84 Colonel A. R. Clarke on the Figure of the Earth. 



the east, the observed or astronomical longitude of A must 

 receive the correction y x sec fa ; so that of B receives a corre- 

 sponding correction ?/ 2 sec fa > an( i the difference of longitude 

 as observed (/. e. of B east of A) must receive the correction 

 y 2 sec fa — y x sec fa. The astronomical difference of longitude 

 thus corrected is to be equated to the corresponding difference 

 of geodetic longitudes as expressed in terms of u and v ; then 

 multiplying by cos fa, we get an equation of the form 

 y 2 =y x sec fa cos fa + uu + /3v + y. 



The above data afford six such equations. Properly speaking, 

 as a direct check upon these equations, we should add to them 

 the six equations of a similar character which would result 

 from a comparison of the observed directions of the meridian 

 at the seven stations we are considering. I have not, however, 

 the quantities for forming these equations. 



Besides the data contained in his last annual report, Colonel 

 Walker has kindly given me provisional results for his great 

 arcs (or arc, for we may consider them as one) — not final 

 results, but yet not likely to be materially altered. The Indian 

 Triangulation contains a vast number of astronomical stations ; 

 but in the problem of the figure of the earth it is not de- 

 sirable that the latitude-points in one of the arcs should be 

 very much more numerous than in the others. The Russian 

 arc of 25° has thirteen astronomical stations ; the English has 

 thirty-four ; but only fifteen are used in this investigation, 

 this number including those of the French arc : the length of 

 the conjoined English and French arcs is 22°. 



Taking fourteen evenly distributed latitudes in the Indian 

 arc, they require the corrections shown in the following Table 

 (the column on the left gives the approximate latitude of each 

 station) : — 



32 2. -4-14-8-562 w + 5-102« + 0-997« 



30 22 -0-25-7-969 w + 4-988^ + 0'998^ 



29 30 + 3-37-7-662m + 4-912u + 0-998« 



27 55 -l-98-7-092tt + 4-742w + 0-998# 



24 25 + 2-22-6-312^ + 4-446v + 0-998^ 



24 7 -0-93-3-725 w + 4-179v + 0-999^ 



22 1 -2-17-4-970m + 3-783u + 0-999« 



20 44 + 5-51-4-511 u + 3-514^ + 0-999^ 



18 3 + 2-65-3-545 w+2-886i; + 0-999^ 



16 10 + 6-09-2-865tt + 2-397v + 0-999a* 



14 55 -1-75-2-418^ + 2-057^ + 1-000^ 



12 59 + 5-18-1-726 u + l-502u + 1-000 x 



10 59 + 0-43-1-005m + 0-893i? + 1-000o; 



8 12 0-00 0-OOOm 0-000w + 1-000 j; 



