330 Mr Sang on Optimum Surveying. 



therefore those of the earth also, with the standard measure of 

 the country. These two purposes are entirely distinct from 

 each other ; the first of them can be attained independently of 

 the second ; but the second necessarily implies the first. 



This general proposition, which, as a matter of course, should 

 influence the whole management of a survey, is one that ap- 

 pears to me to be self-evident. Yet, as the want of distinction 

 between these two purposes constitutes the great defect of the 

 surveyors' calculations, I shall endeavour to render the state- 

 ment clear and undeniable, and to point out the inevitable con^ 

 fusion which arises from not attending to it. 



That the geographical department of the survey is indepen- 

 dent of the other, is evident from this one consideration, that 

 jf there had been no standard in the possession of the Royal 

 Society, the second department would have had no existence. 

 Yet still the geographical department would have been unaf- 

 fected. 



The mere angular data of an extensive survey, without the 

 measurement of any base, ought to be sufficient to determine 

 the figure of the earth, and the proportions which the surface 

 of the district bears to the entire surface of the globe. 



Suppose that, in the neighbourhood of the equator, an entire 

 circuit of triangles could be obtained, and, connected there- 

 with, another complete circuit round one of the meridians, it is 

 clear that, without reference to any arbitrary national standard, 

 the relation might thence be obtained between the circumference 

 of the equator and that of the meridian ; and, further, if the 

 whole surface of the globe could be covered by a net- work of 

 trigons, all the peculiarities of the earth's figure might thence 

 be discovered. 



The powers which belong to this complete system of trian- 

 gulation, are shared by any portion of it. Throwing out of 

 view, for a moment, the difficulties which arise from atmo- 

 spheric refraction, the following is a description of a simple and 

 direct procedure, from which all the effects of local attractions 

 are removed. 



ABC being three stations seen from each other, the horizoi 

 tal and vertical angles observed at these stations would enabl 



