36 



th 130 division, and moved on until it is between the 20' and 40' space beyond the 

 138 mark. The first part of our reading will therefore be 138 20'. 



Second, look along the vernier, beginning from the zero point, and in the direc- 

 tion in which the graduation of the arc runs, until one line of the vernier is found 

 which seems to be a prolongation of an opposite line on the arc. 



Consider each of the vernier spaces between the vernier zero and such a line, 

 as equal to 30" of arc. 



Add the number of minutes and seconds thus obtained to the first reading. The 

 result will be the reading of the circle. 



Thus we notice that the vernier zero is a trifle over half-way of the distance 

 between the 20 7 and 40' marks of the arc. 



And looking along the vernier to the right, we notice that the lines of the ver- 

 nier gradually approach the lines on the arc until the twentieth line of the vernier 

 is precisely opposite a line on the arc. Of course, since each vernier space denotes 

 30", the alternate ones made a little longer in the cut will denote single minutes, 

 and on the vernier therefore the twentieth line would correspond to 10' 00", and 

 since our first reading was between 20' and 40', this vernier reading is to be added 

 to that first reading. 



Thus, 138 20' 



W 00" 



138 30' 00" will be the reading of the vernier, 



using the upper graduation. 



In the same manner we proceed to the left in reading the lower graduation, in 

 which the figures are inclined to the left. Thus in the cut, we should find the zero 

 point of the vernier is beyond the 221 20' mark, and the line of the vernier, which 

 is seemingly a prolongation of a line of the arc, corresponds to 10' 00". Then we 

 have 221 20' 



10 / 00" 



221 30' 00" for the reading of the vernier, using 

 the lower graduation. 



Practically, in reading the vernier, the engineer decides which line is in coinci- 

 dence by the position of the lines on both sides. 



He first notices, roughly, what fractional part of a space on the limb lies between 

 the vernier zero and the last graduation mark it lias passed. This enables him to 

 look immediately to that part of the vernier in which the coincidence occurs. 



Thus in the figure the vernier zero is about half way between 221 20' and 221 40% 

 the engineer therefore immediately looks about half way along the vernier and 

 finds the 10' 00" division to be the one sought. 



When the graduation is to thirty seconds, the engineer will find that if he only 

 chooses, he can work to minutes with this graduation quite as rapidly as with a 

 transit graduated to minutes, by simply disregarding the shortest lines of the vernier. 



The second vernier, which is distant 180, or exactly opposite the one read first, 

 may also be read. Not so much to eliminate any eccentricity of the circle and ver- 

 ni-Ts, as to afford a valuable check upon the angle measured. 



Greater accuracy in the measurement of any angle may be obtained by the 

 principle of repetition. In this case, before and after an angle has been repeated u 

 number of times, all four of the verniers should be read, and if, for example, the, 

 graduations proceed from right to left, the left hand side of each double vernier 

 should be read as usual ; but in the right hand side the line now marked HO on tin; 

 vrnier should be considered 0, and the arrow on the vernier 20. Then, with this 

 convention, onlvthe minutes and seconds of the second vernier should be used. 



But it should be here remarked that the repetition of angles is not now held in 

 such repute by our best engineers, as it was before the present perfection of the art 

 of graduating and centering the circles and verniers of engineering: instruments. 



The engineer who has not used them will find the ground-glass shades a great 

 convenience in reading the vernier. Thev are so placed as not to be readily broken, 

 and they shed a elfjir. white light upon the graduations. 



Gradual ion< on slid >iiv-r are much to be preferred to ^raduatioiirf on any 

 known brass alloy. The surface of the silver can be worked very plane, since it is 

 of uniform texture. The graduations can be cut with the utmost uniformity in 

 width of line and spacing. 



