Astronomical and Nautical Collections. 357 



The table hereafter inserted gives the Logarithms of A and B 

 to four places of figures ; it is of single entry, the argument 

 being the interval, " or elapsed time :" and for the whole cal- 

 culation of the equation Logarithms to only four places of figures 

 suffice. 



Log. A + Log. d D + Log. Tang. L — Log. of the first part ; 



Log. B + Log. dZ) + Log. Tang. D = Log. of the second part. 



Thus we see the whole operation reduced to finding the Loga- 

 rithms A and B by the table, and three others to four places of 

 figures by the ordinary Logarithmic Tables, of which every 

 observer must be possessed. 



In relation to the signs, the factor A is positive if the cor- 

 rection is required for midnight, and negative when it is wanted 

 for noon : 5 is negative when the interval exceeds 12 hours ; 

 dZ) is negative when the declinatory movement is towards the 

 south ; Tang. D is negative if the declination is south ; as is 

 also Tang. L when the observer is in a southern latitude. On 

 the right of each logarithm may be written the sign of the factor 

 it represents, in the form shown in the examples. 



With what has been said, and giving to each part the sign 

 which results from the general rules of multiplication, the cor- 

 rection is obtained with more facility and accuracy united than 

 by any other mode with which I am acquainted : in fact, the cal- 

 culation is very short, symmetrical for both parts, the result 

 exact to the tenth of a second in all cases which offer in practice, 

 and answers for either the sun or the planets. 



The declination of the sun must be taken from the Nautical 

 Almanac, for noon or midnight, as may be required ; but that of • 

 a planet, for the time of its superior or inferior passage. 



Some may consider the attention to the signs of the factors 

 necessary to show that of the product as troublesome, desiring 

 some particular rule as better for assigning the manner in which 

 each part of the equation ought to be applied. Persons of so 

 bad a taste may avail themselves of the following rules when 

 solar altitudes are observed ; which will most frequently be the 

 case. 



The first part is additive when the sun's longitude is greater 

 than 3' and less than 9', otherwise it is subtractive. But the 



