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36

Similar sets can be taken at -f- 90° and + 135° on original set, and the final mean will be free from errors due to eccentricity of axis. It has been my practice to take four sots at 0, 45° 01', 90° 02', and 135° 03' round the circle. The vertical readings arc always taken after 10 a.m. and before 3 p.m. There is sometimes a fair difference in the angles, due to refraction, but the mean of four sets taken on different days should be the best obtainable. Level-corrections. The level is divided from left to right from 0 to 35 divisions, so that when the instrument is face left the larger figures are at the eye end; and when face right, at the object end. The sum of the eye and object bubble readings divided by 2 gives the position of the centre of the bubble. If this coincides with 17-5, the centre division of the scale, there will be no level-correc-tion, but, if not, then the following rule has to be followed : —■ If - -a — comes less than 17-5, then the correction is a plus to the actual circle reading on the circle, whether the instrument is face left or face right; if more than 17-5, then the correction will be a minus to the actual circle reading. To get the value of one division of the level scale I took a number of readings all round the circle by the usual method of slightly altering the lcA r el of the instrument and noting the differences by micrometer and level readings. This worked out at 5-73 seconds, although the Kew certificate which came out with the instrument gave the value as 8 seconds. Adopting my figures, I made out the following table to simplify the working : — • Example IV. E+_o Seconds 2 Correction. 15-50 +11-46 15-75 ±10-03 16-00 + S-59 16-25 + 7-16 16-50 + 5-73 16-75 + 4-30 17-00 + 2-86 17-25 + 1-43 17-50 0-00 17-75 - 1-43 18-00 - 2-86 18-25 — 4-30 18-50 - 5-73 18-75 - 7-16 19-00 - 8-59 19-25 -10-03 19-50 -11-46 In Examples I and 111, to get the level-corrections, work out the value ' J and look up the table in Example IV, keeping an eye on the sign. This correction can be applied to the actual circle-readings before working out the vertical angle, and then the result would be the true vertical angle free of levelerror. For instance, take Example II : the figures would be, to Somes, — Face left 0° 03' 04-5" - 1-4 =0° 03' 03-1" Face right 5 19 56-0 -5-7 = 5 19 50-3 5 16 47-2 True vertical angle = 2 38 23-6 2 41 26-7 5 19 50-3 My own method is to take out the angle as in Example II and apply the correction to angle afterwards. To do this the following rule must be remembered : Change the sign of the correction opposite the lesser of the face-left or face-right readings; take the algebraical sum of the two corrections, and divide by 2. Thus in example we have „ = — 2-15. This gives for the final angle 2° 38' 25-75" - 2-15 = 2° 38' 23-6", which is the same as by method shown above. In obtaining the final vertical angle from the different sets I put down the angles with their corrections for level-error alongside and take the mean.