342 Distance of objects at sea. [Oct- 



the co-efficient = LnAl == 7 then as before : 



2 11 



X = cot E. (rt — 7) in this for .r^ substitute the 

 last found vakie of and we shall have 

 _3 _3 



X = cot E. a — cot E, a2 cot E. X ^ 7''' + 



_3 



+ cot E, 2, a:2, ryS, cc 



the third and fourth terms may be neglected, and it is 

 unnecessary to carry the substitution further, as it would 

 only involve terms with the fifth power of the cotangent. 

 Then as before 



3000. = 3.47712 

 cot 2« = 11.45692 



4.93404 = 85910. feet 1st Term, 



3000. = 3.47712 

 2 



3 6.95424 

 cot 2° = 4.37076 

 7 = 2.28195 



3.60695 = 4045. feet 2d Term, 



81865. log. = 4.913098 

 7.994535 



13' 28" = 808" :== 2.907633 



here the result is too small by 4", equal to about 404 feet, 

 a quantity insensible in practice, so that this formula is 

 sufficiently accurate and far more convenient than any 

 given before, 



C. 



23c^ Jpril 1835, 



