318 HYDROGRAPHICAL SURVEYING [chap, x in. 



Equation of Equal Altitudes. 

 The rigorous expression, according to Chauvenet, is : 

 Sin a -cot I E.T. tanci.tan §. cos. a— cosec. \ E.T.tan.Ltan g. 



wliere a = equation of equal altitudes = — 



I E.T. = | elapsed time= 



c? = declination at upper meridian passage. 

 d— g= ,, ,, observation E. of meridian. 



d + ^= ., „ „ W. 



g=| difference of the declination at tlie 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, 

 A\ hatever may be the difference in the declinations ; the half- 

 elapsed time being found as follows : 



1 E.T.= 



^ 2 



(R-S)+(S^-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, may be taken as 

 equal to the difference of times (as shown by a sidereal chrono- 

 meter) of the observation of the two stars ; the chronometer 

 being, of course, corrected for rate. 



If Ri>R, add24HoR. 



If the western star be observed first, in wliich case S>S\ 

 then S and S^ are treated algebraically. 



d = the mean of the dechnations of the two stars. 

 g= I difference ,, ,, » 



