( 164 ) 
Let us take first the 33 cases in which the petiole remains 
in ZA, as already collected in Table XIX. The changes of 
position from the normal are here so slight that the group 
may serve as a basis for our comparison because we ma 
consider any change of length to be unaffected by the addi- 
tion of a factor due to change of position. The changes of 
position with which we shall have to deal are those involving 
a rotation from a more basal to a more terminal position or 
vice versa. Such changes may be most directly measured 
in terms of the cosine of the position angle. If # is the posi- 
tion angle an increase in the value of I —cos & indicates a 
change from a more basal to a more terminal position, while 
a decrease indicates the opposite change. Fig. ro illustrates 
P 
FIG. Io. Diagram to illustrate method of measuring the basal-terminal 
component of rotation. OP= petiole position. Ox, and Ox,= leaflet 
positions. 
this in diagrammatic form. Thus if OP is the petiole posi- 
tion, Ox, the leaflet position in the normal series, and 
the leaflet position in the operated series, the change of posi- 
tion as regards the basal-terminal direction is represented by 
the distance y, y, = Oy, + Oy, which may be obtained from 
the equation 
(1—cos £*,OP)— (1 —cos £«,OP) = y,4,. 
