GEODESIC INVESTIGATIONS. 69 



in either latitude or lougitiide would misrepresent the position of 

 a station by something close on a hundred feet, — an amount 

 of error that would not be tolerated in the length' of one of the 

 computed sides of the loosest triangulation. 



It is well known that the resultant latitudes and longitudes of 

 sitations obtained by means of calculation, and by direct astro- 

 nomical observations are generally discordant : — at some station ; 

 differing by hundreds of feet, and at others by less amounts ; 

 but scarcely ever agreeing. It has been demonstrated by Pratt, 

 in his treatise " On the Figure of the Earth," that in some 

 instances the error in the length or amplitude of an arc got from 

 astronomical observations is such as to exceed -ro of a mile in 

 about 600 miles. He has computed, by means of the laws of 

 attraction, that at some stations of the Trigonometrical Survey of 

 India, the plumb-line deviates from the vertical or normal due to 

 the spheroidal figure of the earth by as much as 6", 9", 10" and 

 19". And by applying the computed corrections to the observed 

 angles, the geographical j)ositions of the stations astronomically 

 obtained were brought more into harmony with the positions as 

 computed from those in more favourable localities for observa- 

 tions. But (notwithstanding laborious calculations), by taking 

 into account only the visible disturbing forces in the vicinity of 

 the stations — such as ranges of mountains and sea coast — there 

 were discrepancies which were accounted for by assuming unequal 

 local attraction in the spheroidal earth ; and attributing it to the 

 diversity of density of the matter adjacent to the stations. 



Such being the case, it is evident that astronomical observations 

 for latitudes or longitudes should be taken only in favourable 

 localities, in order to get a near approximate to the absolute 

 geographic positions of a few of the principal stations ; and that 

 with such as starting points or data, all the other stations should 

 have their positions computed with the greatest accuracy possible. 



Admitting that the absolute position of one of the stations is 

 correctly obtained by astronomical observation, it is evident we 

 can choose various strings of connected sides of triangles issuing 

 from such station, and so obtain by alternations of the data, 

 computed expressions for the same desired magnitudes ; and then, 

 by means of equations of conditions, eliminate any discrepancies 

 due to imperfect readings of the measured angles between the 

 sides of the triangles. But in carrying out the calculations for 

 any such string of sides, care should be taken to use only the 

 angles which every two of the stations subtend at the intermediate 

 station as actually measured by the altitude and azimuth instru- 

 ment, — subject merely to corrections due to attractions of moun- 

 tains, and to defect of attraction of the sea coast, — for other- 

 wise, we could not, bv mere addition and subtraction of angles. 



