79 



b. Directions. For reducing the north or south distances. Multiply the 

 length of each course by the cosine of its bearing, the results being given signs 

 as above indicated, + for northerly courses, and for southerly courses. Sum 

 these results regarding the signs. 



c. Remarks. This sum will be the distance north or south of the reference 

 point. 



d. Directions. For reducing feet to minutes of Latitude. Find the length of 

 a minute of latitude for the place by this equation. 



= 6076.361 



(14) 



Then divide the traversed distance north or south of the reference point by the 

 value of m found from this equation. 



e. Remarks. The result will be the minutes and decimals of a minute o^ 

 the new point from the reference point. This value of m will be in feet, hence the 

 north or south distance must be in feet. 



16. Remarks. The latitude may be dispensed with during a day's work 

 after the first satisfactory observation. It may be for a longer period if the watch 

 is to ue depended upon. It will be well to find the latitude, and check the work 

 occasionally, where the watch is used. In order to prepare the watch for this work, 

 proceed as follows : 



17. Correcting the Watch. 



a. Directions. For correcting the Watch by a Noon Observation. Having 

 ascertained the bearing of a line without the aid of the watch, as at first directed, 

 near noon set the line of sight in a meridian. Set the telescope so the sun can be 

 seen in it, or received on the screen as it passes the meridian. Note the time by 

 the watch when the sun's west side comes in apparent contact with the vertical 

 cross-wire. Note the watch time when the east side of the sun just touches the 

 vertical wire. Find the time halfway between these two noted times for the time 

 of the meridian passage of the sun's center, or the time of apparant noon, by the 

 watch. 



ft. Remarks. The time as above found should differ from exact noon by 

 just the equation of time for that date and time as given in the Nautical Almanac. 

 Observe the sign there attached to the equation of time. The watch may then be 

 set to true time if not correct. That is, it may be set so that the time of the sun's 

 meridian passage will be just the equation of time, with its sign, from exact noon. 



c. Remarks. The watch may also be corrected directly from an observation, 

 reduced as at first directed in 1O and 12. Here it will be necessary to take the 

 watch time of the observation, as directed in 1C. Having done so, and reduced the 

 observation by 12, proceed as follows : 



(I. Directions. For correcting the Watch by an observation at any time. Hav- 

 ing found A and 2, and knowing <*, find t by the following equation. 



sin A sin z 

 Sm *= cosd < 15 > 



This being in arc, reduce it to time at the rate of four minutes of time to one 

 degree of arc. 



e. Remarks- This result should differ from the watch time of the observation 

 from mean noon, by just the equation of time, with its sign. If it does not, set the 

 watch so it would have done so had the observation been made with the corrected 

 watch. 



18. Remarks. Having corrected the watch by the last method, the value of 

 t in time may be found from the value of t at this observation by noting the time 

 by the watch of another observation, and thence finding the elapsed time. This 

 applied to the first value of t will give its value for the last observation. Thus the 

 value of t may be carried forward as long as the watch runs true. Of course it will 

 occur to many at once that the watch can just as well be used to measure the 

 elapsed time without being corrected. This is too careless. The better way is to 

 keep a careful oversight of the watch by correction. Thereby it may be known 

 how much the watch is to be trusted. It is always best to establish a routine sys- 

 tem in these matters, as soon as practicable, and adhere faithfully to it. 



