O'Reilly — 
Oil a New Form of Goniometer. 
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ment ; and there must necessarily be an arrangement allowing of the 
proper placing of the crystal edge for measurement. The method by 
which this is attained in the Wollaston Goniometer is so simple and 
so perfect that it becomes indispensable. The I method of placing 
the edge of the crystal in the axis of the instrument varies, but 
all the arrangements employed resolve themselves into attaching 
the crystal, by a piece of wax, to a moveable piece which is rendered 
capable of movement in different directions, or planes, so that the 
desired position of the edge may be accurately attained. In the pre- 
sent instrument, those arrangements have been suppressed, for a very 
simple reason, that the intermediary of wax being in all cases 
requisite for attaching the crystal, it is much more simple for the 
observer or student to use his manipulative skill, in attaching it, so 
that he may insure all the conditions necessary for correct measure- 
ment ; and a proper disposal of the piece of wax employed can always 
allow of this result being practically attained. There would, therefore, 
necessarily remain, as fundamental part of the instrument, the 
cylindrical axis carrying the crystal, moveable in a sheath, or exterior 
cylinder carrying the divided scale, whether straight or circular. 
JN'ow if we suppose, traced on the cylindrical axis carrying the 
crystal, a spiral or screw of any given pitch, and if we suppose this 
axis to turn within a cylindrical sheath of at least the length 
of half the pitch of the screw, and that, moreover, the exterior cy- 
linder be cut away so as to form a slit in its surface parallel to the axis 
of the instrument, and of the length of the half pitch, it is clear that the 
spiral traced on the axis must cut the edges of the slit, at distances from 
either extremity of it, proportional to the angle through which the 
axis shall have been turned. It is equally evident that a divided scale 
carrying 90 or 180 division will give, for a half revolution, measurements 
in double or single degrees of this angle. In fact, the divided circle of 
the Wollaston Goniometer is replaced by a spiral on the axis. ]^ow this 
method of measurement is independent of the diameter of this cylin- 
drical axis, and depends entirely for accuracy on its length. We have 
thus the means of reducing considerably the bulk of the instrument, 
while, by taking, as units of division on the straight edge of the slit, 
half millimetres, or millimetres, which can thus most conveniently be 
introduced, we can have the measuring part of the instrument reduced 
to a length of 180 millimetres at most, and practically to 9 millimetres ; 
measuring to single degrees, if the half millimetre be taken as unit, or to 
double degrees if the millimetre. The whole instrument may thus have a 
length not exceeding 25 centimetres, and reducible to about 15, while 
the greatest diameter may not be more than 15 millimetres, and I 
believe, can be reduced to 10 millimetres by nice construction. The 
form of the instrument would even allow of a greater length without 
rendering it at all inconvenient, or unsafe for carriage. 
It remains to show that accuracy is no way lost, at the expense of 
compactness ; in other words, that the vernier arrangement is both 
simple and elfective. The exact determination of the coincidence of 
