620 OPT 
Q has exadily forty threads in an inch; therefore the 
upper plate GDEF will move one inch while the hand a 
moves forty times round ; the four-thoufandth part of 
an inch while the hand moves over one of the divifions 
round the limb; and the twenty-thoufandth part of an 
inch while the index x moves one part of the two hun¬ 
dred round the limb of the circular plate W ; and the 
under plate RNMY will move half an inch, the two- 
thou-fandth part of an inch, and the ten-thoufandth part 
of an inch, the fame way, in the faid refpedtive times. 
Hence, if the under plate, having a large round hole in 
it, be fixed to a telefcope, fo that the frame is movable, 
together with the whole infirument, except the faid lower 
plate; and the ftraight fmooth edge HI of the fixed plate 
ABIH, as likewife the ftraight fmooth edge DE of the 
movable plate GDEF, be perceivable through the round 
hole in the under plate, in the focus of the objedt-glafs; 
then, when the handle of the micrometer is turned, the 
edge HI of the narrow plate ABIH, fixed to the frame, 
and DE of the movable plate, will appear through the te¬ 
lefcope equally to approach to, or recede from, each other. 
By thefe edges we mall be able to meafure the apparent 
diameters of the fun, moon, &c. the manner of doing 
which take as follows: Suppofe, in looking at the moon 
through the telefcope, you have turned the handle till the 
two edges DE and HI are opened, fo as' juft to touch or 
clafp the moon’s edges; and that there were twenty-one 
revolutions of the hand a to complete that opening : firft 
fay, As the focal length of the objedt-glafs, which fup- 
pofe ten feet, is to radius, fo is one inch to the tangent 
of an angle fubtended by one inch in the focus of the ob¬ 
jedt-glafs ; which will be found twenty-eight minutes 
thirty feconds : again, becaufe there are exadily forty 
threads of the ferews in one inch ; fay, If forty revolu¬ 
tions of the hand a give an angle of 28' 30'', what angle 
will twenty-one revolutions give? The anfwer will be, 
fifteen minutes eight feconds; and fitch was the moon’s 
apparent diameter. And fo may the apparent diameters 
of any other objects be taken. It muft be here obferved, 
that the divifions on the top of the plate GDEF are dia¬ 
gonal divifions of the revolutions of the ferews, with dia¬ 
gonal divifions of inches againft them; thus, as the faid 
plate Aides along, thefe diagonals are cut' by divifions 
made on the edge of the narrow plate KL, fixed to the 
oppofite fide of the frame by means of two ferews. Thefe 
diagonal divifions ferve for a regifter to count the revo¬ 
lutions of the ferews, and to Arovv how many there are in 
an inch, or the parts of an inch. 
A confiderableimprovement with regard to the micro¬ 
meter, was communicated to the Royal Society, in 1743, 
by Mr. Servington Savery, of Exeter; an account of 
which, extracted from the minutes by Mr. Short, was 
publifhed in the Phil. Tranf. for 1753. vol. xlviii. art. 26. 
The firft hint of fuch a micrometer was fuggefted by M. 
Itoemer, in 1675; and M. Bouguer propofed a fimilar 
conftruhtion to that of Mr. Savery, in 1748, for which fee 
Heliometer, vol. ix. The late Mr. Dollond made a 
farther improvement in this kind of micrometer; an ac¬ 
count of which was given to the Royal Society by Mr. 
Short, and publifhed in the Phil. Tranf. vol. xlviii. art. 27. 
Inftead of two objefit-glafles, he ufed only one, which 
{after having been truly ground and well centered) he 
neatly cut into two femi-circles, and fitted each ferni- 
circle in a metal frame, fo that their diameters Aiding in 
one another, by means of a threw, may have their centres 
fo brought together as to appear like one glafs, and fo 
form one image ; or, by their centres receding, may form 
two images of the fame object; it being a property of 
fuch glaffes for any fegment to exhibit a perfedl image 
of an objedt, although not fo bright as the whole glafs 
would give it. If proper feales are fitted to this inltru- 
inent, fhowing how far the centres recede relative to the 
focal length of the glafs, they will alfo Aiow'how far the 
two parts of the fame objedt are afunder relative to its 
(di&ince from the objedt-glafs; and confequently give the 
I c s. 
angle under which the diftance of the parts of that objedt 
are feen. This divided objedt-glafs micrometer, which 
was applied by the late Mr. Dollond to the objedt-end of 
a refledting telefcope, and afterwards with equal advan¬ 
tage adapted by his foil to the end of an achromatic te¬ 
lefcope, is fo eafy of ufe, and affords fo large a fcale, that 
it is generally looked upon by aftronomers as the molt 
convenient and exact inftrument for meafuring fmall dif- 
tances in the heavens. However, the common microme¬ 
ter is peculiarly adapted for meafu ring differences of right 
afeenfion and declination' of celeftial objedts, but lefs 
convenient and exadt for meafuring their abfolute dis¬ 
tances ; whereas the objedt-glafs micrometer is peculiarly 
fitted for meafuringdiftances, but has been generally fup- 
poled improper for meafuring differences of right afeen¬ 
fion and declination. But Dr. Mafkelyne has found that 
the latter may be applied with very little trouble, and 
fmall additional expenfe, to this other purpofe as w'ell as 
the former; and he has furniftied the diredtions neceflary 
to be followed when it is ufed in this manner. The ad¬ 
dition requifite for this purpofe is a cell, containing two 
wires, interfering each other at right angles, placed in 
the focus of the eye-glafs of the telefcope, and movable 
round about by the turning of a button. For the de- 
feription of this apparatus, together with the method of 
applying and ufing it, we fiiall refer to Dr. Malkelyne’s 
paper on the fubjedt, in the Phil. Tranf. vol. lxi. art. 49. 
=. After all, the ufe of the objedt-glafs micrometer is at¬ 
tended with difficulties, arifingfrom the alterations in the 
focus of the eye, which are apt to caule it to give dif¬ 
ferent meafures of the fame angle at different times. In 
order to obviate thefe difficulties, Dr. Mafkelyne, in 1776, 
contrived a pri/malic micrometer, or a micrometer confid¬ 
ing of two achromatic prifms, or wedges, applied between 
the objedt-glafs and eye-glafs of an achromatic telefcope, 
by moving of which wedges nearer to, or farther from, the 
objedt-glafs, rhe two images of an objedt produced by 
them appeared to approach to, or recede from, each other, 
fo that the focal length of the objedt-glafs becomes a fcale 
for meafuring the angular diftance of the two images. 
The rationale and ufe of this micrometer are explained 
in the Phil.Tranf. vol. lxvii. art. 36. A fimilar invention 
by the abbe Rochon, and improved by the abbe Bofcovich, 
was alfo communicated to the Royal Society, and pub- 
lilhed in the fame volume of the TranfaCtions, art. 35. 
In the Phil. Tranf. for 1779, the late ingenious Mr. 
Ramfden has deferibed two new micrometers, which he 
contrived with a view of remedying the defers of the 
objedt-glafs micrometer. 
One of thefe is a catoptric micrometer, which, befides 
the advantage it derives from the principle of refledtion, 
of not being difturbed by the heterogeneity of light, 
avoids every defedt of other micrometers, and can have 
no aberration, nor any defedt ariling from the imperfec¬ 
tion of materials or of execution ; as the extreme fim- 
plicity of its conftrudfion requires no additional mirrors 
or glaffes to thofe required for the telefcope ; and, the fe- 
paration of the images being efi’edted by the inclination 
of the two fpecula, and not depending on the focus of 
any lens or mirror, any alteration in the eye of an obferver 
cannot affect the angle meafured. It has peculiar to it- 
felf the advantages of an adjuftment, to make the images 
coincide in a direction perpendicular fo that of their mo¬ 
tion ; and alio of meafuring the diameter of a planet on 
both fides of the zero, which will appear no inconfider- 
able advantage to obfervers who know how much eafier it 
is to afeertain the contadt of the external edges of two 
images than their perfect coincidence. 
A, fig. 5, reprefents the fmall fpeculum of a refledling 
telefcope of Caffegrain’s conftrudfion, to which this mi¬ 
crometer is adapted, divided into two equal parts ; one 
of which is fixed on the end of the arm B; the other end 
of the arm is fixed on a fteel axis X, which crofies the end 
of the telefcope C. The other half of the mirror A is 
fixed on the arm D, which arm at the other end termi¬ 
nates 
