SOLUTIONS OF HOMOGENEOUS AND CENTRAL EQUATIONS. 



1075 



From 45° to 90°, the places are obtained by changing x for y, and the places in the other 

 three quadrants by changing the signs of x and y. 



Table of Computed Places. 



6 



10° 



15° 



20° 



25° 



30° 



35° 



40° 



45° 



Curve 

 6. 



x \ 09947 

 y \ 01754 



09877 

 0-2646 



09766 

 03555 



09603 

 0-4478 



09365 

 05406 



0-9026 

 06320 



0-8557 

 07180 



07936 

 07936 



Curve 



7. 



x S 0-9999 

 y \ 0176 



09998 

 0268 



09996 

 0364 



0-9984 

 0466 



0994 

 0574 



0-982 

 0-687 



0951 

 0798 



0-891 

 0-891 



Curve 



8. 



x j 1002 

 y\ 0177 



1007 

 0270 



1-013 

 0369 



1022 



0-477 



1037 

 0599 



1048 

 0734 



1049 

 0880 



10* 

 10 



Curve 

 9. 



x J 1-006 

 y \ 0178 



1-014 

 0272 



1028 

 0-374 



1051 

 0490 



1091 

 0630 



1-171 

 0-820 



T373 

 1-152 



00 + 

 00 





e 



5° 



7° 30' 



10° 



12° 30' 



15° 



17° 30' 



20° 



22° 30' 



Curve 

 10. 



X 



y 



log r 



1007 

 0088 

 0005 



1016 

 0134 

 0010 



1-030 

 0182 

 0019 



1051 

 0233 

 0032 



1-084 

 0291 

 0050 



1140 

 0360 



0-078 



1-258 

 0458 

 0127 



00 

 00 

 00 



(lAd). Examples of the other Equiaxial Curves. 



The following equiaxial curves of the forms e and £ have been computed and 

 traced : the second column is a reference number, corresponding with that in the sub- 

 joined table of computed places : I, is the inclination of asymptote to transverse axis. 

 The equation of each curve being given in different forms, those containing even 

 powers are referred to a transverse axis X ; those containing odd powers are referred 



* For No. 8, the following additional values are necessary to trace the second inflexion — 





41° 



42° 



43° 



44° 



X 



y 



1-045 

 0-908 



1039 

 0-935 



1-030 

 0961 



1-016 

 0981 



t For No. 9 we find also, = 44° 59'; x = 4-165 ; y = 4 - 163. And for other curves additional places have been com- 

 puted where necessary for tracing the inflexions. 



VOL. XXXV. PART IV. (NO. 23). 8 A 



