Mr. C. V. Boys on an Integrating -Machine. 



347 



axis of x by an amount equal to k or 1, then the angle between 

 this rod and e e is such that its tangent is equal to y 2 ; and if 

 the plane of the front wheel of the cart be kept at right angles 

 to this rod, the cart will integrate y 2 dx. 



To integrate y 3 dx the second rod would be kept parallel 

 to A B, and the point where it cut e e would be distant from 

 the axis of x by an amount equal to y z . If then the 

 plane of the front wheel of the cart were kept parallel to the 

 line connecting this point with B, as shown by the dotted 



Fig-. 3. 



J* 



lines in fig. 3, the machine would integrate y 3 dx. In these 

 cases, as in the integration of products, it would be well to 

 make k so large that the ordinates should never much ex- 

 ceed it. 



To integrate the product of two functions — that is, to find 

 x -yjrx dx, the two curves y = (j)x and y = yjrx would have to be 

 drawn about two axes of at, one above the other, and two 

 tracing-points, each on the line e e, would follow the curves. 

 The fixed centre B would pass over the lower axis of x ; but 

 the epicyclic connexion, instead of joining B with the cart, 

 would connect B with the upper tracing-point, and cause a 

 rod passing through this point to be always at right angles to 

 A B. This upper rod would cut the upper axis of oo at a 



202 



