of Liquid Surfaces of Revolution. 



43 



radius of the rings is a mean proportional between the prin- 

 cipal ordinates of two surfaces in which the modulus of the 

 elliptic integrals is the same, and the principal ordinates of 

 which are a maximum and a minimum respectively. 



Table III. 



9. 



«x/Y. 



X/* v 



X/Y. 

 1-571 



«. 



&/Y. 



X//3 a . 



X/Y. 



o 

 



1-000 



1571 



180 



1-000 



0-000 



o-ooo 



10 



1-008 



1-567 



1579 



190 



0992 



0-008 



0-008 



30 



1-074 



1-527 



1-640 



210 



0-931 



0-073 



0-068 



45 



1-184 



1-458 



1-726 



225 



844 



0179 



0151 



60 



1-372 



1-333 



1-829 



240 



0729 



0-366 



0-267 



80 



1-725 



1-036 



1-787 



260 



0-580 



0-852 



494 



90 



1-810 



0-834 



1-509 



270 



0-552 



1-200 



0-663 



100 



1-725 



0-630 



1-086 



280 



0-580 



1-486 



0-862 



120 



1-372 



0-316 



0-433 



300 



0-729 



1-671 



1-218 



135 



1-184 



0-166 



0-196 



315 



0-844 



1-647 



1-391 



150 



1074 



0071 



0-076 



330 



0-931 



1-607 



1-495 



170 



1-008 



0-008 



0-008 



350 



0-992 



1-576 



1-563 



180 



1000 



0000 



0000 



360 



1-000 



1-571 



1-571 



The " march" of the functions is shown by means of the 

 curves in figs. III., IV., and V. Thus, ifp be the length of the 

 principal ordinate (whether it be a maximum or a minimum), 

 fig. III. shows the relation between p/Y and 0, fig. IV. that 

 between X/p and 0, and fig. V. that between X/Y and 6. 



180 210 240 »70 300 330 30 &0 



Fig.I. (*=0,y=fc)- 



120 150 180 



By plotting the values of X/Y we find that the maximum 

 occurs when #=70°. The corresponding value of <f> x is 54 0, 15, 



