280 Proceedings of Royal Society of Edinburgh. [sess. 
the second board is to eliminate the Y coordinate of the original 
curve. In using the machine the arm P Q is moved so that 
it remains tangent to the original curve, while the frame A B C D 
is moved from left to right, and it and the smaller board to and 
fro as may be necessary in following the curve. 
The machine shown has been constructed to deal with curves in 
which the tangent of the angle of slope does not exceed 5 ; this is 
sufficient for almost all experimental or observational results, since 
it is always possible to flatten out the curve by making the 
horizontal scale large in proportion to the vertical. 
It is, of course, easy to obtain the higher derivatives of the original 
curve by a simple repetition of the process on the successive curves. 
In a future communication I hope to lay before the Society the 
results of the study of a number of meteorological and other curves 
by aid of the differentiator. 
{Issued separately August 15 , 1904 .) 
