Fixed Stars, as observed at GreeTfwich in the Year 1822. 37 



Hence it follows that the value of a, in the Greenwich in- 

 strument, must be very small. Mr. Pond, indeed, considers it 

 as vanishing altogether. However, by keeping entirely to the 

 observations, and resolving the above 29 equations after the 

 method of minimum squares, we shall find 



a = + 0",239, and x = — 0",5082 



and hence the latitude is 



51° 28' 39" + x — «cos<p + 6 simp = 51° 28' 38", 3429+0", 786 b 



in which the dependence of the last term on b could have 

 been removed only by i*eversing the instrument ; a measure 

 however which, by its construction, is rendered impracticable. 

 In order that we may resolve this calculation effectually, I 

 have first determined the probable error of the direct obser- 

 vations, as well as of those of the reflected ones. I find the 

 same result for the former, out of 412, and for the latter out 

 of 265 observations, viz. + 0",799. Whence it appears, that 

 Mr. Pond must have secured the vessel containing the quick- 

 silver from every kind of concussion, since the probable error 

 of the observations by reflection has not been in the least in- 

 creased. From this equality of value by both methods of ob- 

 servation, each of the above equations (resting upon u observa- 

 tions by direct vision, and a' observations by reflection) give 

 the weight a a' : [a + a'). According to this weight I have 

 made the calculations. The coeflicient of the sine of the 

 zenith-distance has received the weight of 366 observations. 



According to the foimulee above mentioned the declination 

 of a star is, from the direct observations, 



= 90° — P-0",1489 — 0",239sin(f5 — 8) + ^'[sinf — cos(ip— 8)] 



and from the observations by reflection 



= P'-167°2'42",8653+0",239sin((p-g)+6[sin^-cos((p-8)] 



Hence it follows that the bend of the instrument, depending 

 on b, can be as little eliminated as in the determination of the 

 latitude : whence nothing remains but to neglect it altogether. 

 For 8 = 2(p — 90° = + 12° 57' it has no influence on the de- 

 clination; for northern declination its coeflUcient is negative; 

 for southern, positive. The declinations resulting from the 

 direct observations and those by reflection, under the assump- 

 tion of b = 0, as well as to the mean taken with respect to the 

 number, is contained in tlie following table : 



