he error must be kept within two feet per mile, or 1' 18". If small 

 angles of deflection, in passing trees, could be measured with pre- 

 cision, there is no reason why an alignment could not be preserved 

 with great accuracy. 



The horizontal circle should be provided 

 with a gradienter, and for this class of work the 

 circle should remain clamped. Whenever the 

 gradienter was at the zero of its scale, the 

 direction would then be secured. * 



The gradienter drum for the horizontal 

 circle should be graduated to read in radians, 

 which requires only that, as usual, the pitch of 

 the thread shall be ^ioo of the radius of the 

 clamp and that the drum shall be adjustable 

 and divided decimally. 



To run a straight line through a forest 

 without cutting large trees: 



The distance Bb ri sin ai, 



Cc -= n sin ai 4- ra sin a2, and 



Dd n sin ai -f- ra sin aa + ra sin am 



or generally, the amount of departure from 

 alignment is 2 r iin a 



At the point F, where it is desired to resume 

 the straight line, 



2> o r " a + r s * as = 



The last equation enables the surveyor to 

 assume either rs or ar> and to calculate the other. 

 Assuming ar>, then 



r sin a 



sin a.-> 

 quite small, approximately, 



or, if all angles are 



a'r, . sin \' 



So far as the final result is concerned, it is 

 about as convenient to measure a in minutes 

 as in radians but it is sometimes desirable to 

 drive stakes on the true line, in which case the 

 deflections in radians are more convenient. 



* For further investigation of this practice, "Engineering", London, Dec. 

 4, 7907, concerning Fergvtson's Pfrcfnlagt Theodolite und Zrit . fur /**/., 7<W. 

 /. 2, concerning Heydt's Zahnkrris* Theodolite. 



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