

On slightly ris- 

 ing ground locate 

 four points, a, 6, 

 .c and d, on the 

 same line, nearly, 

 making be = ca, 

 d ad any con- 

 venient distance, 



preferably not much less than ca, and in some simple 

 ratio with it, for ease of calculation afterwards. Set the instrument 

 fc at c ; take readings A' and B' on a and b respectively, carefully leveling before 

 each sight. Then, unless the instrument is otherwise much out of adjustment, (B 7 A') 

 is the true difference of level of a and b. 



Next set up at d, level carefully, and take readings A" and B'" on a and b respec- 

 tively. [In strictness the centre of the instrument should not be set over d, but beyond, 

 by an additional distance = principal focal length of the object-lens -f- the distance from 

 that lens to the centre of the tripod. (See the Manual, page 87, Fig. 2.) 1 Then (B" 

 A") (B' A') = B'"= error of collimation in the distance &a, that is the error due to 

 the vertical angle between the line of sight and axis of spirit-level. Now, by similar 



triangles, we have B// , . ^ = BIV , M . BIV = 



X M 



ba 



which is the error in the distance bd, and is to be applied to the reading B 7/ . Set the 

 rod to read (B" B' v ). Then : 



For Adjustment of a Dumpy Level. 



Haying first adjusted the spirit-level so that it remains true in all positions about 

 the vertical axis, point the telescope on the rod, properly held at 6, with target set to 

 read (B" B IV ). By means of the capstan-headed screws, raise or lower the horizontal 

 line until it bisects the target. To test the adjustment, set the rod over a, with index 

 reading (B" B 1V ) (B 7 A'), and see if the target is still bisected. 



Adjustment of Attached Level of Transit Telescope. 



The rod being held plumb at 6, with target set to read (B" B iv ), move the tele- 

 scope by vertical tangent-screw until the line of sight bisects the target ; clamp securely. 

 Then bring the bubble to the middle of the tube by means of the level-adjusting nuts 

 alone. Test as in the other case. 



REMARKS. The diagram shows a special case, viz., when (B" A") > (B' A'), 

 or the angle subtended by B v * is one of elevation. If (B" A") = (B 7 A') the line of 

 sight is already level and no adjustment is needed. If (B" A") < (B 7 - A/), B* sub- 

 tends an angle of depression, and is to be added to B r/ . In the latter case, if the slope 

 of the ground is slight, the difference (B" A") may be either zero or a very small 

 quantity, positive or negative ; but in all cases it is added algebraically to (B' A') to 

 obtain B" 7 . 



As in all other methods of adjustment, we assume that the maker has done his part 

 so well that the line of collimation will not be disturbed in any movement of the ob- 

 jective for focusing. Let us suppose that the line of collimation is made truly hori- 

 zontal, and that in its prolongation we have set the centres of two targets, one over a 

 and one over b, the instrument being at d. If now we focus upon the farther target, the 

 image will be bisected by the horizontal spider-line. Then change the focus so as to 

 view the nearer target. If the centre of the objective has not moved truly in the line of 

 collimation, the new image will not be bisected at the focus, and the nearer target will 

 appear to be out of level, when in fact it is not. Hence, since this adjustment requires 

 change of focus, it cannot be made if the above defect, in the movement of the objective, 

 exists. If, however, the distance ad be not too small and the defect alluded to be only 

 slight, the error in changing focus for b and a may be hardly appreciable. The adjust- 

 ment once made approximately, we need not remark that, in the field work, any further 

 error of objective is avoided when taking equidistant sights. 



The Plane Table. 



A description of this instrument, as modified in plan by H. L. Whiting, Esq., 

 assistant U. S. Coast Survey, and constructed by C. L. Berger & Sons, may be found 

 in the Coast Survey Report for 1865. 



The following description of its adjustments, by A. M. Harrison, Esq., assistant 

 U. S. C. S., is taken entire from the same paper : 



" Topography is that branch of surveying by which any portion of the land surface 

 of the earth is mapped in plan on a specified scale or proportion of nature. 



