The bubble is handier to work with when adjusted to reverse in the centre of its run, but it does not really matter, as equally accurate work can be done with it in any other position. Should the bubble not reverse in the centre of its run, adjust the instrument by the levelling screws until it reverses in some position. Say you start with bubble in the centre, and on reversing, it runs towards the eye end of the telescope six divisions, then alter the levelling screws until it is only half this, or three divisions towards the eye end, then, if properly levelled, the telescope will make an entire revolution with the bubble in that position, which will prove that the axis is vertical. The bubble can now be adjusted by the opposing nuts at the one end by means of the tommy pin (provided in the case) until it is in the centre of its run, and it will then reverse in that position instead of three divisions towards the eye end.
221.—Adjustment to Collimation.—Upon a fairly level piece of ground the staff plate, fully described further on, is trodden well down on the ground, and the level is set up at say 3 chains from this, in which position the staff is read as a back sight. Now in the opposite direction in the same line, at 3 chains distance from the level, a second staff plate, or in defect of this if the surface be not firm, a stake or a boulder, is driven firmly down in the earth, and the staff is placed upon this erect and face to the instrument as a foresight. The instrument is turned half round and the second station is read. These readings of the staves taken will be truly level with each other, if the axis of the instrument has been set up quite vertically, so that the bubble has kept its centre in all positions. This is true although the axis may have been out of collimation. This arrangement is shown in Fig. 66, L the first position of the level taking sights at equal distance from S and S′. Let the level be now removed to L′: if correct it should cut the staves SS′ at equal distances above or below the first readings at aa′, which are at equal distances from bb′ readings from L′, therefore level and parallel with the first reading.
Fig. 66.—Adjustment of dumpy level.
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222.—In the dumpy level, as it leaves the hands of any respectable maker, the subsequent adjustments required can never be great, unless the level has suffered a serious fall so as to bend the limb. The rewebbing the stop, if carefully done, would require only a slight readjustment; but it may be convenient to give an exact method for extreme cases, which may be given in detail for clearness, and at the same time we may also consider the influence of the curvature of the earth.
223.—Original Adjustment of the Dumpy Level to Collimation with consideration of the Curvature of the Earth.—Suppose the readings of the two levelling staves at 10 chains apart, taken with the level placed at intermediate distance as before, read 7·50 and 4·50, and that we now place the level linearly at 1 chain outside the first reading and it reads the near staff 6·50 and the distant staff 5·50, by the inclination of the ground, this would be a + and a - reading; but we require both readings of one sign, and as the distant staff reading is much too high, it is clear we require - readings for correction. The correction will be of the difference of reading in proportion to the distances, calling the lower reading minus—
7·50 - 6·50 = -1, 4·50 + 5·50 = +1, difference = 2.
That is -2′, as our readings are - and as the -2′ is in 10 chains, at 1 chain the distance of - the near staff = -·2, and 11 chains the distant staff = -2·2. The correction will therefore be for the near staff 1 chain distant 6·50 - ·2 = 6·30, and for the distant staff at 11 chains 5·50 - 2·2 = 3·30 = -1·2 below each of the first readings. If the telescope be now collimated to the near staff reading 6·30, by adjusting the screws immediately under it for distance between the limb and the telescope, and the bubble be readjusted to the telescope without moving the instrument or touching the parallel plate screws, the adjustment will be perfect, less the small error due to the earth's curvature in 1 chain. If the telescope be adjusted to the distant staff 3·30, curvature of the earth will be corrected by the level for 11 chains, which is 0·0106 foot or ·01 nearly, the smallest reading we have on the staff.
224.—It was claimed by the late William Gravatt for his method of adjustment,[3] which was equivalent to that given above, but more complicated and with three staves, that the fixed correction for curvature at 10 chains would be uniform in the working of the level pro ratâ for all distances. There is some difference of opinion on this subject: at any rate, a 10 chain correction would only be applicable to very approximately level ground where average 10-chain stations could be taken.