Fig. 231. In the following figure, the reading is 20° 40', the index being at a point beyond 20° 30', and the additional space being shown by the Vernier to be 10'. Fig. 232. 30 20 10 30 20 Sometimes 30 spaces on the Vernier are equal to 31 on the circle. Each space on the Vernier will therefore be = 31 × 30' =31', and will be longer than a space on the circle by 1', to which it will therefore read, as in the last case, but the Vernier will be "retrograde." This is the Vernier of the compass, Fig. 148. The peculiar manner in which it is there applied is shown in Fig. 239. If 15 spaces on the Vernier are equal to 16 on the circle, each space on the Vernier will be = will therefore read to 2'. 16 × 30' 15 =32', and the Vernier (351) Circle divided to 20'. If 20 spaces on the Vernier are equal to 19 on the circle, each space of the latter will be = 19 × 20' = 20 19′, and the Vernier will read to 20'19' 1'. = If 40 spaces on the Vernier are equal to 41 on the circle, each 20; and the Ver = 30". It will be retro nier will therefore read to 201 20' grade. In the following figure the reading is 360°, or 0°; and it will be seen that the 40 spaces on the Vernier (numbered to whole minutes) are equal to 13° 40′ on the limb, i. e. to 41 spaces, eack of 20'. If 60 spaces on the Vernier are equal to 59 on the circle, each = will therefore read to 20'19' 40" 20". The following figure shows such an arrangement. The reading in that position would be 40° 46' 20". (352) Circle divided to 15'. If 60 spaces on the Vernier are equal to 59 on the circle, each space on the Vernier will be 59 x 15' 60 = = 14' 45", and the Vernier will read to 15". In the following figure the reading is 10° 20′ 45′′, the index pointing to 10° 15', and something more, which the Vernier shows to be 5' 45' (353) Circle divided to 10'. If 60 spaces on the Vernier be equal to 59 on the limb, the Vernier will read to 10". In the following figure, the reading is 7° 25′ 40′′, the reading on the circle being 7° 20′, and the Vernier showing the remaining space to be 5' 40". 10 9 8 7 6 5 4 3 2 1 (354) Reading backwards. When an index carrying a Vernier is moved backwards, or in a contrary direction to that in which the numbers on the circle run, if we wish to read the space which it has passed over in this direction from the zero point, the Vernier must be read backwards, (i. e. the highest number be called 0), or its actual reading must be subtracted from the value of the smallest space on the circle. The reason is plain; for, since the Vernier shows how far the index, moving in one direction, has gone past one division line, the distance which it is from the next division line (which it may be supposed to have passed, moving in a contrary direction), will be the difference between the reading and the value of one space. Thus, in Fig. 229, page 232, the reading is 358° 15'. But, counting backwards from the 360°, or zero point, it is 1° 45'. Caution on this point is particularly necessary in using small angles of deflection for railroad curves. (355) Arc of excess. * On the sextant and similar instru ments, the divisions of the limb are carried onward a short distance beyond the zero point. This portion of the limb is called the "Arc of excess." When the index of the Vernier points to this arc, the reading must be made as explained in the last article. Thus, in the figure, the reading on the arc from the zero of the limb to the 5 Fig. 23" 0 5 10 9 8 7 6 5 4 3 2 1 zero of the Vernier is 4° 20', and something more, and the reading of the Vernier from 10 towards to the right, where the lines coincide, is 3' 20", (or it is 10'6' 40" 3′ 20′′), and the entire reading is therefore 4° 23′ 20′′. (356) Double Verniers. To avoid the inconveniences of reading backwards, double Verniers are sometimes used. The figure below shows one applied to a Transit. Each of the Verniers is Fig. 238. 30 20 10 20130 10 10 360 350 |