Measuring Surface and Solidity. 235 



the chance of an error in placing the theodolite over the apex of 

 tht? angle to be measured. In drawing out the plan, either the 

 same risk is to be encountered, or the risk of the line transfer- 

 ring the angle not being truly parallel. From observations, I 

 find that in a multitude of angles transferred to paper, with the 

 various scattered apices required by surveyors, that the accu- 

 racy of each cannot be depended on to within less than four or 

 five minutes. Supposing the scale used to be 200 links to an 

 inch, the average length of the lines to be 500 links, and the 

 trigons to be of the best possible shape, this error would be 

 about one link in every line, and, combined with the risk of er- 

 ror in laying off the lengths, it would give three links in every 

 line, or six links in the thousand. The common and unavoid- 

 able changes in the heat and moisture of the air of a room cause 

 considerable contractions and expansions in paper, the rate de- 

 pending on its texture. Experiments induce me to estimate the 

 change of size at one in two hundred. We have thus in 

 protracting and remeasuring a series of figures, a total risk 

 of error of 17 links in the thousand, or 34 acres in the 

 thousand. These errors are supposed to be in lines, forming 

 the best possible shape of trigons. If we were to regard the in- 

 creased risk from the shapes being unavoidably bad, the esti- 

 mate would be doubled. And there can be no doubt, that 

 double or treble this error is frequently made in consequence of 

 following the slovenly, and in truth tedious practice of making 

 the estimations of area depend on the accuracy of the plan. 



A rectilineal figure is given, when all its sides and angles ex- 

 cept three are known. If all the sides and angles, except two 

 or one, be given, the data are checked, or we can discover by 

 calculation, whether they be possible, or consistent with each 

 other. If, in a rectilineal figure, formed by surveying lines, 

 there be an inconsistency, arising from the causes already men- 

 tioned, we may conceive that we will make a nearer approxima- 

 tion to the truth, by dividing the error among all the constitu- 

 ent parts of the figure, so as to make the smallest alteration in 

 each. To such a subdivision of the error it is barely possible 

 to approximate in the form of the parts when protracted. It is 

 very difficult a to make the subdivision of error on the original 



