r polymorphic. Even these may be covered by the i 

 I two or more curves of the same type as the above. 

 In the expression 



y=Ax«e** v (1) 



■ hi Hi in;iy also be written 



y = Aei *10 g *±*# (la) 



It may primarily be noted tliat the modulus of x, or 

 nit by which x is measured, is not material. For w 



Hence, if we put A' = A/c m and ri = w/c p , we shall have 



j/= A'x m e^ v (2a), 



that is to say the form of the function is unchanged, the 

 indices m and p are also unchanged ; the factor A and index 

 n are alone altered. 



An examination of the tracings of this curve, hereinafter 

 given, shews that it is adapted to represent a large variety 

 of physical results and is of wide application. In the 

 present instance, the consideration is, in the main, re- 

 stricted to its employment for the purpose of statistical 

 representation; this will sufficiently reveal the utility of 

 the curve and dispose of the necessity of fully discussing 

 the grave limitations of the conventions of ordinary 

 Algebra, 1 and their incidence in practical solutions. 



The manner in which the type of curve under considera- 

 tion can be conceived to originate, may be presented as 

 follows, — 



When the distribution of the ordinates (frequency) of a 

 curve, about either side of the maximum or minimum 



1 Which for t-xampl, ■! n-.f distinguish the products (+ o) (-6) and 

 (-a) (+6); in which »U Umv h-.-d n .M it -i-y . . 



y x'" where m may be fractional and positive and 

 n which too log -x or log- ( -») demands special 



