Mr Sang 07i Optimum Surveying, S3J5 



But in all the principal triangles the three angles were actu- 

 ally observed, and the observations have been corrected by the 

 above named assumption ; and it is really a matter of doubt 

 whether such a correction be allowable, or whether, admitting 

 the nearness of the assumption, the disagreement of the obser- 

 vations with it ought not to have been taken as evidence of 

 the incompetence of the instruments employed. 



In the surveys of 1787-88 and 1791-94, which were made 

 with the great theodolite, the entire amount of computed sphe- 

 rical excess is 90^^03, the entire amount of observed excess is 

 72''.25, and not merely is the sum total less than the computed 

 sum total, but almost all the terms are so. According to this 

 observed spherical excess on a district of some 1700 square 

 miles, the degree of the earth's circumference ought to measure 

 68,000 fathoms nearly. Again, in the survey of 1795-96, 

 which was made by an instrument of half the size, the spheri- 

 cal excess observed was S2''.75, that computed W.Q9., while 

 the greater number of the terms are in excess. This would 

 give for the length of the degree 57,000 fathoms nearly. Of 

 the remarkable contrast in the precision of the two instruments 

 I shall have occasion to treat in an after paper ; here I shall 

 only ask if it was proper, amid such instrumental deficiencies, 

 to carry the angles corrected for computation to hundredtk 

 parts of a second ? Ought a sailor boy to correct the altitude 

 given by his ebony octant, for the solar parallax ? 



The error of procedure which I have just noticed is one of 

 quality, not of amount ; I have brought it out here for the 

 purpose of rendering more apparent another of the same kind, 

 but of greater magnitude. 



In vol. i., p. 154, there is an investigation given concerning 

 the sum of the azimuths of two stations. Supposing this in- 

 vestigation to be correct (it is in reality grossly erroneous), the 

 surveyors deduced the difference of longitude of the stations ; 

 exactly inverting the above method of spherical excess ; only 

 that the included surface is more extensive, having one of its 

 corners at the North pole. The error thus actually introduced 

 was one of 200 fathoms in the degree of longitude. I have al- 

 ready quoted Dr Tiarks's statement, that an uncertainty of 1" in 

 the observed azimuths would cause a doubt as to the oblate- 



