

THE 



AMERICAN JOURNAL OF SCIENCE 



[THIRD SERIES.] 



Aet. I. — Spiral Goniometry in its Relation to the Measure- 

 ment of Activity ; by Carl Bartjs. 



1. Preliminary. — Under this cumbersome title* I shall 

 refer to the art of measuring variable angles between two 

 coaxially rotating bodies by the displacement of a set of semi- 

 circles terminating in the same diameter in one body, relative 

 to a set of spirals in the other ; or by equivalent systems of 

 spiral and straight edge. Problems which may be reduced to 

 a measurement of the angular magnitude in question are of 

 frequent occurrence in practical physics, and in most instances 

 a moderate degree of accuracy will suffice because the quantity 

 to be measured itself fluctuates within certain limits. As it is 

 such cases which I have chiefly in mind, I will first give an 

 account of the method in various stages of development, and 

 then proceed with the more obvious applications to the evalua- 

 tion of activity and speed. 



2. Dial and Index. — In fig. 1, A A' is a circular disc (to be 

 called the dial in this paper) capable of revolving around an 

 axis passing normally through its center. On this disc a series 

 of concentric, equidistant semicircles are inscribed, in such a 

 way that the locus of their ends is the diameter AA '. BB' is 

 a plate (to be called the index) bounded on one side of a diam- 

 eter by the semicircle BDB', of the same radius as the dial, 



* The instrument for measuring plane angles is the circular protractor ; but the 

 word '-protraction" is uot available. On the other hand the word goniometer 

 like goniometry has been made to refer to solid angles like those between faces of 

 a crystal. As I have no such purpose in view I use the above caption with mis- 

 giving and merely to express an operation which would consistently be called 

 '• circular protraction " m rotating bodies. 



Am. Jour. Sci.— Third Series, Vol. XLVIII, No. 283.— July, 1894. 

 1 



