

Development of Arbitrary Functions. 509 



Table III. Table IV. 



p. 



x .J^x). 







o-oooo 



1 



-f -0640 



2 



■2434 



3 



•5036 



4 



•7921 



5 



•9485 



6 



1-2135 



7 



1-2395 



8 



1-0986 



9 



•8366 



10 



+ -3353 



11 



- -2107 



12 



•7807 



13 



1-2957 



14 



1-6788 



15 



1-8667 



16 



1-8195 



17 



1-5279 



18 



1-0163 



19 



- -3817 



20 



-I- -4154 



21 



1-1561 



22 



1-7807 



23 



2-2002 



24 



23490 



6A 



+1-2485 



15 A 



-1-8783 



P. 



x . Ji(x). 







00000 



1 



4- '1171 



2 



•4268 



3 



•8168 



4 



1-1373 



5 



1-2468 



6 



1-0555 



7 



4- -5601 



8 



- -1542 



9 



•9246 



10 



1-5554 



11 



1-8658 



12 



1-7443 



13 



1-1825 



14 



- -2851 



15 



+ -7485 



16 



1-6705 



17 



2-2544 



18 



2-3065 



19 



1-8114 



20 



4- -8497 



21 



- -3674 



22 



1-5548 



23 



2-4214 



24 



2-7410 



4A 



4-1-2485 



10 A 



-1-8783 



17 A 



4-2-3490 



As an example we have taken a function which has the 

 value 1 at the centre of a circle and the value at the 

 circumference, and which at any place is a linear function of 

 the radius. The outer radius a of the circle is 1. 



In fig. 1 the function is shown graphically by the straight 

 line MDD, and the numbered points in this line correspond to 

 25 equidistant ordinates. In our actual drawing, of which 

 fig. 1 is a reduction, the scale is such that one unit of value 

 of the function corresponds to 10 inches. 



The distances from to any number in the axis of abscissae 

 ON represented in inches ten times the corresponding values 

 of xJi (a) of Table I. Projecting vertically from any point 

 in ON, and horizontally from the corresponding point in DD 

 we obtained points in the curve MBB. We use inches 

 because British planimeters usually measure areas in square 

 inches. We found the area OMBBNO to be 61 17 square 

 inches, and as both coordinates were magnified ten times, the 



Phil. Mag. S. 5. Vol. 40. No. 247. Dec 1895. 2 N 



