814 
SUMMARY OF CURRENT RESEARCHES RELATING TO 
permanently connecting the two. During the grinding process the 
levelling tripod is lifted off by means of the handle H and put on one 
side to save it from damage or derangement. Before using the appa- 
ratus the three legs of the levelling tripod are brought to the same length 
by turning the screws x and y down to the zero of the scale t. The 
levelling tripod is placed in position on the top of the grinding tripod, 
and the two combined on the top of the levelled glass plate. The bubble 
of the spirit-level is brought to its central position by turning the screws 
b of the grinding tripod, and then the levelling tripod is laid aside. A 
small flat face F (not shown) is then ground (with emery and water on 
a glass plate) on the projection v of the steel cylinder, the brass cone 
being laid aside. After ascertaining that the three screws b have worn 
equally during the grinding, which is shown by the bubble being still 
in the centre when the two tripods combined are again tested on the 
levelled glass plate, the face F is polished. The screw x of the levelling 
tripod is next to be brought to one of its extreme positions, e. g. +12° 
on the scale t, the bubble is again brought to its central position by 
means of the screws b, the levelling tripod is lifted off, and a second face 
/' is ground on the projection v. Similarly, after turning the screw x 
to its other extreme position at — 12°, a third face f" is ground. These 
three faces must lie in a zone, if the aj^paratus acts properly, and their 
angles will be very nearly twice 12°. 
(5) Theory. — Assuming that w r e know the position of two faces A 
and B of a crystal, it is required that a new face C shall be ground 
which shall make with A and B the angles b and a. The face F ground 
on the projection v of the steel cylinder serves for orientation. 
For the orientation of the crystal with regard to the plate on which 
it is to be ground, we require to determine the inclination of A and B 
to the steel face F, for this latter face is parallel to the glass grinding 
plate when the levelling-tripod screws stand at zero. In order to arrive 
at the desired face C from the face F the crystal must be so inclined 
that in its new position the grinding plate comes to lie at the same 
angle to the faces A and B as that at which C is required *to lie, or, in 
other words, that C takes the place previously occupied by F. 
The crystal is cemented in approximately the required position, 
judged by eye or with the aid of a hand-goniometer, to the base of the 
brass cone (fig. 98) at li. The brass cone is then rotated within the 
steel cylinder until one of the known faces, e. g. A, falls in the zone of 
the steel faces /' F f" [not figured]. After this adjustment has been made, 
and A thus brought to a position at right angles to the screw-plane passing 
through the screw cr, the angles a ' and b' which B and A make with F 
are measured on a goniometer. The corrections necessary to be made 
in the position of the crystal are then calculated. For the details of the 
method of calculation we must refer our readers to the original paper. 
Our means of correcting the position of the crystal depend on our being 
able to incline it in two planes at right angles to one another, which we 
may assume to be the screw-planes of the levelling tripod. We carry 
out these corrections by turning the micrometer-screws in the reverse 
direction to that which would be required if the crystal occupied the 
position of the spirit-level. We then place the so adjusted levelling 
tripod again on the top of the grinding tripod — which latter we assume 
