420 Major L. Darwin. On the Method of 



of these three points on the ground glass, when, if the distance N 2 A 

 is great enough, F will not be further from the principal focus than 

 the error of observation, and may, therefore, be confounded with it. 

 The angle, BNoC, subtended by the points B and C at the lens, can 

 easily be measured, and, since the incident and emergent rays passing 

 through the nodal points are parallel to each other, the angle C'^B' 

 is thus obtained; the distance, C'B', that is, the distance between the 

 images of the two outside points, can be also measured on the ground 

 glass : C'B' and C'N^B' being given, FN\ can therefore be found ; for 

 since, by supposition, the line AN 2 bisects the angle BN 2 C, 1% is 

 equal to C'B'/2 cot C%B72. This, therefore, is a method by which 

 the principal focal length, as denned above, can be measured. But 

 if, instead of having objects at known angles, only one object is 

 observed, and the camera is revolved round the point N\, through 

 the angle C'lS^B' between the observations, exactly the same 

 result can be obtained ; this is the method adopted at Kew. The 

 movement in parallax of the point N 2 is so small that it may be 

 neglected. The advantage of this method is that a collimating tele- 

 scope can be used as the object, and thus, during dull weather, the 

 work can be carried on indoors. In working with the testing camera, 

 the angle C'NYB' represents the angle through which the swinging 

 beam is revolved about the vertical pivot ; the stops are arranged so 

 that C'NiF = tan" 1 , that is, so that C'B' = 2 FN\ ; and, therefore, 

 twice the distance C'B' measured on the ground glass gives FN\, 

 the principal focal length of the lens. The Kew method, therefore, 

 gives the result required. 



It might at first sight appear that a considerable error would be 

 due to the fact that the adjustment to the central position is merely 

 made by a rough mark, and that it is only the total angle C'NYB' 

 (that is, the angle moved by the swinging beam between the iron 

 stops) which is accurately known. It is true that it can only be 

 said that C'NjF is approximately equal to F^B' ; but if C'N^E 1 is 

 less than 90, and if the line N X F does not differ in direction from the 

 true central position by more than 1, then the principal focal length 

 obtained in this manner does not differ from the truth, for this reason, 

 by more than l/17th per cent. As it is considered that this would 

 represent -an extreme case, it is therefore evident that this is a 

 negligible source of error. 



In order that the Kew method of finding the principal focal length 

 should not be open to any criticism on theoretical grounds, three 

 conditions must be fulfilled : it is obvious that these conditions need 

 not hold good further from the axis of the lens than the points at 

 which the observations were made. 1st. The principal focal surface, 

 or the locus of the focus for very distant objects, must be a plane. 

 2nd. The image must not be distorted. 3rd. The nodal point of 



