Reduction of Latitude. 



233 



planet is flattened, the greater will be the deviation between the 

 normal and radius, at the place where the reduction of latitude is a 

 maximum. 



4. The number o^, j the measure of the earth's oblateness, being 



put for a in formula (6), we shall obtain 

 tang. 4^ 



tang. 5 = : 



'■> from which we have con- 



150.750 + 149.750 X tang.^^^ 

 structed the following table, in which columns A contain the lati- 

 tudes differing by 1°, and columns B the corresponding values of the 

 reduction of latitude for the earth. 



If the value of 6 be required for a latitude between any two con- 

 secutive latitudes of the table, it will be sufficiently accurate for most 

 purposes, to determine it by an interpolation as follows : Let it be 

 required to determine by means of the table, the reduction of lati- 

 tude at a place whose latitude is 41° 24' ^Q". We perceive from 

 the table, that the difference between the values of (5, corresponding 

 to latitudes 41° and 42°, is equal to 2.997''; we then say, as 1° 

 is to 2.997", so is 24' 36" to a fourth terra, which is equal to 

 2.997" X 24' 36" 2.997" X 1476" 

 Jo =■' '^aoo" ~ ^ .229", which, being added to 



the value of ^, corresponding to the latitude 41°, will give the value 

 of the required reduction of latitude ; if the value of (5 had been re- 

 quired for a latitude greater than that at which 5 is a maximum, the 

 term found by interpolation should have been subtracted. When 

 the utmost degree of accuracy is required, then we must resort to the 

 use of the formula from which the table is constructed, and deduce 

 Vol. XXXI.— No. 2. 30 



