OF LOGICAL CLASS-FREQUENCIES, ETC. 
119 
The set of ec[iiations 11. may be obtained from the set I. l)y the transformations 
(2) above, thus affording the verification 
The fact that the model for any values of p^, p.^, and p^ can always be transformed 
into a model for the casej;^ < 0'5, < 0'5, < 0'5 justifies our terming case 
(4), § 20, “ a type of the most general case.” The geometrical transformations here 
suggested would seem to correspond to “ reductions ” of the syllogisms. Thus in 
fig. 5 the point F stands where the point K stood in fig. 4n. But the point F of fig. 4« 
corresponds to a syllogism in Celarenf, Cesare, Camenes or Camostres ; F In fig. 5 to a 
syllogism in Ba>-hara. The transformation of co-ordinates corresponds to a reduction 
of either of the first four forms to the last. 
§ 25. In case any of those wdio read this memoir should care to construct models 
of the congruence-surfaces illustrated in figs. 1-4, I give dimensioned sketches of 
their developments below, figs. 6-9. These developments are on half the scale of 
the projections shown in the preceding figures. An angle with one arc across it is an 
angle of 60°, with two arcs 45° or 135°; an angle blocked in is a right angle. 
Congruence of the Fourth Degree. 
§ 26. The conditions of consistence for the congruence of the fourth degree in 
general recjuire space of four dimensions for their direct representation [cf. V., § 7). 
