CIRCUM-MERIDIAN OBSERVATIONS TAKEN NEAR NOON. 229 



Having thus determined or corrected the declination for 

 each observation, there remains nothing to be done but to ap- 

 ply it according to its sign, either to the zenith distance or al- 

 titude, according as it is north or south, in order to obtain the 

 latitude corresponding to each observation. 



That most justly celebrated astronomer M. Delambre, to 

 whom all practical astronomers are most deeply indebted, fa- 

 voured me with the following formula, for correcting or re- 

 ducing to noon these observations, 



y. 2 Sine 2 I P /Cos H Cos D\ , 2 Sine 4 P /Cos H Cos D\* 

 J -' V^~~ \^W±V) + Sinel" VSme(H±D); C °" tan (H±D ) 



This correction appears to be tedious to compute, but, by t he 



help of the Tables of — w; mel * - and sinei" ' ^ e calculation 



will be much abridged. 



The second factor of the first term requires to be computed 

 only to five places of decimals, and the looking out of three 

 logarithms. The second factor of the second term is formed 



^.t j • Co-sine H Co-sine D , . 



om the preceding one, sine( H ± D) b emg squared, and 



then multiply it by the Co-tangent (H ± D). 



The second part of the above I have omitted, as in observa- 

 tions taken nearly 15' from noon, I have never found the cor- 

 rection resulting from it amount to half a second ; but I have 



been 



still it is requisite to pay attention to it. For this purpose the proportional part 

 of the declination, corresponding to the horary angle of the observation, is to be 

 added to the declination at noon, in order to have it for the instant of observation, 

 when the observation is made before noon, and the declination is diminishing 

 If the observation is made in the afternoon, the proportional part must be sub^ 

 tracted. 



