618 PROCEEDINGS OF SECTION H. 



pairs of readings which will make the telemetric factor m simple, 



one series of factors or grades being assumed and the other derived 



from the formula. 



m (J 



Occasionally horizontal angles may be measured by means of the 

 inclined graduated circle, but the reduction is not convenient. By- 

 projecting O' on O P (the point o) and dividing pp" = P'jo' by 

 po' + o'O the tangent of the horizontal value 0" of the inf lined arc 

 is given, thus : — 



sin. e 



tan. 6 = i — -. : 



COS. cos. t. + sm. ( tan. i 



= tan. e sec. i (1— tan." / sec. 6 + tan.* / sec.^ —..).. . (6) 



The compass needle must generally be employed in determining 

 bearings. 



The adjustments of the instruments should be as follows : — 

 1. Collimation of the sight-line of the telescop^^ by rotation in the 

 containing collars; 2. Setting the axis of the bubble-tube or the 

 telescope parallel to the collimated sight-line; 3. Adjusting the 

 vernier or pointer so that when set at zero the sight-line shall be in 

 the plane of the two axes. These are the permanent adjustments. 

 The only temporary adjustment is the making of the outer axis 

 vertical, which is required each time the instrument is set up, and 

 is performed in the usual manner. Of these adjustments the one 

 requiring special development is 3. 



In deriving the relation between the grade angle and the circle 

 reading the condition of adjustment was assumed ; as it is now 

 otherwise we must write -j- a for 0, and also add a constant, c, 

 in (2). The problem will then be to find «, and readjust so as to 

 make it and to eliminate c. Then -\- a will be equal to 0, and 

 the required condition is satisfied. 



The procedure will be as follows: — Set a staff vertically at a 

 convenient distance so that in the whole revolution of the inner 

 relatively to the outer axis the collimated point of the diaphragm 

 wires will intersect the staff. Mark or note the intersection on the 

 staff at multiples of /3 degrees from 0° to 360°— /i (/^ being a mul- 

 tiple of 360°), and in each instance measure the sloping distance 

 — which will, of course, vary — between the intersection of the 

 inclined axis and the sight-line (O). Finally determine the point 

 on the staff "on the the same level" as this point, O. Then the 

 distance on the staff of each point from this last, divided by its 

 slope distance,*' will be the sine of the corresponding grade angle. 

 Thus we have to express (2) in the more general form — 



sin. 7„ = k vers. {0,„ -f «) + c . . .(") 

 in Avhich the left hand member is the sine of any grade angle, and 



''Tliis must not be derived from the horizontal distance to the staff because in revolving 

 the axis the point O slightly varies its distance. 



