Asfrojio/nirril and Nautical CoUertioiis. ofi.) 



The factor A is negative when the correction is required for 

 noon ; but positive if it is wanted for midnight. 



In like manner, treating of a planet, the factor A is negative 

 if the correction is retjuircd for its superior passage, but positive 

 if wanted for its inferior passage. 



The factor B is positive when the interval is under 12 hours, 

 and negative when the interval is greater. 



This is what the signs affixed to the logarithms in the table 

 indicate. In the logarithmic differences it may readily be seen 

 that the signs merely indicate whether tlic logarithms are in- 

 creasing or diminishing, and are entirely independent of the 

 signs of their columns. 



When the argument falls betwixt two of the times in the 

 table, the use of the simple proportional is sufficient, and the 

 magnitude and inequality of the differences, in some instances, 

 need cause no uneasiness. The log. B, for example, varies 

 unequally and rapidly near 9'', 12'', 14'', and 21''. Let us sup- 

 pose, therefore, dD = + 17' 10", X) — 17° 2', these values pro- 

 duce a maximum in the value of dZ) tang. Z)for the sun. Not- 

 withstanding this, the error from using the simple proportional 

 will not be so much as 0',02, 



If the interval falls betwixt IP 50"" and 12'', or betwixt 12" 

 and 12'' 10"", the second part of the equation is calculated in the 

 first case for 11'' 50'", and in the second for 12'' 10"° : the result 

 will always be a very small quantity; with the knowledge of 

 this, and that with an interval of 12'' the second part is = 0, it 

 will be most easy to find the second part by the given interval. 

 It may be noticed that the same precaution is required for this 

 rare case in using Delambre's tables. 



In relation to the first part of the equation, the use of the 

 simple proportional produces only an error of 0',05, with an in- 

 terval of 20" 6" in the latitude of 60°, dZ> being — 23' 40", 

 which is the maximum for the sun. If the interval were greater, 

 it would be a proof that the altitudes had been taken with less 

 than two hours for a horary angle, and this might produce much 

 greater uncertainty in the result of the observation, than any 



Vol. XIII. 2 C 



