PROC. ENT. SOC. WASH., VOL. 24, NO. 4, APR., 1922 



91 



portions of twojplane curves of which the laws of development 

 or in mathematical language, the formulae, are known. An 

 inspection of these two curves will show that they are so similar 

 in form as to be practically identical: so that it would not he 

 possible by an examination of the morphology of these regions of 

 the curves, to refer them to different species. An inspection 

 of the following table, giving the length at a series of points of 

 the radius vector whose extreme point sweeps out the curves, 

 will serve to show how close the correspondence is in the regions 

 considered: 



Vector! al 



angle 

 Degrees 





 10 

 20 

 30 

 40 

 50 

 60 



70 

 90 

 110 

 130 

 150 

 170 

 180 



Length of Ratlins 



Vector 

 Curve A Curve B 



4.002 

 3.968 

 3.870 

 3.728 

 3.530 

 3.300 

 3.050 



2.800 

 2.280 

 1.860 

 1.570 

 1.390 

 1.289 

 1.290 



4.000 

 3.970 

 3.880 

 3.730 

 3.530 

 3.280 

 3.000 



2.680 

 2.000 

 1.320 

 0.710 

 0.270 

 0.030 

 0.000 



A 



Figure 19. A, B, similar portions of the two curves represented in Figure 20. 



As the table shows, until the radius vector has swept through 

 an angle of about 60 degrees its length is practically the same 

 for the two curves, the slight differences in the figures being due 



