OF LOGICAL CLASS-FEEQUENCIES, ETC. 
117 
tAy C) '' - tA/ I 
J. 
?/-3 = Fj - Vl 
% = 2h - 
since 
(Ay) = (A) - (AC). (By) - (B) - (BC). 
The first surface is therefore changed into the second loy a simple transformation of 
co-ordinates, i.e., if we are dealing with an actual model of the surface, by turning it 
over and shifting it. 
Fig. 5 is drawn to illustrate the nature of an actual transformation. It is drawn 
for the values 
Pj z= 0'35 '£>-z — OA _pg = 0‘55, 
substituting (l —0'45) for the 0‘45 assigned to pg in fig. 4a, p. 115. The two figures 
are similarly lettered. The model of fig. 4 has been turned over, round an axis 
parallel to the axis of x, through a half revolution. 
§ 23. If (1—P 3 ), (1—^ 3 )’ (l~Pi) siiccessivelij substituted for pg, po, 2h trans¬ 
formations are as follows :— 
( 1 .) Substituting (1—for^^g 
/yt . ■— 
yz = Pi - Vi 
% = Fs - 2i 
