617 



VERNIER. 



VERNIER. 



618 



read off to 10", and by estimation to 5". The outer edge was also 

 racked after Hooke's method, but rather, we think, as a check against 

 erroneous reading, than as a means for exact measurement. 



Homer proceeded in a totally different manner. The limb of the 

 circle was divided to 10', and a magnified image of each division was 

 formed in the focus of a microscope, so as exactly to fill the space 

 between eleven threads at equal intervals. Thus the arc was read off 

 to minutes by the threads and the seconds estimated, which they easily 

 might be to 5", according to Horrebow. 



The vernier appears to have come into general use after Flamsteed's 

 time, and in the larger quadrants there were usually two sets of 

 divisions, one into 90 and the other into 96 parts, each with their 

 peculiar vernier : the approximate divisions were brought into exact 

 coincidence and the quantity measured by the revolutions and parts of 

 the tangent-screw, after Hevelius's method. Such were the mural 

 quadrants at Greenwich and elsewhere, erected by Bird, Ramsden, &c., 

 in the last century ; and the portable astronomical quadrant had the 

 same or similar contrivances for subdivision. In the sector employed 

 in the French survey, and described in ' La Me'ridienne de Paris verifie'e,' 

 Paris, 1744, the arc was divided by fine points to every 10'. In making 

 the observation the plumb line was first brought directly over one of 

 these dots, and the star afterwards bisected by a micrometer-screw 

 carrying a wire in the focus of the telescope. The degrees and tens of 

 minutes being read off on the limb, the revolutions and parts of the 

 screw furnished the remaining minutes and seconds. This method of 

 subdivision was applied by La Caille to the sextant with which he 

 observed at the Cape of Good Hope and at Paris. The invention is 

 due to the Chevalier de Louville, whose memoir is to be found in the 

 ' M<!moires de 1'Acade'mie ' for 1714. 



We have already mentioned Rb'mer's optical method of subdivision. 

 The invention of the micrometer-microscope, in which the divisions 

 are first magnified and the intervals measured by the revolutions and 

 parts of a screw carrying a wire or cross-wires in the focus of the 

 object-glass of the microscope, is due to the Due de Chaulnes, whose 

 account was published in 1768 : ' Description d'un Microscope et de 

 differents Micromdtres,' &c. The reader will find some account of the 

 construction and verification of the micrometer-microscope in the 

 article CIRCLE. 



We will now briefly explain the principle of the vernier in its 

 simplest form. H that be well understood, the reader will have little 

 difficulty in making out the value of the divisions in any instrument to 

 which the vernier is applied, though he may require considerable 

 practice before he is able to read off well and quickly. 



No. 1. 



No. 3. 



30- 



39- 



N umber 1 is the figure of a vernier for measuring hundredths of an 

 inch, such as is usually applied to common barometers. The scale is 

 on the left hand, on which the inches and tenths are marked. The 

 portion on the right hand, which can be slipped up or down, remaining 

 always in contact with the scale, is the vernier. It is merely a length 

 of 1 1 parts of the principal scale divided into 10 equal parts. Each of 

 these jart*, therefore, equals 7 J,-, of an inch, or '11 and the difference 

 between a part of the scale and a part of the vernier is '01 inch. In 

 the figure the zero of the vernier is made to coincide, that is, to form 

 one continued line with the division 30 on the scale, and consequently 



10 on the vernier also coincides with 28'9 on the scale. Division 1 on 

 the vernier is, from what we have said, '11 inch below the zero of 

 vernier, while the next lower division on the scale is only '10 below it : 

 hence the vernier division 1 is '01 inch below the division 29'9 on the 

 scale. For the same reason division 2 on the scale is twice as much, or 

 '02 below 29'8 on the scale, and so on, the divisions on the vernier 

 overlapping those on the scale until 10 on the vernier stretches 

 over to exact coincidence with 28'9 on the scale. Now suppose 

 the vernier to be raised '01 inch, it is evident that division 1 of 

 vernier will coincide with 29'9 on the scale. If the vernier were raised 

 02 inch, the vernier division 2 would coincide with 29'S on scale, and 

 so on ; so that in order to read off the hundredths of an inch which 

 the vernier zero advances beyond any tenth in the scale, we have 

 merely to see what vernier division comes nearest to a division of the 

 scale, and set that down for the hundredth required. 



This is the form which was given to the vernier by its inventor, in 

 which the parts of the vernier are larger than those of the scale, and in 

 which the numbering of the parts of the vernier runs contrary to the 

 numbering of the scale. But if, as in No. 2, the vernier has the 

 length of nine divisions of the scale, and this is divided into ten equal 

 parts, each part will be equal to '09 inch, while the divisions of the 

 scale are equal to '1 inch. The vernier in this form is to be numbered 

 forwards, as well as the scale. It is clear that raising the vernier '01 

 will bring the division 1 of the vernier into coincidence ; and so on, 

 exactly as before ; and, therefore that the inches aud tenths being read 

 from the scale, the hundredths are to be taken from the vernier. The 

 reading both scales forward is some advantage in favour of the latter 

 mode, while the size of the vernier divisions is larger, and consequently 

 clearer, in the first. There might perhaps be some advantage in par- 

 ticular cases in uniting both verniers, as the reading- would be made on 

 two divisions and by two sets of independent subdivisions, but we do 

 not remember to have seen this in actual use. 



In modern astronomical and geodesical instruments the vernier 

 usually reads forward. Sometimes, for greater compactness, the zero 

 is placed in the middle of the vernier, and the graduation, after 

 running on to the end of the vernier, is continued from the other end 

 of the scale to the middle, and reads both backwards and forwards. 

 There is a great liability to confusion in these verniers, which can only 

 be avoided, at first, by guessing the value of the subdivision before 

 reading . the vernier. We prefer simple verniers, reading always 

 forward with the zero at one end. 



The ordinary subdivision in English instruments is to minutes, 

 half-minutes, twenty seconds, and ten seconds. Thus if the circle be 

 divided to 30', and the vernier taken equal to 29 half-degrees, and then 

 divided into 30, each part of the vernier will equal Jg of 30' or 29', and 

 the difference between a part of the circle and a part of the vernier be 

 1'. If the circle be divided to every 10', and the vernier taken equal 

 to 69 of these parts ( = 9 60"), and divided to 60, each part of the 

 vernier will be | of 10', that is, will be equal to 690" or 9' 50", and the 

 difference between a part of the circle and a part of the vernier be 10". 

 This division is legible in circles of 8 inches diameter. In circles of 

 18 inches diameter we should still adopt the same division, as it is easy 

 to estimate the difference, and less fatiguing to read an open division 

 than a crowded one. 



The continental artists generally make one circle turn closely, but 

 freely, within another, and nearly in the same plane, as we have seen 

 was directed by Vernier. The reading is much more pleasant and 

 exact in this way. Troughton objected to it, that if a particle of 

 dust should get between the circles it would necessarily grind and 

 tear the edges of the circles, leaving a muddy and ragged ditch between 

 them. We do not know whether this objection is confirmed by 

 experience. The English artists generally place their verniers on thin 

 plates which move upon the divided circles. There is some chance of 

 rubbing, and a certainty of wearing, if the verniers press on the circle ; 

 and if they stand off from it they are awkward to read, with a chance 

 of considerable error from parallax. The subdivision by the vernier 

 seems to be preferred by the German artists in general to that by 

 micrometer microscopes, which are in England universally applied to 

 large meridian circles, and indeed to all considerable instruments where 

 the fixing of the microscopes is not subjected to a varying effect of 

 gravity. On the side of the verniers may be pleaded cheapness, and 

 freedom from changes, such as those which the scale of a microscope 

 suffers when the distance between the limb and the object-glass of the 

 microscope, or the body of the microscope itself, from expansion or 

 other cause, is altered. On the other hand, the micrometer micro- 

 scope certainly admits greater magnifying power, keeps the observer 

 away from the instrument, can be fixed with greater firmness, and 

 remains more steady. It is not easy to fix a vernier firmly without 

 running the risk of affecting the motion of the circle. On the whole 

 we prefer the micrometer microscope, although it must be admitted 

 that the perfection which the continental artists give to the centering 

 of their circles and verniers may well cause a difference of opinion. 

 For small instruments, and those which, like the declination circle of 

 an equatorial, are placed under different strains in different positions, 

 the vernier is indispensable. 



There is difficulty very often in getting the proper light on the 

 divisions. It is desirable that those of the vernier as well as those of 

 the limb should appear sharp and black, and the divisions before and 



