Self- Calculating Sextant. 525 



simple inspection, and more accurately, we think, by it than 

 by any circuitous process.* To say nothing of the pleasure 

 of being informed on the spot, which in many cases may be 

 most important, as in the vicinity of a hostile fortress, when 

 a person with this instrument in his hand, might in a few 

 minutes furnish information which could not otherwise be 

 had in as many hours ; superseding at once the necessity for 

 books and tables. 



We are also of opinion that the method now recommend- 

 ed is more scientific, and accurate in its results, than the 

 former circuitous one. The reasons of which are — 



] st. That, in respect of science, it is surely more scienti- 

 fic in design to ascertain the cotangent directly by inspection, 

 than directly by reference to the arc. 



2d. That, on the circular limb, half the arc (by reason of 

 reflex vision) measures the whole angle; on the line of 

 cotangents (by reason of the same), double the radius be- 

 comes the measure of the cotangent ; in other words, reflex 

 vision, which reduces the scale on the limb one-half, dou- 

 bles that on the line of cotangents, and thus creates a differ- 

 ence as four to one in favour of the accuracy of the latter. 



3d. That all tables of Logarithms, Sines, Tangents, and 

 Secants give interminate decimals, or mere approximations, 

 which cannot vie in accuracy with direct results. 



It may be objected to the instrument, that, taking cogniz- 

 ance only of right-angled triangles, the cases to which the 

 cotangent scale is applicable must be few. On the contrary, 

 it is surprising the number of important problems to which 

 it may be applied, whether on the vertical or horizontal 

 plane. Besides, it affords a fine exercise of ingenuity to 



* The process of observation, in this case, is nearly identical with 

 the former, the only difference is that, referring to the line of cotan- 

 gents, we have a direct answer on a scale of four times the relative 

 dimensions. 



