836 , . GONIOMETER. ih, OD 
‘Goniometer, Copper»... » 80.427. 
=e Din.) (vis. ceed ierikeays 
100.000 
~ Mr Murdoch has recently discovered not only the 
proper composition, but also the mode of manufacturing 
gongs; and in the course of his investigation has ob- 
tained several interesting results, which we hope to be 
able to communicate in asubsequent article. SeeGehlen’s 
Journal, Second Series, vol. ix. p. 408; and Thomson’s 
Annals of Philosophy, vol. ii. p. 208. 315, 316. 
GONIOMETER, from ywvie an angle, and wergew to 
measure, is the name of a class of instruments for mea- 
suring the inclination of one plane surface to another. 
As the principal use of these instruments is to mea- 
sure the angles of crystallised bodies, they were first 
introduced, and are now principally used, by mineralo- 
gists; although those which depend on the principle of 
reflexion, are of the most essential utility in many 
branches of physics, particularly in optical experiments. 
€ommon In our article CrysTattocrapny, p. 454, we have al- 
gaa ready described the goniometer used by Romé de Lisle, 
and M. Hauy, and invented by M. Carangeau, (see Plate 
CCXXIII. Fig. 34.) and in the same article we have 
given drawings and descriptions of the new reflecting 
iometers invented by Dr Wollaston and Dr Brewster. 
See Plate CCXXIV. Figs. 1. and 2. The present arti- 
cle will therefore embrace some additional remarks on 
the applicacion of the principle of reflexion, and an ac- 
count of some other goniometrical instruments which 
could not with propriety have been introduced under 
the head of CrysTaLLoGrapPny. 
The reflecting goniometers of Dr Wollaston and Dr 
Brewster were invented nearly about the same time, 
without any communication between their respective 
authors ; but though these instruments resemble one 
another in so far as they both make use of the principle 
of reflexion, yet they differ very widely in the applica- 
tion of that principle, and in the mode of measuring the 
angles of crystals, 
One of the advantages which Dr Brewster’s gonio- 
Reflecting meter possesses over that of Dr Wollaston’s, is, that the 
goniometers former is capable of measuring a hollow angle, such as 
by ke gone abc, represented in Plate CCLXXVII. Fig. I. and’2. 
Eeewter, ot one in which the crystal abc, Fig. 3. is imbedded 
in. a stony mass from which it cannot easily be detach- 
Pirate ed. The case represented in Fig. 2: is‘one which ac- 
ae tually occurs in measuring the angle-which the edge of 
8 1,% 3 the interrupting stratum, or crystallised’ vein of some 
specimens; of Iceland spar, forms with the surfaces of the 
rhomboid: The determination of this angle is of the 
utmost importance, and? is incapable of being measured 
by any goniometrical instrument with which we are 
acquainted, excepting that of Dr Brewster's. See Philo- 
sophical Transactions for 1815, p. 277. 
_ This goniometer will measure the angles of crystals 
with great ‘accuracy, and little trouble, if the surfaces 
are moderately smooth, and reflect the smallest’ quan- 
tity of light. When the surface has the appearance of 
being perfectly rough: and irregular, the oblique re- 
flection generally gives'a very distinct image of a ver- 
tical bar, when the image of'a horizontal line or of any 
other object could not possibly be obtained. It fre- 
goenuly happens, however, that the crystal does not re- 
flect sufficient light to form an image, or is so irregular 
in its surface, or is so inconveniently placed in the spe- 
cimen, that a variety of different contrivances must be 
adopted for measuring its angles. In a specimen of 
Allanite, for example, belonging to Mf Allan, the-cry- 
stals are situated in such a manner; that’ their’ angles* 
could not be measured by any goniometer: without’ 
A 
breaking eb soncrebaansitieelte “parts of the mineral, 
When the planes of the crystal are smooth, but un- 
polished, a small piece of parallel glass AB, Fig. 4. or 5 
any other reflecting substance, with parallel sides, is 
successively: upon the surfaces of the c 
CDE; the coincidence of the direct image of a rectili- © 
neal object with the image reflected piece of 
glass, is observed as before, and the angle’ in 
precisely the same manner. If the two surfaces of the re- 
flector should not be parallel, the aberration will be cors 
rected by reversing its position on the second surface 
of the crystal. 
When’ the ‘planes of the-etyitil are sovered Wide 
asperities which prevent the piece of glass from 
parallel to these planes, we mtist make ‘use of ther 
flector AB, Fig. 5. supported by’ three slender feet, and 
so formed that the r ing plane mn is © 
Jel to the plane op, passing through the extremities of 
the three feet. The three feet are then placed 
those points of the surface where there are no 
and the coincidence of the images is 
reflector : RE ee ee { 
the crystal, the coincidence images again: 
vel and thie le of the planes anesstted as before. 
As the surface \e crystal may always be broi 
seein 
be proper to have two or three of these ri 
veils of different sizes, and with their feet at 
distances, in order to accommodate themselves to the 
smooth parts of the crystal. Dae ote 
5 th bd 
be fixed on each surface with bee’s wax, in 
presented in Fig. 6. where C is the erystal, and A, B Fig 
the two reflecting tripods. If the ae of the crys 
stal should prevent us from adopting either of these 
methods, which was the case in the specimen of Al-< 
lanite already mentioned, we must have recourse to 
the goniometrical mictoscope, which is intended to 
measure the angles formed by two lines when the eye 
is perpendicular to the plane of the angle. 
te we conceive the two surfaces of a crystal to be cut 
by a plane perpendicular to their common section, the — 
apparent angle contained’ by the two lines which form 
boundary: of the’section, when the eye is perpendia’ 
cular to the section, is evidently the inclination of the 
planes. But if the cutting plane is not 
to the common section, the apparent angles of the lines ; 
which form the vanes wo of the: orp besgeitheci 
an eye perpendicular, to it, 18 ev ly Fy 
ves Aha’ the real angle of the crystal, ording to the 
position of the cutting plane. If the observer, how= 
ever, places himself in such a manner, that the co 
mon section of the planes’ is: parallel to the axis of. 
eye, then the apparent angle formed’ by the ou 
lines of the section, whatever be the’ position of the 
ting-plane, is the real angle of the crystal. By placing 
the crystal therefore, in this position, in the 
the goniometrical microscope; whicly shall be hereafter 
described, and measuring the’ apparent’ angle formed 
by the’ bounding lines, we obtain, by a very simple 
process, the inclination of the planes. 
This will be understood’ from Fig. 7, in’ which ig 
ABCDEF is a crystal, ABC a section of it i 
cular to AD; and A 4 ¢ an oblique section. . Now, 
though BAC is the real angle of the crystal, yet, when — 
a ie ite bin me 
the oblique section Adc is viewed by the obs 
O; its bounding lines Ab, A’c are apparently coinci+ 
in the 
of 
ding, a drop of varnish or melted bee's 
wax may be placed round each of its feet. pen 9 
k 
Le 
Fl 
‘* 
