ANALYTIC GEo.Mi-:n;v xni.108. 



away that the logarithms of any two radii vectores are in 



tin* .same ratio as art- tin. angles which these lines form with 

 the initial line. 



IT.. in this definition it follows that the equation of the 



curve is 



logp = *0, . . . (1) 



where & is a constant. 



If A- he unity, and logarithms to the base a be employed, 

 this equation may be written in the form 



This equation shows that if 6 = oo, p = ; that p in- 

 creases from to 1, while 

 increases from oo to 



x*^^ \ \# ; and that p continues 



to increase from 1 to oo, 

 while increases from 

 E to -f- oo ; the curve has, 



therefore, an infinite number of spires. 



If the constant a equals 2, then p takes the values -J, J, 

 1, 2, 4, 8, , when is assigned the values (in radia: 

 ..., 2, 1, 0, 1, 2, 3, ; Fig. 139 represents the locus of 

 equation (2), a being equal to 2, for values of from -ITT 

 to -f 3. In this figure Z FOE = ^ EOA = /.AOB=/. J: 

 =ZC07>=57.3, and OF = OE = , CU = 1, OB = 1, 

 = 4, and 01>=8. 



