RELATION BETWEEN RENTS AND INCOMES 107 



R a movable one, as on a slide rule, corresponding values always 

 being opposite each other. 



eMCDIA N RCNT 



5 6 7 6 9/0 ^C"-*! 30 40 X> lOO ZOO ecNT5 



I ' 'i' ' | ' '. "i 'i V '' I ^'i''' l I I ' I ' nl . i .l ' i | ' 1 1 i'i " | \ 'I ' l ' I ' I ' l' i' l i i ' i - 



■2 .3 4 .5 £ 7 .^ .9 t P ?. J 4 5fi7fi9IOX 



I I I ' I I I ' I I I I "' I I I I — I I I I I I I I I I I I I I I I I I 

 '10/. 



^^~1 



^^,x\ 



-6 -4 -Z Q £. 4 .6 .3 /.0/og,oX\ 



Fig. 9 



Equation (2) above for the logarithmic skew curve gives the fre- 

 quency per unit of X. The frequency, per unit of rent when expressed 

 in dollars, is 1/M times that value, and substituting for X from 

 equation (3), there results 



Y \ _ (logi?/M)' 



M Ra\/2r 



(4) 



If it is desired to make computations from this equation, it is best 

 to use the base 10 for logarithms rather than the natural base. For 

 this purpose the equation becomes approximately 



Y .1733 ^Q_|i^(iog,„i?/M)2^ ^^^ 



M R aio 



For convenience it may be set down that 



(Tio = 0.4343 a„ 

 and 



(X, = 2.3026 cTio, 



although it will very rarely be necessary to make such computations. 

 It has been stated above that the median value of X (or rents 

 expressed in dollars) may be logically regarded as the origin of the 

 logarithmic skew curve, although X is not equal to zero at this point, 

 but is equal to 1. If some of the other forms of statistical averages are 

 also known, the properties of the curve may be better understood. 

 To determine the mode, the first derivative of equation (2) of the 

 curve is equated to zero, and there results 



\ogX ^ - a\ 

 or 



X = e-^ (6) 



— 20 ~ 2.3026 cr,o» 



