. The London, Edinburgh and Dublin philosophical magazine and journal of science. gain. The product of 8 and A willtherefore be larger for either a very small or a very largevalue of 8 than it will be for an intermediate value. That is, of Methods for Observing Small Rotations. 89 it is important not to make the distance either between thedouble cross-wires or the lines on the scale too small, nor onthe other hand too large. When we know the law of varia-tion of A with 8 we can determine exactly what separationwould give the best result in a given case. Let us supposeas before that the conditi
. The London, Edinburgh and Dublin philosophical magazine and journal of science. gain. The product of 8 and A willtherefore be larger for either a very small or a very largevalue of 8 than it will be for an intermediate value. That is, of Methods for Observing Small Rotations. 89 it is important not to make the distance either between thedouble cross-wires or the lines on the scale too small, nor onthe other hand too large. When we know the law of varia-tion of A with 8 we can determine exactly what separationwould give the best result in a given case. Let us supposeas before that the conditions are such that the final (retinal)images of object and reference-wire have the same when 8 is zero the two outer images merge into oneand we have the case previously considered, in which wefound that the smallest observable movement under themost favourable circumstances was that which produced aseparation 2 = 0-9«. Suppose next that the two outer objects are separated byan amount equal to about twice their own width, as in fig. 2. Fig. 2. «- ——— g=4«. X. The central image, if midway between the outer two, wouldbe clearly separated from each of them, and it would be easyto determine its position to within, say, \ the whole interval8, i. e., to within about 08 a, a somewhat higher degree ofaccuracy than before. When the separation 8 is madegreater (say five times the width (2a) of the images, as infig. 3), experience shows that it is possible to locate thecentral object to within -JQ to Jq the interval, /. e., to within^ to \ the resolving power of the instrument*. With stillgreater separation the accuracy may be slightly, but onlyslightly, increased. It is obvious that the narrower the * This is on the assumption that the position can be located bymicrometric methods, one object being made to bisect the interval be-tween the other two. If simple eye estimates only can be made, theaccuracy will be less, probably at most not more than ¥V the separationor \
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