500 



JIEPORT — 1894. 



Tiot at all, or else as often in one as in the opposite sense. Each separate 

 part in which the plane is divided by the curve will be swept over a 

 certain number of times, which is easily determined by applying the rule. 



In the figure these numbers are inserted. 



Fig. 5. 



This generalisation of the meaning of an area has long been adopted 

 in geometry, principally through the writings of Mobius. According to 

 Cremona, it was first given by De Morgan.' 



Fig. 6. 



To build a planimeter on these geometrical lines we have to add a 

 suitable recording apparatus. The simple wheel rolling on the paper is not 

 any longer sufi&cient, as the length of the generating line or ' rod ' QT varies. 



' Camhr. and BuMin Math. Journ., vol. v. 1850. 



