28 



PROCEEDINGS OF THE CANADIAN INSTITUTE. 



pointer is placed on CA, the other side of the triangle, on a slide so 

 arranged that it shall always rest in contact with the curve. At 0, 



A 



C D 



the intersection of GA with the axis of the parabola, is fixed an 

 anchor pivot by which the triangle is anchored to the paper on 

 which the area to be measured is j)lotted. The instrument is, when 

 anchored, capable of revolving freely about O, while at the same 

 time the parabola may be made to slide upon the triangle. By 

 revolving the instrument and sliding the parabola the tracing pointer 

 may be made to follow the boundary of any figure. 



If the wheel is perfectly turned and mounted the sliding of the 

 parabola will cause the wheel to slide without revolving, and the 

 turning of the instrument about will cause the wheel to i^evolve 

 without slidino-. 



Let X be an area to be measured and let A and B be two posi- 

 tions of the tracing pointer very near together, and let C and D be 

 the corresponding positions of the wheel. Let a. be the circular 

 measure of the angle BOA. We may suppose that the pointer is 

 moved from A to B by revolving the instrument about without 



