378 FERGUSON'S LECTURES. 



LECT. the form of arithmetical rules, simple and easy to those 

 ^ ,^, who have learned the elements of trigonometry. For 

 in practical arts of this kind, arithmetic should be used 

 as far as it can go ; and scales never trusted to, except 

 in the final construction, where they are absolutely 

 necessary in laying down the calculated hour-distances 

 on the plane of the dial. And although the inimitable 

 artists of this metropolis have no occasion for such in- 

 structions, yet they may be of some use to students, 

 and to private gentlemen who amuse themselves this 

 way. 



RULE I. 



To Jind the angles which the hour-lines on any dial 

 make with the substile. 



To the logarithmic sine of the given latitude, or of the 

 stile's elevation above the plane of the dial, add the 

 , logarithmic tangent of the hour distant from the 

 meridian, "*or from the substile ;" 7 and the sum minus 

 radius will be the logarithmic tangent of the angle 

 sought. 



For, in fig/ 2. K C is to KM in the ratio com- 

 pounded of the ratio of A' C to K G ( K R) and of 

 K G to K M ; which, making C K the radius, 10,000000, 

 or 10,0000, or 10, or 1, are the ratio of 10,000000, or 

 of 10,0000 or of 10, or of 1, to K GxKM. 



Thus, in a horizontal dial, for latitude 51o 30', to find 

 the angular distance of XI in the forenoon, or I in the 

 afternoon, from XII. 



Note 116. That is, of 15, 30, 45, 60, 75, for the hours of I, H, III, 

 JIII, V in the afternoon : and XI, X, IX, VIII, VII in the forenoon. 

 Note by ike Author. 



Note 117. In all horizontal dials, the erect north or south dials, 

 the substile and meridian are the same : but in all declining dials, 

 the substile line makes an angle with the meridian. Idem. 



