February 1, 1887.] 



♦ KNOWLEDGE ♦ 



79 



by Tycho Brah6 ; in which case, the sharp straight edge of 

 the observing arm, or a hair coinciding with a radius of the 

 quadrant, cut the diagonal scale. Eeference to fig. 2 (p. 78), 

 though, will show that while absolutely true as a means of 

 subdividing a straight measure of length, diagonal lines only 

 afford an approximate measure of a circular arc, although 

 this approximation was sufficiently near for the purpose of 

 astronomers in Tycho's day. It is, however, to a certain 

 Captain Vernier that we are indebted for a method of sub- 

 dividinggraduation both on straight and curved lines, remark- 

 able at once for its elegance and accuracy. His device, now 

 universally known as a " Vernier," must be familiar to 

 every one who has ever seen an upright barometer or a 

 sextant. It was originally described by him in a tract 

 publi.*hed in Brussels in 16.31. The principle on which it 

 is based may be gathered from a study of fig. 3, which 

 represents it as applied to a common barometer. 



-30 



c 



3 

 I 



7 



"I— 



i 



3 

 2 



t 



28 



-30 



-29 



Fig. 3. 



Fig. 4. 



In the figure above, s I is the scale of inches and tenths 

 engraved on the right-hand side of the mercury tube, B m. 

 It really starts from the surface of the quicksilver in the 

 cistern ; but as' the mercury never falls much below 28 inches 

 at the sea-level, the scale begins somewhere about there, 

 and, as it stands, shows the height of the mercury in inches 

 and tenths. In order, then, to measure the tenths of these 

 tenths, or the hundredths of an inch, the vernier is employed, 

 as shown above. In this its original form it consists of a 

 little scale, v, measuring exactly one inch and one- tenth, but 

 itself divided into only 10 equal pai-ts. Now as these 10 

 divisions on the vernier equal to 11 on the scale of inches, it 

 is obvious at a glance that e;ich division of the vernier must 

 be equal to 1 ,',,th division of the inch scale — i.e. to yVVths 

 (Oil) inch. Suppose, then, that the top line on the vernier 

 accurately coincides with any given one on the inch scale, 

 then will that immediately below it difi'er -r,',,Tth of an 

 inch from the nest division on the inch scale, the second 

 beneath it , n„ths inch from the corresponding division, and 

 so on. Looking, then, at our figure, we see that the line 

 marked 6 on the vernier coincides with that corresponding 

 to 29-1 inches. Hence that marked .5 must be -01 inch 

 above its corresponding line, line 4 02, line 3 -03, line 2 'O-l, 

 line 1 -05, and the top of the vernier -06 of a division 

 above the line over which it stands. This, however, we .see 

 is 29-7, and hence the barometer reads 29-76 inches. This, 

 as we have said, was the form of the vernier as originally 



devised and described by its inventor ; but it will be noted 

 that, whereas the inches and tenths of the primary scala 

 read upwards, in this construction the hundredths are read 

 downwards. Let us see if it be not possible to obviate the 

 slight confusion which might arise from this, and make both 

 scale and vernier read in the same direction. The method 

 of doing so is extremely simple, and is illustrated in fig. i. 



Instead of di^^ding" 11 of the primary divisions in 10 

 equal parts, we here take 9 of those primary parts for such 

 divisions ; so that, in the case of any two lines being coin- 

 cident, the vernier line above falls short of the corresponding 

 one on the inch scale by -01 inch, and so on. Evidently in 

 this case the divisions of the vernier will read upwards the 

 Siime as those on the primary scale. Our figure represents 

 the instrument as reading 29-72. In astronomical and 

 surveying instruments and the like, the vernier thus reads 

 forwards, though in all cases in which extreme delicacy of 

 measurement is necessary, the vernier, itself in such instru- 

 ments has been superseded by the micrometer microscope, 

 to be referred to further on. Reverting for a moment to 

 the barometer : in all standard instruments 24 of the primary 

 divisions, each equal to ^Lth of an inch, are taken as the 

 length of the scale of the vernier, which is divided into 25 

 equal parts. Hence aach of these falls short of a fixed 

 division by J, th of ^V^li or ^i^jth of an inch, and as this is 

 halved in the case' of the apparent coincidence of t%TO 

 adjacent paire of lines, the height of the mercury is read in 

 such instruments to the -nr.ioth (•001) of an inch. 



After our description of the vernier, as applied to the 

 subdivision of a sti-aight scale, little need be added as to its 

 application to the circular graduated " limb " of an instru- 

 ment. In those mostly in popular use, such as the 

 theodolite, sextant, and "the like, the graduation on the 

 primary arc or cii-cle is to 30', 20', or 10' ; then, by the aid 

 of the vernier, these would be subdivided to 1', 20', or 10" 

 respectively. For example, if the circle is divided to 30', 

 then taking 29' as the whole length of the vernier, and 

 dividing this into 30 equal parts, in the case of two coincident 

 lines the pair next beyond them wiU be separated by ^'^th 

 or 1', the pair above that again by jj'^jth or 2', and so on; 

 and so the scale Ktn be read to a single minute. It may 

 serve to show how enormous is the gain from the use of the 

 vernier in such a case if we mention that the ordinary 

 pocket sextant, with a radius of less than 1-7 inch, is thus 

 read to minutes: whereas if we divided a cii-cle itself to 

 this degree of angular minuteness and made each minute 

 = -02 inch (smaller di\isions would in such case be useless), 

 the circle itself would have to be some lU feet in diameter 1 

 If the arc were divided into 10', then taking 59 of such 

 primary divisions ( = 9°-.50' in the limb) for the total length 

 of our vernier, and subdividing this into 60 equal parts, it 

 will be evident that the 60th part of 10', i.e. 10", may thus 

 be read off. Six-inch sextants are now so divided. 



We cannot take leave of the vernier without inviting 

 attention to a blunder which has been copied from book to 

 book for the last hundred years. Sometimes it takes the 

 form of the expression " the Nonius or Vernier," at others 

 (as on p. 766 of Chambers's, usually marvellously accurate, 

 " Descriptive Astronomy ") we find Nonius described as the 

 inventor of the vernier. He was nothing whatever of the 

 sort, the " Nonius " and the " Vernier " differing wholly in 

 principle. The attentive reader has, it is to be hoped, by 

 this time thoroughly gi-asped the idea underlying the con- 

 struction of the vernier. The gi-aduation suggested by 

 Nonius was this : — Forty-five concentric circles were to be 

 described upon the limb of the instrument and divided into 

 four quadrants by diameters intersecting at right angles, 

 then the outside quadrant was to be divided into 90 equal 

 parts, the next into 89, the third into 88, and so to the 



