VERNIER. 



the fmall quantity fliort of perfeA coincidence ; and examin- 

 ing the places of the preceding and following ftrokes will 

 greatly affift in forming this judgniient. 



If we were to fubftitute 21 for 19 fpaces on the limb, 

 the refult would be the fame, with the inconvenience of 

 reading backwards, and of fubtrafting inftead of adding ; 

 7° _ 420' _ 

 420 



for 



as before ; but inftruments of 



21 X 20 



modern conftruftion are exempt from this inconvenience, by 

 having always one more divilion on the fcale of the vernier, 

 than on the equal arc of the liir.b. 



In Troughton's fnuff-box fextant, which is a ver)"^ con- 

 venient inftrument for the pocket, the radius of the divided 

 arc is only about ij inch, and the degree is divided, there- 

 fore, into two fpaces only, fo that 30' are neceffarily indi- 

 cated by the vernier ; and as 29 fpaces on the limb are taken 

 equal to 30 on the vernier, the fmallell quantity indicated 



. 14° 30' 870' , ^ r , , ,■ r , 



IS z= — ■ :^ 1 , as before ; and the readincroi the 



29 X 30 870 ^ 



coincidences that indicate the laft 30' is progrefllve, like the 

 reading on the limb of the inftrument. 



In the common ebony fextant, the degree is fometimes di- 

 vided into four parts, by reafon of the increafed length of the 

 radius ; confequently, when the reading is in a forward direc- 

 tion, fifteen divifionson the vernier occupy the fame arc as four- 

 teen on the limb ; and the fmalleft. quantity indicated thereby is 



3° 30' 210' 

 ■ = =1'; but the brafs fextants made and 



14 X 15 210 



divided by the beft makers, have the minute fubdivided into 

 twenty, fifteen, ten, or even five feconds, according to the 

 length of the radius, by means of a vernier with divifions and 

 fubdivifions, afting with divifions and fubdivifions on the 

 limb, which is a refinement of the original invention, intro- 

 duced by Troughton, in confequence of the fuperior excel- 

 lence of modern dividing. We have now before us one of 

 Ramfden's beft brafs fextants of 95 inches radius, on the 

 limb of which the degree is divided into three parts, and 

 40 divifions on the arc of the vernier meafure 39 divifions 



780' 46800" 



on the limb ; therefore 



13 



30" 



39 X 40 1560 1560 

 is the fmalleft quantity that the vernier will indicate, and 

 every alternate ftroke thereon counts one minute as the coin- 

 cidence advances. This mode of reading the vernier doubles 

 its former accuracy. But on the hmb of this fame inftru- 

 ment, the late Mr. W. Walker prevailed on Mr. Troughton 

 to divide a fecond arc, within the former, which by our mea- 

 furement is only of nine inches radius : in this inner arc, 

 which reads with the inner arc of the vernier, the degree is 

 firft divided into halves, and then each half is fubdivided into 

 five fmaller divifions, by fhorter ftrokes very delicately cut, 

 fo that the degree is di\'ided into ten fmall fpaces, of 6' each, 

 which are to be read before the vernier's fubdivifion of one 

 of thefe fpaces is examined. On the fcale of the inner 

 vernier are 7 2 fmall divifions, co-extenfive with 7 1 on the 

 limb ; and as each of thefe is = &, we have 71 x & = 426', 

 or 25560" for the whole arc of meafurement : confequently 



25560" 25560" 



= = 5" is the fmalleft quantity that can 



71 X 72 5112 n 7 



be indicated by fuch a vernier, and accordingly we obferve 

 on the fcale of the Vernier twelve fmall or fubdividing fpaces 

 between each minute ftroke ; i. e. every twelfth ftroke is a 

 long one, and they are numbered i, 2, 3, &c. up to 6, which 

 is the value of one of the faialleft divifions on the limb, and 



8 



confequently the value of each fubdivifion on the fcale is t't 

 of i', or 5" : and yet, by the help of a high magnifier, placed 

 in the centre of an illuminating rcfleftor of plaifter of Paris, 

 this fmall quantity may be clearly difcriminated. When 

 Ramfden firft faw this wonderful application of the powers 

 of the dividing engine, he called his workmen together, to 

 witnefs what he at firft confidered the folly of attempting 

 greater accuracy than was prafticablc ; but a clofe examina- 

 tion of the divifions convinced him, that his preconceived 

 opinion had ftood in the way even of his own improvements. 



Sometimes a divided head or nut has been fixed on the 

 end of the tangent-fcrew of flow motion, particularly by the 

 older makers of pillar and mural aftronomical quadrants, in 

 order to fubdivide the divifions of the vernier, as may be feen 

 at Greenwich, Richmond, and other obfervatories ; but when 

 this apparatus has been in ufe fome time, the parts become loofe 

 and inaccurate, even allowing that the mealuring fcrew itfelf 

 can be confidered as perfeft in all refpefts. On an examina- 

 tion of fome of Graham's, the Siflbns' and Bird's quadrants, 

 we find that though the accuracy of i'' is profefTed by the 

 conftruftion, yet very little dependence can be placed on 

 fuch profeffion after the parts have been for years in ufe. Of 

 this conclufion Ramfden was no doubt fenfible, when he 

 introduced into his larger inftruments the microfcopic read- 

 ings, with a good fcrew at the focus of the eye-piece of a 

 compound microfcope, where there is not fo much ftrefs on 

 the fcrew as at the periphery of the arc, where the fcrew 

 forms alfo a part of the clamping apparatus. To this adop- 

 tion of the ufe of a compound microfcope, in conjunftion 

 with the fubfequent improvements in the art of dividing, 

 much of the claim to fuperior excellence in our Englifh aftro- 

 nomical inftruments is to be attributed, which claim is ftill 

 further fupported by the invention of the achromatic objeft- 

 glafs and improved eye-pieces of the telefcopic portion. 



Hitherto we have confidered the principle and application 

 of a fingle vernier only, which is in itfelf an ufeful and 

 beautiful contrivance ; and, as we have faid, may be ap- 

 plied with advantage to fubdivide a ftraight line ; as, for in- 

 ftance, the fcale of a barometer into hundredth parts of an 

 ir.ch, or the fcale of Dollond's divided objeft-glafs micro- 

 meter into the five-hundredth parts, or more ; but with an 

 entire circle that is graduated all round, the accuracy of 

 an obfervation is greatly augmented, nay enfured, by the 

 ule of different verniers reading at different parts of the 

 limb at the fame time. At firft two diametrically oppofite 

 verniers were introduced, as has been afferted, by one of the 

 SifTons, though, we underiland, not with a view to reading 

 at oppofite fides of the circle, by way of correfting the ob- 

 fervation by an average ; feeing that the remote end of the 

 vernier bar had only a fingle ftroke anfwering to zero of the 

 other ; but fubfequently, in tranfit and other inftruments 

 ufed with a fpirit-level, the double vernier became a valuable 

 appendage, partiqularly when the conftruftion of the inftru- 

 ment admitted of inverfion of the pofition of the axis, fo 

 as to procure a double obfervation ; and thence the true 

 zero of the graduation of the meafuriiig limb. This ufeful 

 property was extended, we believe, by Troughton, firft by 

 introducing four, and then, with equal advantage, three 

 equidiftant verniers of fimilar powers. We have fhewn the 

 great ufe of additional verniers, at confiderable length, 

 under our article Circle, particularly with refpeft to the 

 property that three pofTefs of correfting for the excentricity 

 as well as inequality of the divifions of a circular inftrj- 

 ment ; and that as great accuracy may be expefted from 

 one fro^^ obfervation with Troughton's reflefting circle, or 

 from a pair of reverfed obfervations with a theodolite, with 

 either circle, that has three verniers, as can be obtained by 



a repe. 



