1903 - 4 .] J. Erskine Murray on a Differentiating Machine. 279 
plate of celluloid, not shown in the diagram, on the under side 
of which are two dots by which the machine is guided along the 
curve. The line through the dots is parallel to P Q. The 
celluloid rests on the paper on which the original curve is drawn, 
thus supporting the outer end of the frame ABCD. 
Since the distance AY between the pin and the centre line 
A b 
Fig. 1. 
of S T is constant, and since RY / AY = dy/dx , it is clear that 
the distance R V which R is displaced above or below the zero 
line A Y measures the tangent of the angle of slope of the 
curve, i.e. dy/dx. A pen at the end T of S T records the 
movements of R, and therefore traces a curve of which the 
ordinates are proportional to the rate of change of the ordinate 
of the original curve. It should be noticed that the purpose of 
