OF THE UNITED STATES. 405 



rest in this part of the work, I considered the utility of the 

 work would be much extended, both for the general 2;overn- 

 inent and those States, the proportional expenditure much 

 diminislied by their distribution, and thr final execution more 

 accelerated than could be possil)lc by any other means. In 

 the execution of the triangulation, it was easy to sui! some 

 peculiar want or interest of any State. This would iiave 

 added doiiljle value to the woik for this State, without in- 

 creasing the expenditures and the work by any amount worlli 

 consideration. 



Some remarks upon the best methods of transferring the 

 result of the triangulation to paper may be inserted here ; as 

 frequently nuich of the accuracy of the work is lost by in- 

 sufficient methods, and ihese are left to the knowledge and 

 practical skill and experience of the operator, though the an- 

 alytical formuhc of calculation and the principles of projec- 

 tion have been treated repeatedly and extensively. 



In former works I have always found the calculation of 

 the points in degrees, minutes, seconds, and decimals more 

 convenient for tliis use than those in linear measures ; and 

 as the ap|)roximation can be carried, l)y the decimals of se- 

 conds, farther than it is possible to subdivide actually upon 

 paper, tliere is no accuracy lost, particularly as all the deci- 

 mals are always preserved in summing up any number of 

 results that concin' in the determination of a j)oint, just as 

 the logarithms obtained in the calculation are always used 

 in any place where the results are required, and not again a 

 logarithm of the number found anew; any loss in the frac- 

 tions in transferring to paper having thereby no farthei inllu- 

 ence than upon the point itself. 



1 made a table of the values of the minutes, seconds, and 

 decimals of latitude and longitude for all those jjar's of the 

 projection whicli had been calcidated, for the suiidivisiDns of 

 the different trapezii, which were traced by the projeciinn, 

 and which I conunonly made only of five minutes at most, 

 both in lutitudf and longitude, in order to bring the distances 



VOL. ir. — .1 c 



