78 

 When (5) or (6) is used - = 22* ....... (10) 



Find Sin p = sin A cos <j> ...... (12) 



Sin p and cos p are at the same place in the table. 

 d. Example. ^ = 42 16' 30" N. z = 52 43' 30" 



<5 = 18 13' 20" N. * = 2C 21' 45" 



Checks. 



3' 10" 

 4'65" 

 _d=12 1'35" 



= 0.2342195 Tan = 9.9586273. Sin = 9.8278148 Cos = 9.8691875 

 Tan^Q dj = 9.3284570 Tan V= 9.2477939. Cos ^=9.9933068 Sin A =9. 9943079 

 Cot y 2 z =0.3048785 Cos A= 9.2064212. Cos p = Q. 8345080 Ship = 9^634954 

 Tan %(*#)= 9.8675550 3894. 



346 318. At same place in table. 



204 A = 9915'22"5 



i/ 2 (k &') = 36 23' 45" Sin <j> = 9.8278148 Cos A 7 = 9.993306,1 



y 2 z = 262r45" Sin 6 = 9.4951325 Cos k = 9.660623:2 



^= 10 2' 00" 0.3326823 0.332683'J 



* = 62 45' 30" 



e. Remarks. Look out tan 0, cos 0, and sin 0, at one search. Use either check 

 as may be preferred. This operation need not be performed oftener than the 

 flemands of the work require, the plate being used mean time. 



13. Bemarks. 



The observations and reductions can be always made, according to the process 

 given, without a watch, but the latitude of the place must be known. It must bo 

 carried on as the survey proceeds, by measurement, or an observation made ti> 

 determine it with the instrument. If it becomes necessary to find the latitude i'i 

 may be done as follows : 



14. Finding the Latitude by the Sun. 



a. Directions. For Observations. Near noon begin to observe the sun 

 a little before it reaches its greatest altitude. By means of the slow-motion 

 screws keep the sun's image exactly in place on the screen, or by direct sight keep 

 the cross-wires exactly on the sun. As it moves upward just carefully follow it, 

 recollecting that the object is to get its greatest altitude. Be careful to stop fol- 

 lowing it when it turns and begins to descend. 



b. Directions. For Reductions. Find 0, as in 12, b. Find the sun's appar- 

 ent declination, <f, as in 11, c. Then 



z -f 6 = $>, the required latitude ..... (13) 

 Be sure to observe the Algebraic signs, as 6 may be + or . 



c. Remarks. Having the latitude in this way, the observations and reduc- 

 tions may be conducted according to the processes above given. The latitude once 

 carefully ascertained by this or some other method, may be preserved by the dis- 

 tance traversed north or south of the point of the last observation for latitude. It 

 will at once appear that the measurement and observation may be made to check 

 each other. The method of reducing the change in latitude by linear measurement 

 may be as follows: 



15. Finding the Latitude by Linear Measurement. 



a. Conditions. The latitude of the point measured from, or reckoned from, 

 must be known. The measurements must be reduced to the north and south 

 direction from the reference point. Let reduced distances north be -f-i and those 

 south be . Let all signs be observed. Let the true bearings, or directions of all 

 lines with the meridian of the reference point, be given. Let any number of courses 

 be run in any direction. 



