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, the elimination of the error in the wire interval is conven- 

 iently made in the same manner. With a ratio of 1:100, using a 

 rod graduated to feet, the reduction is simplified by determining 

 the logarithm of the true K, rod in feet, and horizontal distance in 

 chains units, accomplishing the reduction of K I cos 2 v by logarith- 

 mic functions." 



To Verify the Constant, K, measure a base of 500 feet or 

 200 meters as the case may be. If K = 100, the stadia wires will 

 intercept 1 meter on a metric rod at 100 meters + ( c -f- f ) from the 

 center of the instrument, or 1 ft. on a rod held at 1 00 feet -f- ( c + f ). 

 Set up the instrument (c + f) back of the first hub so that this 

 constant will not thereafter enter the calculations. Read the interval 

 to the nearest hundredth of a foot by use of the target. If the 

 interval is less than 5 ft. at 500 ft. the constant will be greater than 

 100, and 'vice versa. Suppose the interval to be 4.95. Substituting 

 in the value of D (p. 104) we have: 



500 = 4.95 <, or 4 = 500 ~ 4.95 = 101 or 1 : 101 



t i 



Intermediate points may also be checked up and an average 

 struck, but the atmospheric conditions should be as nearly as possible 

 alike. Prof. L. S. Smith has shown * that differential retraction 

 between the upper and lower wires will make the intercept on the 

 rod greater in the morning and evening than at midday by a vari- 

 able error up to .004ft. per ft. of interval, and that this phenomenon is 

 more noticeable near to the ground than in the air strata some dis- 

 tance above. It is a most fruitful source of error in stadia survey- 

 ing. He therefore lays down the following rules : 



1. Every instrument man should determine for himself his vjire inter- 



val or make observations for graduating special rods. 



2, Determine the wire interval for various distances but only betiveen 



the limits expected infield vjork y and for several hours distributed 

 through one or more days, under conditions ivhich do not differ 

 radically from the country to be surveyed. 



.?. For a radical change of field or season conditions, re-determine the 

 vjire interval or rod graduation. 



4. Avoid reading the lovjer cross voire near the ground either in the 



interval determinations or in the field ivork, but the interval 

 determination readings should agree in this respect ivith the 

 average field practice. We add: 



5. For reading distances under Li 00 ft., set the lovjer vuire on an 



intergralfoot division; count the number of feet, tenths and hun- 

 dredths to the upfier vjire and estimate the fraction. Readings 

 taken ivith nvhole intervals are tvjice as accurate as vjith half 

 intervals, but ivhen the sum of the half intervals equal the 

 reading nvith the ivhole interval the check is significant.** 



* Bui. i'niv. It'n. Vol. / .\'o. 5, 1895. 

 ** J. A. McDonald in Canadian Rnginffr, Jul\ M. 1914. 



106 



