Let A 771 p n b, Plate CCCLXXV. Fig. 5. be the in tenor circumference of the micrometer scale, and let nt n be the object to be measured. Bisect the arch or 71 in /1, and draw C in, C p, C n. The line C /i will be at right angles to in n, and therefore in n will be twice the sins of half the arch ni p n. Consequently. A t : n= Rad : Sine of nz /2 72 ; therefore m n X 11=sti.
sin m n 712 /i 72 X AB. and in P x AB; a formu la by which the angle subtended by the cuord of number ol degrees may be easily found. The first part sin. p n of the formula, viz. is constant, while AB varies with the size of ine micrometer, and with the magnilying power which is applied. Dr. B. therel•re computed the followmg fable, containing the vain e of the constant part of the formula for every degree or di vision of the scale.
A series of micrometers, principally for the purposes of microscopical observations, were constructed by the Iate .Mr. Coventry of Southwark, with a degree of deli cacy and accuracy which was never before equalled. They consisted ol glass, ivory, and silver scales, on which are drawn parallel lines from the 10th to the 10,•00dth part of an tuck.
Mr. Barton of the mint, well known for his me chanical ingenuity, has carried the art of dividing mi crometrical scales to the highest c;,,gree ol perketion. The engine which he uses was given to him oy his late father-in-law, the cerebrated Mr. Harrison. It was constructed uy Mr. Han israi himself, and its merits de p, nd chiefly on the beauty and excellence of the screw ; the apparatus for cutting wnich. by an excellent inclin ed plane, also accompanied the engine The plate in the screw is not ei,ided higher than 2000dth parts of an inch ; but Mr Balton has drawn die isions on glass, so minute as the I uaa..0dth part of an inch. In drawing lines of ,:000 in an inch, Mr. Barton often leaves out one line by design ; and one of tnc greatest prools of the stability ol the engine is. teat after having taken off the brass table with the work upon it, wnen the omission is distinctly perceived. he can restore it to its placc, and introduce the line without its being distinguish able from the rest.
For farther information on fixed micrometers, see Huygen's Systema Saturni, p. 32. Cassini, Phil.
Trans. No. 236. Smilh's Optics. vol. ii p. 342 Ca vallo, Phil. Trans. 1791, p. 283. Cavallo's .tat. Philo sophy, vol. iii Phil. Mag. vole xxix p. 2S. Brewster's Treatise on .11zo Philosophical Instruments. p. 48. Br•r noulli, Mem. -lcad. Berl. 1173, p. 193. Watt, in the Edinburgh Philosophical Journal, vol. ii. p. 121.
On Wire Micrometers, in which the Wires or Fibres are opened and shut mechanically.
IN the original micrometer of Mr. Gascoigne, two metallic edges were made to separate from and ap proach one another ; and when his instrument was shown to Dr. Hooke, he immediately suggested the substitution of fine wires in place of the edges of me tallic plates, and they have accordingly been retained in almost all the subsequent forms of the instrument.
The wire micrometer,as constructed by Messrs. Au zout and Picard, underwent various improvements in the hands of Dr. Bradley and other astronomers, and in our article AsTROOMV, we have given a drawing and description or one of the most improved kind, as made by Mr. Troughton.
In all micrometers with moveable their sepa ration and approach is effected by means of a screw with about 100 threads in an inch, and as every revo lution of the screw is again divided upon a circular plait! into McItlis of an inch, the 10.0 .0dth part of an inch may be perceived in the number ol the wires. Sometinu s the screws are made with 2u0 or even 300 threads in an inch, with the view of giving additional delicacy to the scale, hut in cases of this kind the threads are so minute, that they have not the requisite strength for a microrneler.
The double screw of Mr. Hunter, wl.ich we have al ready described in our article MEenastes, furnishes us with the means of obtaining a very slow motion in the moveable wires by means of two screws, with dif ferent numbers of threads in an inch, the effect being the same as if a single screw was employed, having the size of its threads equal to the difference of the size of the threads of the two screws.
The very same contrivance, with a slight modiftea tion, has been proposed by AI. Prony, under the name of the nonius screw, for the purpose of moving the wires of micrometers. It is represented in Plate CCCLXXV. Fig. 6. where AB is an axis divided into three parts, ab. cd, of The screws upon the parts ab, of have the same number of ihreads in an inch, and pass through two female screws in the fixed supports C, D. The axle AB moves horizontally, and any part of its axis describes at each turn of the handle II, a space equal to the distance between the threads. The middle screw cd has a greater or lesser number of threads in an inch than ab or ef, the difference between the two being as small as we chusc. It passes through a female screw M, which carries the moveable micrometer wire,and the piece AI is prevented from turning by a groove in CD, in which its lower extremity is guided. Tnc screw M therefore will be carried backwards towards II by the screw cd more or less rapidly than it advances forwards along with the axis AB, according as the number of threads in cd is less or greater than those in ab and ef. Tire threads in the screws ab, If, may be of any magnitude, as the piece M advances or recedes in virtue of their difference. It is found difficult in practice io make the two screws ab, tf, so equal that they experience no re sistance in the parts C, D ; but one of the two may be suppressed, if supplied by a simple axis, which is in fact reducing it exactly to Mr Hunter's screw.