Relation to the Measurement of Activity. 5 



will commence to recede behind the second limb of the index, 

 nntil with 360° the last has disappeared, and the initial position 

 of dial and index recurs. The procedure is therefore capable 

 of indefinite repetition, all the readings being made from the 

 center outward. 



Similar remarks apply for clockwise rotation of the index on 

 the dial, except that the reading now begins at the circum- 

 ference. 



6. Eccentricity. — Retaining the same dial, if an index of 

 smaller angular opening were used, there would often be two 

 readings simultaneously in view in different parts of the field, 

 at an angular distance apart equal to the given angle of the 

 open sector. Thus with a single sector of 60° there are two 

 readings between 150° and 180° of the forward radius corre- 

 sponding to 90° to 120° of the rearward radius, supposing the 

 index to be twisted counter-clockwise. Repetition is necessarily 

 interrupted for measurement must cease at 330° of the forward 

 radius of the sector. The latter condition could easily be met 

 by choosing a larger dial so that the spirals would sweep over 

 an angle greater than 180°. But as increased size is not a de- 

 sideratum, the end in view may be gained more satisfactorily 

 by cutting two diametrically opposite sectors of 60° each, out 

 of the index. In such a case there are always two readings in 

 the held. 



Leaving the ulterior advantages gained by this method to 

 be considered in the next paragraph, I will here point out that 

 the result obtained as a mean of the two simultaneous readings 

 in question is essentially more nearly correct. For let the 

 rotation of the index be as above : then at the advance radius 

 of the sector, the reading will generally fall short of the true 

 angle, seeing that the ends of the partial circles here emerge 

 from behind the index ; whereas at the other radius of the 

 sector the reading will generally be in excess of the true angle, 

 for here the partial circles recede behind the index. In all 

 cases however the latter reading will oe as much in excess of 

 the true angle as the former falls short of it, and therefore the 

 mean value will be free from sj'stematic error (eccentricity as 

 it may be called) to less than one-half of the angular value of 

 the distance between two consecutive partial circles — in the 

 most unfavorable case. It is thus that two readings virtually 

 double the efficient size of the dial caet. par., or double the 

 number of concentric circles. 



Furthermore, if by reason of close graduation, or of indis- 

 tinct demarcation, or the like, the projecting ends of a number 

 of consecutive partial circles escape detection in case of a spin- 

 ning dial, it is clear that the first of the visible circles will be 

 symmetrically located on each side of the true angle. Even if 



