THE MEASUREMENT OF MICROSCOPIC OBJECTS. 295 



attached to the eye-piece ; to this disc a vernier is applied, with 

 which crossed-threads extended in the eye-piece revolve round the 

 point of intersection. In practice the apex of the angle to be 

 measured falls upon this point of 

 intersection, while the two threads 

 are brought alternately to cover the 

 legs of the angle. The angle of 

 the rotation is read off by the 

 vernier. Other opticians apply the 

 graduation to the rotating stage, so 

 that in making measurements the 

 crossed-threads in the eye-piece re- 

 main stationary while the stage is 

 rotated with the object. This ar- FlG ' 164< 



rangement has the disadvantage that the object changes its place 

 in the field of view in consequence of defective centering of the 

 stage. To remedy this defect the stage should be centered very 

 accurately by adjusting screws acting in two directions. We 

 therefore prefer the eye-piece goniometer. 



In default of a goniometer, a drawing may be made of the angle 

 with the camera lucida ; the two legs are then produced by means 

 of a rule, and the angle measured with an ordinary protractor. 



Whatever method of measuring we adopt, there always remains 

 a source of error to be counteracted, which is not dependent upon 

 the accuracy of the measuring instrument. Though we should 

 entirely disregard the numerous irregularities which influence the 

 distinctness of the lines and disturb the parallelism of edges 

 which ought to be parallel, or if we suppose the legs of the 

 angle required adjusted with all desirable accuracy, yet it cannot 

 be affirmed with certainty whether the plane of the angle coincides 

 exactly with that of the field of view or is inclined to it. It is 

 evident that an elevation or depression of the apex makes the 

 angle appear too large, whilst turning it round one leg makes it 

 too small ; hence the results of measurement may differ considerably 

 according to position, and unequal angles may even appear equal. 

 This disadvantage cannot be wholly eliminated in crystallographical 

 researches; it may be checked to some extent by repeating 

 the measurements of equivalent surfaces. In many cases, also, 

 it is possible to control these inclinations so that we know 

 certainly whether the actual measurement of an angle differs in 



