1904-5.] Dr Hugh Marshall: Crystallographical Notes. 383 
Crystallographical Notes. 
By Hugh Marshall, D.Sc., B.R.S. 
(MS. received November 21, 1904. Read December 5, 1904.) 
I. Axes of Compound Symmetry of the Second Order. 
In recent years, since the more or less general adoption of the 
systematic classification of crystals under the thirty-two possible 
types of symmetry, it has become usual to dispense with the 
‘ centre of symmetry ’ as one of the elements of crystal symmetry, 
and to adopt in its place the 4 axis of compound symmetry of the 
second order.’ The derivation of symmetrical directions from any 
given one by means of a compound axis of order n involves not 
Fig. 1. 
merely rotation through the angle 27 r/n about that axis, but also 
reflection in the plane at right angles to the axis. If the axis A 
(fig. 1) is of second order, then B, by rotation about A through 7 r, 
would give B', but this by reflection in the normal plane P gives 
B", and the latter (not B') is therefore symmetrical to B with 
reference to the compound axis A. But B" is evidently parallel 
to B, and oppositely directed, so that it follows that in crystals 
possessing an axis of compound symmetry of the second order (or 
