. The London, Edinburgh and Dublin philosophical magazine and journal of science. oexplain this apparent contradiction we must consider a littlemore closely just how angular measurements of position areusually made. As a rule the angular motion is determinedby observing the motion of the image of a point either actuallymoving with the system (microscope and pointer), or appa-rently moving with (mirror and scale), with reference tosome fixed point. The image and fixed point are examinedeither with the eye directly or with the aid of an the first case the reference-point is a li
. The London, Edinburgh and Dublin philosophical magazine and journal of science. oexplain this apparent contradiction we must consider a littlemore closely just how angular measurements of position areusually made. As a rule the angular motion is determinedby observing the motion of the image of a point either actuallymoving with the system (microscope and pointer), or appa-rently moving with (mirror and scale), with reference tosome fixed point. The image and fixed point are examinedeither with the eye directly or with the aid of an the first case the reference-point is a line or series of linesengraved on a screen upon which the moving image is pro-jected ; in the second case it is generally a cross-wire placedin the focus of the observing eyepiece. In either case theobject examined is, when the highest degree of accuracy isaimed at, a narrow line whose image is represented at thefocal plane of the mirror or objective (rectangular aperture)by the diffraction pattern of fig. 1. The problem is to determine the position of the centre of Fi<?. this pattern with reference to a fixed line (or wire) parallelto the axis of symmetry ao. When the relative position isjudged by means of the eye it makes no difference whetherthe image is thrown on a ruled screen or seen through anejepiece. In either case the image of the diffraction pattern,as formed on the retina, is another diffraction pattern similar * The scale having black lines on a very brightly illuminated field, theeffect of diffraction would be to make the images of the lines appearnarrower than their geometrical images. t It does not matter which, for it is the motion of the image only withwhich we are concerned. of Methods for Observing Small Rotations. 87 in every respect to the first save that it is broadened in theinverse ratio of the aperture of the eye to the aperture of themirror or objective ; the only effect of interposing the latter*being to change the apparent magnitude of an obje
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