OPTICS. 
Mr. Smeaton’s equatorial micrometer, together with its 
Xife in an observation of a t ran fit of Mercury, is defcribed 
and exhibited in the Phil. Tranf. vol. Ixxvii. art. 33. We 
have alfo the delcription of a micrometer for taking the 
angle of pofition, with drawings for illuftrating its con- 
jftruClion, as it was executed by Meffrs. Nairrie ancj Blunt, 
in a paper by J)r. Herfchel, Phil. Tranf. vol.lxxi. p. 500. 
and a further account of its ufe, and the mode of improv¬ 
ing it, by Dr. Herfchel, Phil. Tranf. vol. Ixxv. p. 46. Mr. 
Troughton’s micrometer is applied to the eye-piece of a 
telefcope for meafuring exceedingly fmall angles, as the 
diameters' of the heavenly bodies, &c. - 
Mr. Brewfter has alio directed his attention to the im¬ 
provement of micrometers, and has invented one in par¬ 
ticular which appears to be highly deferving of notice in 
this place. In this inftrument a pair of Jixcil wires is 
made to fubtend different angles by varying the magni¬ 
fying power of the telefcope, by Aiding one tube within 
another; whereas, in all other micrometers with wires, 
this effeCt is produced by mechanical contrivances. Mr. 
Brewfter’s method of hunting and opening the wires op¬ 
tically, is therefore free from all thofe fources of error to 
which other micrometers are fubjeCt, and renders it par¬ 
ticularly ufeful to the practical aftronomer ; while the 
mode of changing the magnifying-power, by the motion 
of a fecond objeCt-glafs, affords a length of fcale equal to 
the local diftanceof the principal objeCt-glafs. Thefame 
principle is peculiarly applicable to the .Gregorian tele¬ 
fcope ; for the magnifying-power of this inftrument can 
be changed by merely increafing or diminifhing the dif- 
tance of the eye-piece from the large fpeculum. 
In the common micrometer, which can manifeftly, as 
well as Mr. Cavallo’s and Mr. Brewfter’s, be ufed in the 
menfuration of diftances, the focal length of the telefcope 
to which it is attached remains always the fame; fo that 
a correction computed from an optical theorem mull be 
applied to every angle that is meafured: but, in Mr. 
Brewfter’s telefcope and micromater, the focal length 
varies in the fame proportion as the diftance of the ob- 
jeCt; and, confequently, no corredfion of the angles can 
be neceffary. To obviate tire neceftity of having a ftand 
for the inftrument, which would prevent its ufefulnefs at 
fea, Mr. Brewfter divides the fecond or movable objeCl- 
glafs into two, as in the divided objeCt-glafs micrometer. 
By this contrivance two images are formed, and thefe 
images are feparated or made to form different angles at 
the eye, by bringing the movable objeCt-glafs nearer to 
the fixed one. In determining the angle, therefore, we 
have only to bring the two images of the objeCt into con- 
tadi; and fuch contafl the eye is capable of afeertaining 
even during the agitation of a carriage, as the two images 
retain the lame relative pofition, whatever be their abfo- 
lute motion. This ingenious inftrument, being formed 
with Aiding tubes, is very portable and convenient; and 
will be found extremely ufeful to military gentlemen, 
and others, who may wifh to afeertain diftances without 
a more cumberfome apparatus. See Halley’s Nat. Phil, 
by Gregory, vol. ii. p. 427. 
The late Mr. Cavallo contrived a micrometer of very 
Ample and eafy conftruCtion. It confifts of a fmall femi- 
tranfparent fcale or flip of mother-of-pearl, about the 20th 
part of an inch broad, and of the thicknefs of common 
writing-paper. It is divided into a number of equal parts 
by means of parallel lines, every fifth and tenth of which 
divifions is a little longer than the reft. This micrometer, 
or divided fcale, is fituated within the tube at the focus 
of the eye-lens of the telefcope, where the image of the 
objedt is formed,and with its divided edge pafiing through 
the centre of the field of view ; though this is not abfio- 
lutely necefiary. It is immaterial whether the telefcope 
be a refradior or a refledtor, provided the eye-lens be con¬ 
vex, and not concave, as in the Galilean telefcope. The 
fimpleft way of fixing it, is to flick it upon the diaphragm, 
■which generally ftands within the tube, at the focal dif- 
Vol. XVII. No, 1203. 
629 
tance of the eye-lens. By looking through the telefcope, 
the image of the objedt and the micrometer will appear to 
coincide: hence the obferver may eafily fee how many 
divifions of the latter meafure the length or breadth of 
the former; and, knowing the value of the divifions of the 
micrometer, he may eafily determine the angle which is 
fubtended by the objedt. 
There are feveral methods of afeertaining the value of 
the divifions of a micrometer in a given telefcope. The 
following is one of the eafieft. 
Diredt the telefcope to the fun, and obferve how many 
divifions of the micrometer meafure its diameter exadtly ; 
then take out of the Nautical Almanac the diameter of 
the fun for the day in which the obfervation is made ; 
divide it by the above-mentioned number of divifions, 
and the quotient is the value of one divifion of the micro¬ 
meter. Thus, fuppofe that 26£ divifions of the micro¬ 
meter meafure the diameter of the fun, and the Nautical 
Almanac gives for the meafure of the angle which is 
fubtended by the fame diameter, 3 i' 22", or (by reducing 
it all into feconds) 1882". Divide 1882'' by 26'$, and the 
quotient, neglecting a fmall remainder, is 71", or 1' 11"; 
which is the value of one divifion of the micrometer; the 
double of which is the value of two divifions; the treble 
is the value of three divifions; and fo forth. See Ca¬ 
vallo’s Philofophy, vol. iii. and Phil. Tranf. for 1771. 
art. 19. 
Mr. (now Dr.) Brewfter’s circular mother-of-pearl mi¬ 
crometer is an improvement upon the above. In the 
Phil. Mag. vol. xxix. he has given an account of the cir- 
cumffances which led to the invention, and of its advan¬ 
tages. In the winter of 1805 (lie obferves), when I was 
employed in delineating the l’urface of the moon, I wiftied 
to meafure the diameter of the lunar fpots by applying 
Mr. Cavallo’s micrometer to a thirty-inch achromatic 
telefcope made by Berge. But, as the eye-piece was 
moved by a rack and pinion, and confequently couldriiot 
turn round its axis, the micrometer muft have remained 
ftationary, and could only meafure angles in one direc¬ 
tion. This difficulty, indeed, might have been fur- 
mounted by a mechanical contrivance for turning the 
diaphragm about its centre, or more fimply by giving a 
motion of rotation to the tube which contains the third 
and fourth eye-glaffes. Such a change in the eye-piece, 
however, w”as both inconvenient and difficult to be made. 
Mr. Cavallo’s micrometer, therefore, has this great difad- 
vantage, that it cannot be ufed in reflecting telefcopes, or 
in any achromatic telefcope where the adjuftment of the 
eye-piece is afteCted by rackwork, unlefs the ftruCture of 
thefe inftruments is altered for the purpofe. Another 
difadvantage of this micrometer arifes from the fiip of 
mother-of-pearl pafiing through the centre of the field. 
The picture in the focus of the eye-glafs is broken into 
two parts, and the view’ is rendered (till more unpleafant 
by the inequality of the fegments into which the field is 
divided. In addition to thefe difadvantages, the different 
divifions of the micrometer are at unequal diftances from 
the eye-glafs which views them, and therefore can neither 
appear equally diftinCt, nor fubtend equal angles at the 
eye. Finding that Mr. Cavallo’s inftrument laboured 
under thefe imperfections, I thought of a circular mother- 
of-pearl micrometer, which is free from them all, and has 
like wife the advantage of a kind of diagonal fcale, increaf¬ 
ing in accuracy with the angle to be meafured. This 
micrometer, which I got executed by Miller and Adie, 
optical-inftrument-makers in Edinburgh, I have often 
ufed, both in determining fmall angles in the heavens, 
and fuch as are fubtended by terreflrial objeCts ; &c. &c. 
We muft refer to the volume above quoted, p. 48. for a 
particular defeription of the inftrument, and the tables 
and calculations upon which it proceeds. 
II. The micrometer, as we have already noticed, has 
not only been applied to telefcopes, and employed for 
aftronomical purpofes, but there have alfo been various 
7 X contrivances 
