OF DIALING. 379 



To the logarithmic sine of 51 3tf 9.89354"* 

 Add the logarithmic tang, of 15^ 0* 9 42805 



The sum radius is .... 9.32159= 

 the logarithmic tangent of 11 50', or of the angle 

 which the hour-line of XI or I makes with the hour-line 

 of XII. 



And by computing in this manner, with the sine of 

 the latitude, and the tangents of 30, 45, 60, and 75, 

 for the hours of II, III, IIII, and V in the afternoon : or 

 of X, IX, VIII, and YH in the forenoon ; you will find, 

 their angular distances from XII to be 24 18', 38 3', 

 53 35', and 71 6' ; which are all that there is occasion 



to compute for. And these distances may be set off 



from XII by a line of chords ; or rather, by taking 1000 

 from a scale of equal parts, and setting that extent as 

 a radius from C to XII ; and then, taking 209 of the 

 same parts (which, in the tables, are the natural tangent 

 of 11 50') and setting them from XII to XI and to I, 

 on the line h o, (see engraving, page 374) which is per- 

 pendicular to C XII : and so for the rest of the hour- 

 lines which, in the table of natural tangents, against the 

 above distances, are 451, 782, 1355, and 2920, of such 

 equal parts from XII, as the radius C XII contains 

 1000. And lastly, set off 1257 (the natural tangent of 

 51 30') for the angle of the stile's height, which is 

 equal to the latitude of the place. 



The reason why I prefer the use of the tabular num- 

 bers, and of a scale decimally divided, to that of the 

 line of chords, is because there is the least chance of 

 mistake and error in this way ; and likewise, because in 

 some cases it gives us the advantage of a nonius 1 division. 



-Vote us. In which cose, the radios C K is supposed to be dirided 

 into 1000000 equal parts. Xott by the Author. 



