Relation to the Measurement of Activity. 3 



semicircles stand out from the dial (§ 6). It is therefore expe- 

 dient to tax the eyes in the smallest degree possible by using a 

 dull Mack index and also a dull black dial, on which the semi- 

 circles are inscribed with white paint. I have availed myself 

 of the black cardboard much used by photographers, upon 

 which the circular lines could be inscribed with a ruling pen* 

 by suitably thinning " flake white " or "Chemnitz white" with 

 turpentine. In larger practice such dials could be printed on 

 card board from a copper plate. 



To guide the eye it is of course necessary to accentuate con- 

 secutive 5° and 10° circles in the usual way. Moreover a 

 fixed narrow radial scale, containing the running numbers of 

 each of the successive intervals of ,10°, and placed directly in 

 front of the whirling system of dial and index, further facili- 

 tates the reading. Indeed it is now quite as clear as an ordi- 

 nary scale. 



3. Instead of the arrangement -given in figure 1, it is obvi- 

 ously admissible to allow the semicircles of the dial to termi- 

 nate in spirals while the counting edge of the index is a diam- 

 eter. If carried out in the plan of figure 1, however, such a 

 goniometer if adapted to measure positive angles would not at 

 once be available for negative angles seeing that a rotation of 

 the index 180° around its diameter is necessary for this pur- 

 pose. An auxiliary adjustment of this kind would, as a rule, 

 be objectionable in practice ; and therefore the design A, 

 figure 2, in which the locus of the edges of the partial circles 



of the dials are symmetrically intersecting spirals, is preferable. 

 The index in this case is the blank semicircle BB ', and its 

 initial position on the dial is shown by the dotted line aa. 

 O is a small circle used for attachment. 



Remarks similar to those of § 2 may be made with reference 

 to the measurement of angles greater than 90°. In this case 

 the counting edges of the index BB' are to be made the 

 bounding radii of a sector and the spiral loci of A are to be 



* The convenience of a ruling pen for such purposes was pointed out to me by 

 Prof. F. H. Bigelow. 



