318 HYDROGRAPHICAL SURVEYING [chap. xiii. 



Equation of Equal Altitudes. 

 The rigorous expression, according to Chauvenet, if? : 

 Sin a = cot | E.T. tan c^.tan g. cos. a— cosec. | E.T.tanJ.tan g. 



where adequation of equal altitudes = 



I E.T. = I elapsed time= 



c? = declination at upper meridian passage. 

 (Z— S= ,, ,, observation E. of meridian. 



c? + g= ., „ „ W. 



3=1 difference of the declination at the two times 

 of observation. 

 h and h^ = Hour angles from noon at East and West 

 observations respectively. 



In the case of equal altitudes of two stars, one east and the 

 other west of meridian, the above formula is strictly accurate, 

 whatever may be the difference in the declinations ; the half- 

 elapsed time being found as follows : 



I E.T. = 



(R-S) + (Si-Ri) 



2 



(R-Ri) + (Si-S) 



2 



Where, R and R^ = Right ascensions of star E. and star W. 

 S and S^= Sidereal time of observation of star E. 

 and star W. respectively. 

 S^-S, the difference of the sidereal times, mav be taken as 



