AT THE OBSERVATORY AT PARAMATTA. 



3a 



= 0, and the reduction to the meridian R = t A ; but now 



R = T A + C 

 C is too great for a correction whereof the greater part should always be col- 

 lected in the first term. 



A = S - S + A = S - (S - A); therefore x A = r S - t (S — A); and 



R = ^S - T (S- A) + p (S- A) + cot ^/ A (S- A) sin l" - cot ^ jo2 (s_S) 



« + M 



•A)sinl" 



= tS- ;>2cot^(S- S) - P' S^°^ {' + 



— p^ A cos 2 



sin 2 



!} 



(S 



omitting cubes and higher powers. 



The last term is almost always insensible, and may be neglected ; and in the 

 room of Z,, which is unknown, z or the observed zenith distance may be used in 



the calculation, which together with my having assumed pp — — = z — Z, = a 



never causes the error to amount to one second of arc in the reduction as long 

 as this is not above two degrees. 



Correction of the Hour-angle for change of Equation of Time. 



BroT in his Astronomie, vol. i. p. 451, finds it necessary to correct the hour- 

 angle for daily rate of clock, but neglects at the same time a greater source of 

 error. In solar observations the observed hour-angle is apparent solar time, 

 whilst the interval per clock corrected for sidereal acceleration is mean time, 

 and should be diminished in both solstices by a proportional part of the daily 

 retardation of apparent solar time upon mean time, given in the Nautical 

 Almanac in the column of daily diiference of equation of time. This is a 

 gaining rate of the clock of 13" in the northern, but of 30" in the southern 

 solstice, and more therefore than any clock ought to have. These conside- 

 rations are unimportant in the northern parts of Europe ; but nobody will 

 dispute their importance where the zenith distance is 10°, when an error of 

 l" in the hour-angle of 24 minutes causes an error of 10" in latitude; I have 

 therefore annexed a Table showing the correction to be subtracted from the 

 hour-angle during the southern solstice. 



MDCCCXXIX. 



