Measuring Surface and Solidity. 33 



offsets, and they determine the position of a series of 

 points in the boundary, with regard to the side of the larger 

 figure, technically called a surveying line, in a manner theoreti- 

 cally the most accurate possible, and which also practically gives 

 very true results, even although the surveying line and boun- 

 dary be widely separate. With the management of offsets, 

 therefore, I do not interfere. The distance between the sur- 

 veying line and the boundary must be actually traversed at each 

 offset ; and the trouble of moving from one line to the other, 

 demands that they be as close together as possible, and that 

 they never exceed a certain distance, determined by the curva- 

 ture or irregularity of the boundary, and the degree of accuracy 

 aimed at. 



With regard, therefore, to the position of the surveying 

 lines forming the outer boundaries of the large trigons, the sur- 

 veyor's choice is very limited ; and it is also apparent from their 

 connexion with offsets, that their lengths must be actually mea- 

 sured. The choice of the forms of the trigons is therefore also 

 limited by these circumstances, as well as by the nature of the 

 surface of the ground. 



In order to obtain data for the interior trigons, either their 

 sides or their angles must be measured, or a mixture of both. 

 The measuring of lines on the ground by the common chain is 

 well known to give only an approximation to the truth. The 

 errors are occasioned by the roughness of the surface, by the 

 elongation or contraction of the chain, from the force employed, 

 or from the variation of heat ; but, above all, by the difficulty 

 of applying its end to the exact spot formerly occupied by its 

 beginning. Since the data obtained in the field are thus erro- 

 neous, the trigons should be of that form which is least altered 

 by a slight variation of the sides or angles. But this arrange- 

 ment, from the causes already mentioned, is scarcely ever prac- 

 ticable, and many of the trigons are unavoidably of such a shape 

 that the errors in measurement are likely to produce greater er- 

 rors in the plans, and in the calculated extent. 



The area of the trigons is arrived at, by its relation to their 

 three sides, to two sides, and the sine of the contained angle, or 

 to the sines of the two angles and the interjacent side. When 

 ft *)<)) i:l 



