2 C Ba/rus — Spiral Goniometry in its 



and on the other side by two symmetric confluent spirals BC 

 and B'C. The plate BB' when in position, is placed imme- 

 diately in front of AA' as shown by the dotted lines on the 

 dial, and is capable of revolving normally around the same 

 axis C independently of AA' . Since the curves BC and 

 BO are by definition such that equal angular increments (in 

 degrees of arc, say) correspond to equal radial increments (in 

 millimeters, say) the number of ends of the semicircles visible 

 beyond the spiral edge of BB' is numerically identical with 

 the angular displacement of AA' relative to BB', reckoned 



from the fiducial position (no circles visible) given in the 

 diagram, fig. 1. Now if the system AA', BB' revolves as a 

 whole, the ends of the semicircles will tend to appear like com- 

 plete circles, and this more fully in proportion as the speed is 

 greater. It is therefore merely necessary to count the number 

 of visible circles from the circumference inward, in order to 

 measure the angle between A A', and BB', no matter whether 

 the rotation be right-handed or left-handed, nor what its speed 

 may be. Two spirals BC and B'C have been provided in 

 order to admit of changes in the sign of rotation. 



The maximum angle measurable in this way is clearly greater 

 than 90°, and clearly less than 180° in this simple contrivance 

 (cf. § 4) ; for if the spirals be symmetrically prolonged in the 

 directions CB and CB', and if the partial circles instead of 

 terminating in a semicircle be similarly contained in a sector, 

 the measurable angle will increase until the sector vanishes. 



If d<p be an angular increment and dr the corresponding 

 radial increment of the spiral, then 



dr <x dcp, 



and therefore the method is equally sensitive at all parts of the 

 angular field, though perhaps the central parts are more fully 

 controlled by the eye. The error in reading is in the most 

 unfavorable case equal to the angular value of the distance 

 between two consecutive semicircles on the dial, increased by 

 the angular value of an arc, which is just visible on rotation. 

 The latter quantity depends on the sharpness with which the 



