Astronomical and Nautical Collections. 355 



If the interval expressed in hours is called 7', it is easy to 

 s^e that }5° T—P + P'. 



If the diurnal movement in declination is expressed by d D, 

 it also follows that 



24" : T :: dD : X — —. dD ' ' 



24 



Substituting these values in the expression ofi (P' — P) and 

 dividing by 15 to reduce it to time, it results that 

 i (P' ^ p\ IT 



^^ 360. Sine 



{<) 



^ AD Tans. D 



360. Tangr. 



(•-^) 



= AdD Tang. h — BdD Tang. D 

 And in the last place, substituting in the equation (C) 

 The hour of apparent time by the chronometer =: |^ (i/ + i/) 



— ildDTang. L 

 + BdZ>Tang. jD 



The two last terms jointly form what is denominated the 

 equation, to equal altitudes. 



If another corresponding altitude is observed the subsequent 

 forenoon, and designated by the same letters, but with two 

 accents, to distinguish the quantities appertaining to this third 

 observation, we shall have 



24" + ii" - a' + — f 

 15 



H" — 24" + a" - JL P" 

 15 



And consequently 



15 



The quantity ^ (a + a") will be the time that the chronometer 

 was /as< at midnight, or what is the same, the time of apparent 

 midnight by the chronometer. 



We shall also have in this case 



X tp" - F) = if. Tang. L 



^ ^ ^ Sine i (P' + P") ^ 



Tang, i {P + F) 



Tang. Zy 



