124 



KANSAS UNIVERSITY QUARTERLY. 



The correction obtained by taking the average of all these eleven 

 observations is .00023125 inches, for ever}' degree through which 

 the shaft rotates. 



The correction is a constant quantity for each instrument; whether 

 it is the same for all similar instruments regardless of size I am 

 unable to state, as the above mentioned instrument is the only one 

 which has been constructed as yet. 



The dimensions of the instrument experimented upon are as 

 follows: 



Shaft 12 inches long, diameter of wheel, length of cross-bar, and 

 set-scre\v 2 inches. Distance of set-screw from centre of shaft 2 3/| 

 inches. Width of wheel through hub i inch. Size of shaft H inch. 

 Instrument not graduated. 



The theory of the Curvimeter may be proved as follows: 



Taking a=^x — c sin (^, and b==ry-i-c cos *, as co-ordinates of the 

 centre of curvature, then differentiating with respect to s, by 

 means of the properties of the Differential Co-efficient of an arc 

 (rectanglar co-ordinates) and the Radius of Curvature we have: 

 da dx 

 ds ds 



db dy dc do dc 



1 — =J — -r- i cos 4>- 



ds ds • ds 

 And directly from these two equations 



-c sm <j)-3— =— j-cos ({>. 

 ds ds 



\ds / \ ds/ \ds/ 



D, representing the 



length of the arc of evolute measured from a fixed point. 

 Therefore 



dD dc 



ds^— Zs Hence AD==bAc. 



That is, the difference between an\' two radii of curvature is 

 equal to the length of arc included between these radii on the arc 

 of evolute. 



