OF ARTS AND SCIENCES : JANUARY 10, 1865. 



889 



2A^ 



= e^ = 2.908442 



log e^ 



log X- e^ 

 logxe 



•2 0^ = 62 

 (2 a a'f = 7242.01 



52 — 2 



0.463660 



0.825686 Table in Coast Survey Report, 



1.289346 1854, p. 136.* 



.644673 

 ± 4".412 Limit by Peirce's Criterion. (7) 



2 a'2= 1250.65 2 a a' = 85.10 



c = 2a^-2a'^—(2a a'Y = 57791.79. 



log 2 a'2 



logc 



log d" 



\ogd 



log mean error 



lo2 mean error of result 



v. 



3.096118 

 4.761868 

 8.334250 

 9.167125 



9.80876 

 8.97589 



X. 



log 2 a^ 1.71600 



4.76187 



log d'^ 6.95413 



log d' 8.47706 



9.80876 



8.28582 



Mean error A' 0".0946 (8) Mean error x 0".0193 (9) 



log constant 0.22807 0.22807 



log prob. error of result 9.20396 8.51389 



Probable error A' 0".1599 (10) Prob. error a; 0".0327 (11) 



(A) are the fifty-two observations. Each equation should be = 0, 

 the quantities in the column A are the errors of each observation. The 

 column A^ contains the squares of these errors, and the values of \' and 

 X are those which make -2" A^ (the sum of the squares of the errors) a 

 minimum, and are, therefore, the most probable values. (3) gives the 

 quantity 1".0885, as the probable error of a single observation. (7) 

 gives 4". 41 as the limit, by Peirce's Criterion, for a doubtful observa- 

 tion. (10) gives, as the probable error of the resulting latitude, 0".l 6. 

 It is more likely than not that the result is within this amount of the 

 truth. The common tables will show that it is 100 to 1 that my lati- 

 tude is within 0".61 ; 200 to 1 that it is within 0".67; and 300 to 1 

 that it is within 0".78 of the truth. 



The prime vertical transit was one hundred feet south of the centre 

 of the dome, which is 1".0 of arc, which is to be added to my result. 

 a Lyras's place was taken from the P^nglish Nautical Almanac. Its 

 declination {d) is 1".0 different in the American, and 0".l less in the 



VOL. VI. 42 



