!< FUNCTIONS. 



Sines 



Cosines 



160' 



Tangents 



and 



Cotangents 



0' 280 



FlO. 3. 

 STADIA MEASUREMENTS. 



Hor. dis.: The true horizontal distance from the center of the instrument to the rod. 

 Diff. elev.: The true vertical distance from the height of the instrument to the 

 center point between the two targets of the rod. 



"r": Vertical rod reading. 



"K": The wire interval or ratio, to be determined in the field by frequent tests 

 under working conditions in comparison with steel tape measurement, solving the 

 formula given below for " K," hor. dis. known. 



"c": Distance from the center of the instrument to the object glass. 

 /": Distance from the plane of the cross-wires to the object glass. 



Hor. dis. = K r cos* v + (c + f\ cos v. 

 Diff. elev. = K r } sin 2 + (e + /) sin r. 



In public land surveying it Is convenient to have fixed stadia wires with a ratio of 

 1:132 so that the sum of two rod readings in feet will be equivalent to a ratio of 1:66, 

 or a reduced distance in chains; it Ls also convenient to reduce the error in the wire 

 interval to the error in 10 chs., and to eliminate the error by applying to the reduced 

 distance the proper amount taken from the table of proportional parts. With a ratio 

 of 1:100, using a rod graduated to links, tin- diminution of the error in the wire inter- 

 val is conveniently made in the same manner. Wit ha ratio of 1:100, using a rod grad- 

 uated to feet, the reduction is simplified by determining the logarithm of the true 

 ! in feet and horizontal distance in chains units, accomplishing the reduction 

 of K rcosc by logarithmic functions. 



TIME. 



Conrtrsion of standard time into local mean time. Watch reading watch error in 

 standard time by comparison correction for longitude; the correction for 1. 

 is additive east and subtractive west of the standard meridian of the time belt; the 

 conversion table "degrees to time" Is Convenient in this reduction. 



Conversion of apparent time into local mean time. Apparent time of observation 

 the equation of time; the equation of time is to be taken from the Ephemeris for the 

 date of observation and corrected for the longitude and time of observation, conven- 

 iently interpolated as the interval from <;nvn\vi-h noon to the time of observation; 



221 



