234 Mr J. Sang on a Systematic Method of 



these quantities are at once discovered from the field operations, 

 the calculations are simple ; but in the greater number of cases 

 where angular measurement is employed, an intricate and la- 

 borious process must be first undergone. So tedious are the 

 operations, that, in fact, in nine cases out of ten, the artist cuts 

 them short, by drawing out a plan of the ground from the data 

 obtained in the field, and remeasuring from the paper others 

 more convenient. This method is even recommended in respect- 

 able treatises on land-surveying. 



The errors acquired in the field are of no moment compared 

 with those consequent to transferring the data to paper, in the 

 shape of a plan. It is true, one source of error, that of repeat- 

 ing the measuring instrument, is much lessened, for the scale 

 which corresponds to the chain can conveniently be of such a 

 length as to embrace the longest line required, and thus leave 

 only an error in both its terminations. The scale also may be 

 made of a material whose rate of expansion is very small, and 

 from the precision to which the art of dividing has arrived, its 

 divisions may be conceived to be perfect. The instruments 

 called protractors, for marking out angles on the paper, may also 

 be as well divided as the theodolite, or other angular instrument 

 employed in the field. But to counterbalance these advantages, 

 there are the diminished size of the figures, and the expansion 

 of the paper on which they are traced. 



The eye cannot be applied, for a few hours, to a traverse 

 scale with eighty divisions in the inch, without much pain. 

 The smallest scale in use for the naked eye has sixty divisions 

 to the inch. The fifth part of a division of this scale by means 

 of a sliding index and needle, may be transferred to paper ; or, 

 we may lay down a line in that particular manner, without the 

 aid of a microscope, and by estimating the fraction of the divi- 

 sion by the eye alone, to the accuracy of the yjo^ P art f an 

 inch. But the method is only applicable to a few of the lines, 

 and I believe I am far within the truth, in estimating the ut- 

 most accuracy with which distances, lying in all the accidental 

 directions of a survey, can be transferred to paper in the com- 

 mon way, by means of a scale and needle, or by compasses, to 

 be the j J th part of an inch. The transferring of circular di- 

 visions to paper is liable to a greater risk. In the field there is 



