v.— A New Mode of Representing Discon- 

 tinuous Functions. By Mr. Robt. Rawson. 



(Read February 10th, 1846.) 



1. Mathematical discontinuity may be explained 

 in the following manner : 



Fig. 1. 



Let AC, Fig 1, represent 

 any curved line, and from A 

 draw the straight line AB in 

 any direction, upon AB demit ^ 

 the perpendicular B C. Now, if ABrrr and 

 BC =3/, the relation which exists between x andy 

 is called the equation of the curved line AC; 

 .r is generally taken for the independent variable, 

 and y the dependent variable, which is said to be 

 some explicit or implicit function of .r, either 

 algebraical or transcendental ; this function is 

 usually expressed in the following manner : 



