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UNIVERSITY OF COLORADO STUDIES 



constructed linkages for s^w", and the primitive inverse m=5'", for 



au-\-h 



the circular transformation s^ , and finaUy a compound link- 



cu-^d "^ ^ 



age for the general algebraic function, provided the linear factors 



were known. All this is consumed by my treatment oif^u, s)=0. 



3. Linkage for u=e^^z 



The application of (2) to special cases is complicated. I have 

 devised a simple linkage for rotation. Designating in the complex 

 plane the points by the same letters as the complex numbers which 

 they represent, the transformation 



of z into 11 (^ = con8tant) represents a rotation of z through an angle 

 6,' i. e., ou—oz, <iuoz = 6 =const. 



Mechanically this rotation is accomplished by the linkage of 

 Fig. 2. All links except AC=BD are equal. AC=BD may be 

 assumed so that <AOC=<BOD = ^. From the ligure it follows 

 that <AOB=<COD, hence also <zOB=<uOC and <zOC= 



Fier. 2 



