one to which we needpay attention. G is adequately represented by R, where II is the lengthof a radius of image x irrespective of its direction. Dr. G. J. Stoney on Microscopic Vision. 505 the inclination of the beam to the optic axis. All points ofthese lines are in the phase 6 at the time t. Proceed in the same way with another beam whose inclina-tion to the opic axis is a,
The London, Edinburgh and Dublin philosophical magazine and journal of science . G, the graspor numerical aperture of an objective, the direction of which is immaterial,and of which, therefore, the scalar part is the only one to which we needpay attention. G is adequately represented by R, where II is the lengthof a radius of image x irrespective of its direction. Dr. G. J. Stoney on Microscopic Vision. 505 the inclination of the beam to the optic axis. All points ofthese lines are in the phase 6 at the time t. Proceed in the same way with another beam whose inclina-tion to the opic axis is a, and which lies in a plane of incidenceinclined at an angle to the plane of incidence of the firstbeam. It produces on the image plane a system of parallellines in the phase 6 at the time t; which lines stand atintervals S/=\/sm a\ and are inclined at the angle to thefirst set. Let fig. 1 represent the image plane with the two systemsof lines drawn upon it. They form parallelograms ; and ifwe draw the dotted lines of the figure, which are diagonals Fig- 1. to these parallelograms, we find that the one beam is alwaysin the same phase as the other at every point of these dottedlines—in other words, these dotted lines are the middle lines ofthe equidistant luminous bands which constitute the ridingproduced by the two beams on the image plane. Let a be the spacing of this ruling, i. <?. the interval 506 Dr. G. J. Stonoy on Microscopic Vision. between the dotted lines. Then a, 8, and 8! are the threeperpendiculars of one of the triangles of fig. 1, both in actualmagnitude and in position. Now the lengths of the perpen-diculars of a triangle are inversely as its sides. Take thenthe reciprocals of cr, 8, and 8 without changing their positionsand 111 1 gj g( a a) °) C7 and are in the positions of the three perpendiculars of fig. the triangle of fig. 2 with its three sides parallel to theperpendiculars of fig. 1. Its sides will then be proportional toa, b, and c. Again 8=\/
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