204 



MICROMETER. 



PLATB 

 CCLXXV. 



Fig- 12. 



Dr. Brew 



ster's mi- 

 troraeter 

 for reflect 

 ing tele- 



copei. 



lens next die eye from the remaining lenses*. If the 

 small tube, which contains the field-glass and the first 

 eye-glass, be pulled out beyond its natural position, 

 the magnifying power of the instrument will be in- 

 creased ; and if the same tube be pushed farther in 

 than its natural position, the magnifying power will 

 be diminished. It will be found in general, that if 

 the tube already mentioned be allowed to move over 

 the space of four inches, that is, about two inches on 

 each side of its natural position, the magnifying power 

 at one extremity of this space will not be very far from 

 double of what it is at the other extremity. 



The eye-piece micrometer is represented in Plate 

 CCCLXXV. Fig. 12. with all the lenses in their natu- 

 ral position. The part AFG, containing the two lenses 

 A, C, is fixed to the telescope, and a space is left be- 

 tween the tube AC and the outer tube, in order to per- 

 mit the moveable part of the eye-piece to get suffi- 

 ciently near to the lens C, and also to a sufficient dis- 

 tance from it. The other tube DB, containing the 

 field-glass D, and the first eye-glass B, is moved out 

 and in by a rack and pinion E. The scale is engraven 

 upon the upper surface I n, and the divisions are point- 

 ed out by the index of a vernier placed at the extremi- 

 ty m of the outer tube FG. The zero of the scale is 

 the point marked out by the index of the vernier, when 

 the tube DB is pushed in as far as possible ; and the 

 divisions may be read off, if necessary, by means of a 

 convex glass at F, fixed to the tube AFG. 



The value of the scale of this micrometer may be 

 determined by direct experiment, by the methods which 

 have already been described. 



The following method, however, is more simple, 

 and perhaps equally accurate. After having found 

 the greatest angle subtended by a pair of wires, placed 

 in the focus of the eye-glass, or the angle when the 

 index is at the zero of the scale, by the method in 

 p. 203, note, take the eye-piece out of the telescope, and 

 having pushed the tube which contains the moveable 

 lens or lenses as far in as possible, direct it as a micro- 

 scope to a scale minutely dividedt. Mark the position 

 of the index when the wires comprehend exactly a 

 certain number of these divisions, say 50, which they 

 may be made to do, by a very trifling motion of the 

 moveable tube, and make this point the zero of the 

 scale. Let the moveable tube be now pulled out till 

 the wires successively comprehend 48, 46, 44, 42, &c. 

 of the divisions, or any other numbers, diminishing in 

 arithmetical progression, and mark these points upon 

 the tube. By this means,, a scale will be formed, in 

 which the divisions correspond to equal variations in 

 the angle. If it should be found convenient to divide 

 the scale into equal parts, the value of the divisions 

 may be found in the same way. 



In applying to the reflecting telescopes of Gregory 

 and Cassegrain the principle which has been already 

 explained, we are led to the formation of a microme- 

 ter, remarkable for the simplicity of its construction ; 

 and what, at first sight, may appear paradoxical, tve 

 may convert a Gregorian or a Cassegrainian telescope in- 

 to a very accurate micrometer, almost ivMoitt ike aid of 

 any additional apparatus. 



It will be readily seen by those who understand the 

 theory of these telescopes, that their magnifying power 



may be increased merely by varying the distance be- Wire 

 tween the eye-piece and the great speculum ; and then Microme- 

 producing distinct vision by a new adjustment of the ^ **"* 

 small mirror. Hence a pair of wires fixed in the eye- """>"" 

 piece may be made to subtend different angles, solely 

 by having that part of the instrument moveable along 

 a portion of the common axis of the two mirrors. 



In order to understand this, let SS, Fig. 13. be Fig. 13. 

 the great speculum of a Gregorian telescope, having 

 a round hole in its centre, and placed at the ex- 

 tremity of the tube AA ; and let M be the small spe- 

 culum, whose focus is G, and centre H, attached to 

 an arm MQ, arid moveable along the axis of the in- 

 strument by means of a screw and milled head. The 

 rays RR, proceeding from the lower part of any object, 

 and falling upon the speculum SS, will be reflected to 

 R', and will there form an image of that part of the 

 object. In like manner, the rays r r will form an, 

 image of the upper part of the object at r'. The rays 

 diverging from the image R' ?', and intercepted by the 

 small speculum M, will form another image R" r" , at 

 the distance MF ; which being viewed by the eye-glass 

 at E, whose focal distance is FE, will appear distinct 

 and magnified to the observer. 



Let us now suppose that the lens E, or the eye-piece 

 of the telescope, (which is generally a Huygenian eye- 

 piece, with two glasses,) is moved by a suitable appa- 

 ratus into the position E', and that a point F' is taken, 

 so that F'E' may be equal to FE. Then it is mani- 

 fest, that, in order to have a distinct view of the object 

 in this new position of the eye-piece, the image form- 

 ed by the small speculum must be brought to F' in the 

 focus of the lens E'. But as the place of the first 

 image R' r' is in no respects changed by the change 

 of position in the eye-piece, the formation of the image 

 at F can be effected only by bringing the small mirror 

 M into a position M', nearer the image RV than it was 

 before ; and as the space MM' through which it has 

 been moved, in order to converge the rays to F', must 

 necessarily be less than FF'=EE', the space through 

 which the eye-glass has moved ; the distance M'F' of 

 the new image at F' from the small mirror must be 

 greater than MF, the distance of the other image at F, 

 in the ratio of M'F' to MF ; and the magnifying power 

 of the instrument must at the same time be increased, 

 and the angle subtended by the wires diminished. 



In the formation of this micrometer, we may either 

 construct the scale from calculation, after the two ex- 

 treme points of it have been fixed experimentally, by 

 the method already described ; or all the points of the 

 scale may be determined by direct experiment. It 

 would perhaps be more convenient to divide the scale 

 into equal parts, and to construct a table from experi- 



the angle 

 ivisions." 



ment, for the purpose of shewing, by inspection,! 

 which corresponds to any number of these equal di 



CHAP. IV. 



On Double Image Micrometers, in which the Lenses, Mir- On double 

 rors, and Prisms, are opened and shut mechanically, 'mage mi- 

 crometers, 



The first hint of 'a double image micrometer seems in which 

 to have been communicated, in 1675, by the celebrated 'he l<=nse, 

 Danish astronomer M. Roemer. It appears, however, m '"rs, 



to have remained so entirely unnoticed, that it was not an 



are opened 



* An instrument of nearly the same kind with the following, has been described by Mr. Ezekiel Walker, in the Phil Mag Aug. and shut 

 1811, Vol. xxxviii. p. 127, as an invention of his own. So early as the end of the year 1305, I sent a drawing and description of tha mechani- 

 eye-piece micrometer to Mr. Carey, optical instrument maker, London. In 1806, one of the instruments made for me by Messrs. Mil- cally. 

 ler and Adie. Edinburgh, was examined by Professor Playfair ; and since that time it has been in the possession of a friend in London, 

 t Xbt beautiful micrometrical scales formerly constructed by Mr. Coventry, anil now by Mr. Barton, are admirably adapted for this purpose. 



