Surveying and Lerelling. 159 



giving instructions on this subject, I, have found it convenient 

 to draw up a few rules, and construct some auxiliary tables, 

 for the use of the practical man, without troubling him with 

 the mathematical investigations. These I beg leave to lay be- 

 fore this Society, and should they meet with the approbation of 

 its members, the publication of them will, perhaps, be useful to 

 that class of surveyors. 



The tables are formed upon the usual formulae, derived from 

 the consideration that the earth is an oblate elliptical spheroid, 

 of 3J5 of compression. 



This I arrived at some years ago, and I have generally been 

 endeavouring to test the accuracy of the measures of the earth's 

 axes which I had then adopted, by a careful comparison of 

 them with those that successively came to my knowledge, and 

 the general accuracy of my numbers, will be obvious from the 

 following values : — 



llence, the mean equatorial radius derived from all these is 

 less than what I have obtained by 5 feet only, while the polar 

 semiaxis is greater by 853 feet. These means give a compres- 

 sion of ^ nearly, and the differences, in general, are so small, 

 as in this case to be quite immaterial in almost any practical 

 application to the purposes of surveying. It is clear, there- 

 fore, that the data on which my tables are founded, differ little 

 from those of the highest authority, and consequently the re- 

 sults derived from their employment are sufficiently worthy of 

 confidence. 



In deducing latitudes, longitudes, azimuths, and heights, 

 geodetically, it is necessary to convert any distance measured 

 in feet on the earth's surface into arcs, and hence the radius of 

 curvature of the measured arc, in any given position on the 

 terrestrial spheroid, is required by the principles oi the conic 

 sections. 



