OP THE UNITED STATES. iOi 



bring the object end of it pei pendiculaily over tlie micros- 

 cope A, wbich position 1 call reversed, and observe the 

 same objects which I had ol)served before ; without any al- 

 teration in the adjustments of the instrument, not even its 

 general levelling, if tjjere has been no accidental derange- 

 ment, l)ut in every case without any alteration whatever in 

 the adjustments of the transit telescope. 



3. Then the theodolite itself is tuined round horizontally 

 for one change of legs or about 130°. So thai all ani:;les 

 will now be read by each microscope at i^O"^ from the for- 

 mer situation. In this position the instrument is again care- 

 fully levelled and adjusted in all respects. 



4. In this second position the two operations before de- 

 scribed are repeated ; that is the same objects are again ob- 

 served in botii the direct and the reversed position of (he 

 transit. 



o. After this the theodolite is again moved horizontally 

 for one change of legs in the same direction as before, so as 

 to come into the third possible situation, and each micros- 

 cope to read again on the limb at 120° from its former situ- 

 ation. 



6. In this third position, the same objects are again ob- 

 served, both in the direct and in the reversed position of the 

 transit; after the instrument has been adjusted in all respects 

 as in any one of the two former positions. 



By this method each angle is observed six times in the 

 systematic order required for the compensation of all errors 

 arising from tlie causes heretofore treated, and with much 

 less trouble than if an equal iiuml)er of observations were 

 made by the merely accidental positions of the instrument, 

 and as many ol)scrvations would most probably be taken at 

 all events of such points as would l)e considered as re(|niring 

 great accuracy. The final angles are thus determined by 

 the influence of eighteen angles on jnuts of the division sym- 

 metrically siiiialcd. 



Experience has completely sanctioned tiiis method of ob- 



