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156 



MATHEMATICAL and 



U 



L 



E 



S 



Take the difFcrencc in the time between the forenoon 

 obfervations of the two days, and alfo between the after- 

 noon obfcrvations. 



Call half the difference of the two differences X; 

 And half the fum of the two differences Y. 

 Let the half interval, between the two obfervations of 

 the fame day, be Z. 



Then, if the timesof thealtitudesobfervcdon the fecond 

 day be both nearer 12, or both farther from 12 per clock 

 than on the firft day—X will be the daily variation of the 

 clock, from apparent time, and Y will be the daily differ- 

 ence in time of the Sun's coming to the fame altitude, 

 arifing from the change of declination. And the propor- 

 tion will be — 



24''- : Y : : Z : E, the equation fought; which will be 

 found the fame (without any fenfible difference) as the 

 equation obtained from the tables. 



But if one of the obfervations on the fecond day be nearer 

 12, and the other more remote from 12, than on the firft 



day — 



Then Y will become the daily variation of the clock from 

 apparent time, and X will be the daily difference in time 

 of the Sun's being at the fame altitude; 



And the proportion will be — 24\ : X : : Z : E. 



The equation, E, thus obtained, is to be fubtraded from 

 the mean noon, if the Sun's meridian altitude be daily in- 

 creafing ; but to be added if it be daily decreafmg. The 

 reafon of all this is very plain; and an example or two 

 will make the method familiar — 



Suppofe the following correfponding altitudes were 

 taken — 



^ 

 ^ 



D. 



Nov. 8. 



9- 



Morning;. 

 H, m. lee. 



9.58.31 

 10 I, 16 



Afternoon. 

 H. m. fee. 



2. 



2. 



4. 9 

 I. 52 



Required 



