Warder and Shipley—Floating Magnets. 287 
An inspection of the first eight figures will show a marked 
qualitative contrast; for when the force varies according to the 
law expressed by equation (1) there is a decided tendency toward 
concentration of magnets near the center of the field, while 
under law (2) the tendency is toward a greater concentration 
in the periphery of the figure; under law (1), an angle of the 
polygon is sometimes very obtuse, under law (2) much greater 
apparent regularity is seen. In fig. 9, the magnet being re- 
versed, the centralizing tendency becomes negative, and we 
obtain the figure discussed by Mayer and by Pierce in Nature, 
vol. xviii, pages 258, 881. In our experiments, the figures 1 
and 2, 7 and 8, seemed to be more stable than 8 to 6; Nos. 1 
k 
. = 7 ‘ (1 a) 
j F,=r X constant (2 a) 
Tf we suppose the attracting magnetic pole to be above the 
plane of floating magnets, equation (1) would become 
r * 
way 
a. 
and when the ratio < becomes very great, we have (as a close 
approximation) 
F, =r X constant (1 }),--as in eq. (2 @) 
_ In both forms of experiment, the force very near the center 
increases directly as the distance; but it soon reaches a maxi 
mum under law (1), and then rapidly diminishes, so that 
three, or at least two, of the floating magnets are hel 
near each other in the central part of the figure. As al- 
