CALCULATION OF MOTION OF GROUND 97 
base paralle! to itself. When AA’ is turned the block FF’ also turns so that 
it is always parallel to AA’. When the lever SL is turned through an angle 0 
the end P of the bar PR moves a distance / tan 6 where / is the distaace from 
S to PR. 
The integraph is moved along parallel to the zero line of the curve of 
which the area is desired and the point P is made to follow the curve by 
moving the lever SL. When the base is moved a distance dx the pencil moves 
along a distance ds such that ds cos 6=dx. Let ds sin 9=dz so that dz/dx 
=tan 6. If the first curve is given by y=f(x) then y =/ tan 0. Hence y =ldz/dx 
or ydx =ldz so that lz = fydx-z is the distance the pencil moves side ways so 
that the pencil draws a curve giving the area of the first curve. 
In the instrument which was made the lengths AA’, BB’, FF’ were each 
two inches and / was made one cm. The links were made of stainless steel 
3/8 by 1/16 inch. The wheels were 7/8 inch ball bearings. The block FF’ 
was 3X11 inches. 
This instrument enables the curves for a; and a, to be drawn quickly and 
with sufficient accuracy for most purposes. In using it one side of the base is 
kept against a straight edge fastened te the drawing board. 
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