A CURVIMETER. 1 23 



the knife-edge upon the curve — a mark on the highest point of the 

 knife-edge coinciding with the point from which measurement is to 

 begin on the curve. The position of the wheel on the shaft being 

 noted, the curve is then traced with the knife-edge, which is kept 

 wholly within the curve and therefore tangent to it. The shaft 

 would therefore be kept tangent to the curve also, the wheel rolling 

 slowly and smoothly upon the paper, changing its direction of mo- 

 tion as the shaft changes its position. When the other extremity 

 of the curve is reached the wheel is found to have changed its posi- 

 tion, and this change of position, or the difference between the 

 initial and final positions of the wheel on the shaft give the length 

 of the curve plus a correction which will now be explained. 



The only use of the point is in finding the correction, and after 

 the correction has once been found for an instrument the point is no 

 longer of any value. As will readily be seen, when the shaft is 

 rotated about the point as a centre the wheel will tend to work off the 

 shaft. This tendency to work off is due to the friction of the knife- 

 edge upon the paper as it changes its direction of motion. By 

 rotating the shaft about the point as centre through a given angle 

 and noting the distance the wheel works off, then rotating back 

 through the same angle, and again noting the distance the wheel 

 has moved, Vv^e know at once, if these two distances are not equal, 

 that the cross-bar is not perpendicular to the surface upon which 

 it stands. This can be remedied by adjusting the set-screw until 

 the two distances above mentioned are equal, then the cross- 

 bar must be at right angles with the plane upon which it stands. 

 These two distances can be made equal regardless of the size of 

 angle through which the shaft is rotated, and when the above 

 named condition has been reached the correction for the angle 

 through which the instrument is rotated is known, then the correc- 

 tion for one degree readily follows. 



We then have the correction for the instrument for one degree, a 

 constant quantity, and in nieasuring a given curve, the angle 

 through which the instrument rotates being known, we can easily 

 find the correction for the curve. Subtracting this correction from 

 the length noted on the shaft by the change of position of the wheel, 

 we have the exact length of said curve. 



The following table gives the results of a series of experiments 

 performed to obtain the correction of an instrument constructed by 

 Mr. J. E. Crosby. The first column represents the number of ob- 

 servations taken; columns two and three give the distance worked 

 off while rotating through go" ; and column five represents the 

 positions of the wheel from the cross-bar at the beginning of each 

 observation. 



