1S2 Mr Galbraith on Workman's Correction 



at 45°, and diminishes towards the equator and poles. The me- 

 ridional difFcrence of latitude may therefore be augmented or di- 

 minished by correcting the latitudes for the spheroidal figure of 

 the earth. If they are both less than 45°, the meridional dif- 

 ference of latitude will be diminished ; if the one be less than 45°, 

 and the other greater, the meridional difference of latitude may 

 be the same on the spheroid and on the sphere ; and if they are 

 both greater than 45°, the meridional difference of latitude may 

 be increased. 



These remarks will be rendered more palpable to practical 

 seamen, by an example wrought at length by both methods, and 

 then comparing their results, than by a direct demonstration. 

 Thus, taking Mr J. R. Young's example, page 126 of his Tri- 

 gonometry, lately published, and employing Mendoza Rios' 

 Table of Meridional Parts, — 



1. App. Lat. Sl'lS' M. P. 3597.50 Red. Lat Lat. 51° T M. P. 3579.94 



2. 37 2392.63 36 49 2378.87 



Diff. 858 = 14 18 1204.87 1201.07 



Hence the course is 33°5', to distance 1 024 miles. 



As radius, . . . 10.000000 10.000000 



Is to tan. 33' 5' . . 9.813899 9.813899 



So is Mer. D. Lat. 1204.87 . 3.080939 1201.07 3.079568 



To differ, of Long, 784.94 . 2.894838 782.50 2.893467 



Now, by middle latitude sailing, not corrected by Work- 

 man's table, the difference of longitude is . ' 779 miles 

 Hence difference of longitude on the spheroid, 782.5 



Error by the common method, — 3.5 



Difference of latitude by Workman's table, . 786.6 miles 

 The same on the spheroid, . . . 782.5 



Error by Workman's proposed correction, -}- 4.1 



greater in excess than the uncorrected method is in defect. 



The same results would nearly arise from a recomputation of 

 the example given by my friend Mr Riddle of Greenwich, in 



