GONIOMETER. 



h3^;e been found nearly accurate enough for tlie purpofet for of the rcflecling furface, the rcflccled image of fome 

 which they arc required, many intcrclling quellions in the tant chimney may be feen inverted beneath its true n 



tnodern Tcience of cryC.allography requiring a much more 

 exacl determination of tiie angle than can poffibly be obtaiii- 

 ed by inftruments of this conllruction. 



We are indebted to Dr. W^olhillon for having removed all 

 thefe difficulticj, by the invention of an inftrument which 

 ^ acconiplidies all that the moll fcrnpulons natnralift can pof- 

 Clily defire. The principle of this invention is entirely op- 

 tical, and {Piute XIX. AHjc.-lla>iy,fg. 2.) reprcfents the in- 

 Urument as made and fold by Mr. Carey, in the Strand; but 

 the reader, when acquaiiitcd witli the nature of it, will rea- 

 dily fee that any perion poifelTcd of a graduated inftrument, 

 fuch as a theodolite, tranfit, &c. may, without great diffi- 

 culty, apply it to the incafurenient of angles., though in a 

 much lefs commodious manner than on an inftrument made 

 exprefsly for the purpoL', 



Dr. WoUaftou's method coufifts in employing a ray of 

 light refletied from the fiu-facc, inllead of ih.e furface it- 

 felf; and thus, for a radius of i-joth of an inch, we may 

 fubiiitute either the diilance of the eye from the cryllal, 

 which would naturally be twelve or fifteen inches, or for 

 greater accuracy we may, by a fecond mode, fubiiitute the 

 diftance of objecls feen at a hundred yards or more from 

 us. The inllrument dcfcrlbed by Dr. Wollafton, in the 

 Tranfaclions for 1809, confifts of a circle, _/5V. 3, gradu- 

 ated on its edge, and mounted on an horizontal axle fup- 

 ported by an upright pillar. This axle, being perforated, 

 admits the pafiage of a fmaller axle through it, to which 

 any cryllal of moderate fize may be attached by a piece of 

 wax, with its edge, or interfeclion of the furfaces, hori- 

 zontal and parallel to the axis of motion. This pofition of 

 the crytlal is firft adjufted, fo that by turning the fmalkr 

 axle, each of the two furfaces, vi'hofe inclination is to be 

 meafured, will reflect the fame light to the eye. The circle 

 is then fet to zero, or 180 , by an index attached to the 

 pillar that fupj'orls it. 



The fniall axle is then turned till the further furface re- 

 flects the light of the candle, or other definite objedl, to 

 the eye; and laftly, (the eye being kept lleadily in the 

 fame place, ) the circle is tiu-ned by its larger axle, till the 

 fecond furface reflefts the fame light. This fecond furface 

 is thus afcertained to be in the fame pofition as the former 

 furface had been: the anidc thron>{h which the circle has 

 moved, is, in facl, the fupplement to the inclination of the 

 furfaces; but as the graduations on its margin are numbered 

 accordingly in the inverted order, the angle is correctly 

 fhewn by tlie index, witliout requiring any computation. 



It may be here obferved, that it is by no n-.eans ncccflary 

 to have a clean uniform fraflure for this application of the 

 inftrument to the ilruflure of laminated fubftances; for 

 fince all thofe fmall portions of a (battered furface that are 

 parallel to one another, (though not in the fame plane,) 

 gliften at once with the fame light, the angle of an irregidar 

 (urface may be determined nearly as well as when the re- 

 flefting furfaces are aflually in the fame plane. In this 

 method of taking the meafure of an angle, when the eye 

 and candle are only ten or twelve inches dillant, a fmall 

 error may arife from parallax, if the interledlioa of the 

 planes or edge of the cryllal be not accurately in a line 

 with the axis of motion. But fuch an error may be ren- 

 dered infenfible, even in that mode of ufing the inllrument, 

 by due care in placing the cryftal ; and when the furfaces 

 are fufficiently frnooth to reflect a dillinft image ot obje&s, 

 all errors from the fame fource niay be entirely obvratcd by 

 another niode of ufnig it. 



For this purpofe, if tlic eye be brough.t witliiji ;'.u incii 



dlf. 

 mney may be leen inverted beneath its true place, 

 and, by turning the fmall axis, may be brought to corrc- 

 fpond apparently with the bottom of the houfc, or fome 

 other diftant horizontal line. In this pofition the furfacr 

 accurately bifefts the angle which the height of that houfe 

 fubtends at the eye, or rather at the reflecting furface; 

 then, by turning the whole circle and cryftal together, the 

 other furface, however fmall, may be brought exaftly into 

 the fame pofition ; and the angle of the furfaces may thus 

 be meafured, with a degree ofprecifion that has not hitherto 

 been expected in goniometry. 



The accuracy,, indeed, of this inftrument is fuch, tial a 

 circle of moderate dimenfions, with a vernier adapted to it, 

 will probably afford corredtions to many former obferva- 

 tions. Dr, Wollafton has remarked one inftance of a mif- 

 take that prevails, refpefting the common carbonate of lime, 

 which he mentions, bccaufe this fubllanee is very likely to 

 be employed as a teft of the corredlnefs of fuch a gonio- 

 meter, by any one who is not convinced of its accuracy, 

 from a diftinft conception of the principles of its conftruc- 

 tion. 



The inclination of the furfaces of a primitive cryftal of 

 carbonate of lime, is ftated with great appearance of preci- 

 fion to be 104' 28' 40": a refult deduced from the fup- 

 pofed pofition of its axis, at a:i angle of 45°, with each of 

 the furfaces, and from other feducing circumllanccs of appa- 

 rent harmony by fi-.nple ratios. 



But however ftrong the prefumption might be, that th:» 

 angle, which by meaiiiremenl approached to 45% is actually 

 fo, it mull iieverthelefb be, in' fact, about 45" 20'; for the- 

 inclination of ll'.c furfaces to each other is found to be very 

 nearly, if not accurately, 105'', as it was formerly deter- 

 mined to be by Hnygcns; and fince the meafure of the 

 fuperlicial angle, given by fir Ifaac Newton, correfponds 

 with this determination of Hnygens, his evidence mav be 

 confidered as a further confirmation of the fame refult ;' for 

 it may be prefumed, that he would not adopt the meafures 

 of others without a careful examination. 



Esplanat'ion of the Figurt. 



ah. Is the principal circle of the goniometer, graduated 

 on its edge. 



c c. The axle of the circle. 

 d, A nulled head, by which the circle is turned. 



e e. The fmall axle for turning the cryftal, without mov- 

 ing the circle. 



f, A milled head on the fmall axle. 



g, A brafs plate fupjjorted by the pillar, and gradu- 

 ated as a vernier to every five minutes. 



/>, The extremity of a fmall fi)ring, by which tlie cir- 

 cle is flopped at 180 , without the trouble of reading off. 



i i and h k. Are two centres of motion, tlie one liori- 

 zontal, the other vertical, for adjufling the pofition of 3 

 cryftal; one turned by the handle /, the other bv the milled 

 head m. 



The cryftal being attached to a fcrcw head at the point 

 iL, in the centre of all the motions, willi one of its furfaces 

 ;is nearly parallel as may be to the milled head m, is next 

 rendered truly parallel to the axis, by turning the handle / 

 till the refleiited image of a horizontal hue is feen to be truly 

 horizontal. By means c\f the milled licad J\ the fecond fur- 

 face is tlien brought into the pofition of the iirft, and if the 

 refletled image from this furface is found not to Iw hori- 

 zontal, it is rendered fo by turning the milled head m, and. 

 fince this motion is parallel to the firft f;uface, it does not 

 derange the preceding adjuftirent, 



CONIO. 



