OF DIALING 387 



But we may often, from the foregoing rules, resolve LECT. 

 the same problem without much trouble; especially if' 

 we suppose the master of the ship to know within 2 or 

 3 degrees what his latitude is. Thus, 



Assume the two nearest probable limits of the lati- 

 tude, and by the theorem ff ' -compute the hours of 



observation for both suppositions. If one interval of 

 those computed hours coincides with the interval ob- 

 served, the question is solved. If not, the two distances 

 of the intervals computed, from the true interval, will 

 give a proportional part to be added to, or subtracted 

 from, one of the latitudes assumed. And if more exact- 

 ness is required, the operation may be repeated with the 

 latitude already found. 



But whichever way the question is solved, a proper 

 allowance is to be made for the difference of latitude 

 arising from the ship's course in the time between the 

 two observations. 



Of the double horizontal dial; and the Babylonian and 

 Italian dials. 



To the gnomonic projection, there is sometimes added 

 a stenographic projection of the hour-circles, and the 

 parallels of the sun's declination, on the same horizontal 

 plane ; the upright side of the gnomon being sloped into 

 an edge, standing perpendicularly over the center of 

 the projection : so that the dial, being in its due position, 

 the shadow of that perpendicular edge is a vertical cir- 

 cle passing through the sun, in the stereographic pro- 

 jection. 



The months being duly marked on this dial, the sun's 



declination, and the length of the day at any time, are 



had by inspection (as also his altitude, by means of a 



scale of tangents.) But its chief property is, that it may 



2 c 2 



