202 



MICROMETER. 



PLATE 

 CCCLXXV. 

 Fig. 8. 



Hence it appears, that when the different values of b 

 are in arithmetical progression, the angle of the wires 

 varies at the same rate, and therefore the scale which 

 measures these angular variations is a scale of equal 

 parts. The magnifying power, however, does not vary 

 "" md consequently a scale for 



if any scale were wanted, is 



Wire strument.maybeeffectedbydifferentcontrivances.-.-by tof?***? *' JSJ^L* =eobUinSm Uiese M."- 

 Microme- diansine the distance between die two parts of the achro- and 6=0, 1, 2, 3, 4, si 



rnadf eylpieceTby separating one or more of the lenses two formulae the results m the followmg table. ^^ 



of the compound object glass ; or by making a convex, 

 a concave, or a meniscus lens move along the axis of the 

 telescope, between the object glass and its principal focus. 

 The last of these contrivances, which is, for many 

 reasons, preferable to any of the other two, is re- 

 presented in Fig. 8. where O is the object glass, 

 whose principal focus is at /, and L the separate 

 lens, which is moveable between O and J. I he 

 parallel rays R, R, converging to /, after refraction by 

 the object glass O, are intercepted by the lens L, and 

 made to converge to a point F, where they form an 

 image of the object from which they proceed. The fo- 

 cal distance of the object glass O has therefore been 

 diminished by the interposition of the lens L, and conse- 

 quently the magnifying power of the telescope, and the 

 angle subtended by a pair of fixed wires in the eye- 

 piece, have suffered a corresponding change. When 

 the lens is at /, in contact with the object glass, the fo- 

 cus of parallel rays will be about Hf ; the magnifying 

 power will be the least possible, and the angle of the 

 wires will be a maximum ; and when the lens is at /', 

 so that its distance from O is equal to Of, the focus of 

 parallel rays will be at/; the magnifying power wi 

 be the greatest possible, and the angle of the wires will 

 be a minimum. When the lens L has any intermediate 

 position between I and I', the magnifying power and 

 the angle of the wires have an intermediate value, 

 which depends upon the distance of the lens from the 

 object glass. Hence it appears, that the scale which 

 measures these variations in the angle of the wires, may 

 always be equal to the focal length of the object glass ; 

 and it may be shewn in the following manner, that it 

 is a scale of equal parts, the changes upon the angle 

 being always proportional to the variation in the posi- 

 tion of the moveable lens. 



The point / being that to which the rays incident 

 upon L always converge, we shall have, by the princi- 

 ples of optics, F+L/: F=L/: LF, F being equal to 

 the focal length of the lens L. Now it is obvious, that 

 the magnitude of the image formed at F, after refrac- 

 tion through both the lenses, will be to the magnitude- 

 of the image formed at/ by the object glass O, (or by 

 both lenses when L is at I',) as LF is to L/; for the 

 image formed at /is the virtual object from which the 

 image at F is formed, and the magnitude of the image 



mage a , 



is always to the magnitude of the object directly as 

 their respective distances from the lens. Hence the 

 magnifying power of the telescope when the lens L is 

 in these two positions, is in the ratio of LF to L/, con- 

 sequently the angle subtended by the wires, which 

 must always be inversely as the magnifying power, will 

 beasL/toLF. 



By making L/=i, the preceding formula becomes 



F4-& :F=6 : LF. Hence LF=IA-. Then calling 



A the least angle subtend. ' ' by the wires, or the angle 

 which they subtend when the lens L is at I', and * the 

 angle which they subtend when the lens is at L or in 

 any other position, we have A:*=LF:L/, that is 



A: *=-:l>, and=A+^-=the angle for any 



distance b. Calling P the greatest magnifying power, 

 and ir the magnifying power for any distance b, we 



shall have ?:*=& 



:::-=, 

 r-J-o 



and Ts-i 



power 



avmg mua O,^,K... the nature of the scale, we 



now proceed to point out the method of construct- 

 ing it. It is obvious that the length of the scale is ar- 

 bitrary and may be made equal either to the whole fo- 

 cal length Of of die object glass, or to any portion of 

 it If the lens L moves along the whole length of the 

 axis Of, the angle subtended by the wires can be va- 

 ried to a greater degree than if the lens moves only 

 along a portion of the axis; but as this advantage may 

 be obtained by a contrivance hereafter to be described, 

 it will be found more convenient for astronomical pur- 

 poses to make the lens moveable only along a part of 

 the axis, as from L towards/. 



Let us suppose, therefore, that when the object glass 

 O is 36 inches in focal length, 10 inches will be a con- 

 venient length for the scale, and that the telescope is 

 constructed so that the lens L can move freely through 

 that space reckoned from/, the next thing to be deter- 

 mined is the focal length of the lens L. It is evident 

 that a lens of 6 inches focal length will produce a much 

 greater diminution of magnifying power, and conse- 

 quently a much greater increase upon the angle of the 

 wires in moving from/ to L than a lens of greater fo- 

 cal length ; so that the value of the whole scale in mi- 

 nutes or seconds, or the increase in the angle occasion- 

 ed by the motion of the lens from / to L, must be in- 

 versely as the focal length of the moveable lens, 

 the angle of the wires is 26 minutes, for example, and 

 if the magnifying power of the telescope is d.mm.sh- 

 ed from 40 to 30 by the motion of the lens from/ to 

 L then when the lens is at L, the angle of the w.res 

 will be 34' 40", for 30 : 40=26' : 34' 40". Hence we 

 have a scale of 10 inches to measure 26' 34' 40", or 

 8' 40", and therefore every tenth of an inch on the scale 

 will be equal to 5".2. 



If we employ a lens of much greater focal length, 

 so as to diminish the magnifying power only from 4 

 to 35, and if the angle of the wires is 29 minute* 

 then when the lens is at L, the angle of the wires w,ll 

 be 33' 9" nearly, for 35 : 40=29' : 33' 9". And hence 

 we have a scale of 10 inches to measure 2933 I , 

 or 4.' 9", consequently every tenth of an inch on the 

 scale corresponds to 3".3. From this it will be mani- 

 fest that the accuracy of the scale is increased by in- 

 creasing the focal length of the moveable lens. 



The two preceding examples are suited to a micro- 

 meter for measuring the diameters of the sun and moon 



