80 Spherical Radiation and Vibrations in Conical Pipes. 
antidodes in fig. 1. In this diagram the graph ?/ = # is shown 
by a full line and the branches of 3/ = tan .2? by broken lines. 
The abscissse of their intersections show the values of the 
roots of the equation, tan#=0. 
Fig. 1. — Vibrating Segments of an Open Cone. 
The circles show the equidistant antinodes and the crosses show the 
nodes located by the intersections of x=y and y=tan x. 
IT /27T ^ >37T 
6a 6 3 
W „ >'5T '67T 
6s $6 
77T ft/ID/ a /vs. 
(THE 0S SHOW THE MIUE3 
\0F THE ROOTS OF EQifAr/OAf 
^ TAN X=X 
To show the segments of one pipe of fixed length when 
emitting its various tones, a number of such diagrams would 
be needed. To avoid this repetition, a series of pipes is shown 
