OPTICS. 
G24 
from the centre of the glafs to the object you were view¬ 
ing; and afterwards, applying the compafles to any ruler 
with a diagonal fcale of the parts of an inch marked on it, 
you will eafily find how many parts of an inch the faid 
diftance is. When that is known, compute how many 
times thofe parts of an inch are contained in eight inches, 
the common ftandard of fight, and that will give you the 
number of times the diameter is magnified ; Iqu'aring the 
diameter will give you the fuperficies ; and, if it be an ob¬ 
ject whofe depth or whole contents you would learn, mul¬ 
tiplying the fuperficies by the diameter will fliow the cube, 
or bulk. 
The magnifying power of a compound microfcope mull 
be computed from the effedl of all the lenles ; or it 
may be alcertained experimentally in the following man¬ 
ner : Place part of a divided ruler before the microfcope, 
fo that, looking through the inftrument, you may fee 
one of its divifions magnified ; then open the other eye 
alfo, and looking with it at the ruler out of the micro¬ 
fcope, you will perceive the image of the magnified divi- 
fion as it were projected upon the ruler; and you may ea¬ 
fily fee how many divifions of the unmagnified ruler mea- 
fure, or are equal to, the fingle magnified divifion, and 
that number is the magnifying power of that microfcope. 
Thus, if the ruler be divided after the common way into 
inches and tenths, and if you find that one magnified 
tenth is equal to three inches, you may conclude that 
the microfcope magnifies 30 times. 
Micrometers'. Plate XIII. 
The micrometer is an inftrument by which fmall angles, 
or the apparent magnitudes of objedts viewed through 
telefcopes or microfcopes, are meafured with great exadt- 
nefs. 
I. The firft telefcopic micrometers were only mechani¬ 
cal contrivances for meafuring the image of an objedt in 
the focus of an objedl-glafs. Before thefe contrivances 
were thought of, aftronomers were accuftomed to mealure 
the field of view in each of their telefcopes, by obferving 
how much of the moon they could fee through it, the 
femi-diameter being reckoned at 15 or 16 minutes ; and 
other diftances were eftimated by the eye, comparing 
them with the field of view. Mr. Gafcoigne, an Englilh 
gentleman, however, fell upon a much more accurate 
method before the year 1641, and had a Treatife on Op¬ 
tics prepared for the prefs ; but he was killed during the 
civil wars in the fervice of Charles I. and his manulcript 
was never found. His inftrument, however, fell into the 
hands of Mr. R. Townley, who fays, that by the help of 
it he could mark above 40,000 divifions in a foot. Phil. 
Tran]’. N° 25. 
Mr. Gafcoigne’s inftrument being fliown to Dr. Hooke, 
he gave a drawing and defcription of it, and propofed fe- 
veral improvements. Mr. Gafcoigne divided the image of 
an objedt in the focus of the objedl-glafs, by the approach 
of two pieces of metal ground to a very fine edge, in the 
place of which Dr. Hooke would fubftitute two fine hairs 
ftretched parallel to one another. 
Mr. Huygens (1659) meafured the apparent diameters 
of the planets, by firft determining the quantity of the 
field of view in his telefcope ; which, he fays, is beft done 
by obferving the time that a ftar takes up in pafling over 
it, and then preparing two or three long and (lender brafs 
plates, of various breadths, the fides of which were very 
ftraight, and converging to a fmall angle.. In ufing thele 
pieces of brafs, he made them Aide in two flits, cut in the 
fides of the tube, oppofite to the place of the image, and 
obferved in what place it juft covered the diameter of any 
planet, or any fmall diftance that he wanted to meafure. 
It was obferved, however, by fir Ifaac .Newton, that the 
diameters of planets, meafured in this manner, will be 
larger than they fliould be, as all lucid objects appear to 
be when they are viewed upon dark one?. 
In the Ephemerides of the marquis of Malvafia, pub- 
Jifhed in 1662, it appears that he had a method of meafuring 
fmall diftances between fixed ftars and the diameters of 
the planets, and alfo of taking accurate draughts of the 
fpots of the moon by a net of filver wire, fixed in the focus 
of the eye-glafs. He likewife contrived to make one of 
two ftars pafs along the threads of this net, by turning it, 
or the telefcope, as much as was neceflary for that purpofe 5 
and he counted, by a pendulum-clock beating feconds, 
the time that elapfed in its paflage from one wire to an¬ 
other, which gave him the number of minutes and feconds 
of a degree contained between the intervals of the wires 
of his net, with refpedt to the focal length of his tele¬ 
fcope. 
In 1666, MelTrs. Auzout and Picard publifhed a de¬ 
fcription of a micrometer, which was nearly the fame 
with that of the marquis of Malvafia, excepting the me¬ 
thod of dividing it, which they performed with more ex- 
adtnefs by a fcrew. In fome cafes they ufed threads of 
filk, as being finer than filver wires. Dechales alfo re¬ 
commends a micrometer confiding of fine wires, orfilken 
threads, the diftances of«which were exadtly 'known, dif- 
pofed in the form of a net, as peculiarly convenient for 
taking a map of the moon. 
M. de la Hire fays, that there is no method more Ample 
or commodious for obferving the digits of an eclipfe than 
a net in the focus of the telefcope. Thefe, he fays, were 
generally made of filken threads ; and that for this parti¬ 
cular purpofe fix concentric circles had alfo been made 
ufe of, drawn upon oiled paper; but he advifes to draw 
the circles on very thin pieces of glafs with the point of a 
diamond. He alfo gives feveral particular diredtions to 
aftift perfons in the ufe of them. See Phil. Tranf. vol. i. 
and xlviii. Hooke’s Pofthumous Works. Huygens’s 
Obf. on Saturn’s Ring, 1659. Adi. Par. 1701 and 1717. 
The moft common and Ample micrometer is fliown at 
fig. 1. Plate XIII. Let ABCD be a fedlion of the tele¬ 
fcope at the principal focus of the objedl-glafs, or where 
the wires are fituated, which are placed in a fhort- tube 
containing the eye-glafs, and may be turned into any po- 
fition by turning that tube ; mn is a fine wire extended 
over its centre; vw, xy, are two parallel wires well defined, 
and perpendicular to mn; vtv is fixed, and xy moves pa¬ 
rallel to it by means of a fcrew, which carries two indexes 
over a graduated plate, to fhow the number of revolutions 
and parts of a revolution which it makes. Now to mea¬ 
fure any angle, we muft firft afcertain the number of re¬ 
volutions and parts of a revolution correfponding to fome 
known angle, which may be thus done : ift, Bring the 
inner edges of the wires exadlly to coincide, and fet each 
index to o ; turn the fcrew, and feparate the wares to any 
diftance ; and obferve the time a ftar m is in pafling along 
the wire mn from one vertical wire to the other ; for that 
time, turned into minutes and feconds of a degree, will be 
the angle anfwering to the number of revolutions, or the 
angle correfponding to the diftance. Thus, if d=z cof. of 
the liar’s declination, we have 15' dm, the angle corref¬ 
ponding to this diftance; and hence, by proportion, we 
find the angle anfwering to any other. 2dly, Set up an 
objedt of a known diameter, or two objedts at a given 
diftance, and turn the fcrew till the vertical wires become 
tangents to the objedt, or till their opening juft takes in 
the diftance of the two objedts upon the wire mn ; then 
from the diameter, or diftance of the two objects from 
each other, and their diftance from the glafs, calculate the 
angle, and obferve the number of revolutions and parts 
correfponding. 3dly, Take the diameter of the fun on 
any day* by making the wires tangents to the oppofite 
limbs, and find, from the Nautical Almanac, his diame¬ 
ter on that day. Here it will be beft to take the upper 
and lower limbs of the Tun when on the meridian, as he 
has then no motion perpendicular to the horizon. If 
the edges do not coincide when the indexes ftand at o, 
we muft allow for the error. Inftead of making a propor¬ 
tion, it is better to have a table calculated to fhow the 
angle correfponding to every revolution and parts of a re¬ 
volution, But the obferver muft remember, that, when 
1 the 
