T R A 



(3) Given the error in altitude to find the error in time, 

 Lat a, be the error in altitude, then 



sin. azini. X cos. lat. . 

 Hence for a given error in altitude & is the least when the body is o 

 the prime vertical, the altitude .*. should be taken near the east or west 

 points. ' 



Time of sun's passing the meridian, or the horizontal or vertical wire 

 of a telescope. ( Vince.) 



(1) Let d" = diameter of the sun estimated in seconds of a great cir- 

 cle 3 then the time of passing the meridian ia 



d v ' X sec. declin. 

 15" , ' 



The same will do for the moon if d" its diameter. 

 (2). The time of passing an horizontal wire is 



d" , rad. 



The same expression must also give the time which the sun takes ia 

 rising. 



If d" 1980" the horizontal refraction, we have the time that refrac- 

 tion accelerates the rising of the sun 



jo.,,, y rad.a 



cos. lat. X i-iu. azim. 



(3) The time in which the sun would pass the vertical wire of a tele- 

 scope is 



- X <r^ ; , where 8= formed by the circles of 



ID" cos. 8 X cos. dec. ' 



altitude and declination. 



TORSION, elasticity of. See EJastic Bodies, equilibrium of, 



TRADE.WIXD.-5ee Wind. 



TRANSITS of Mercury and Venus. ( Vincc.) 



Let P =' the periodic timo of the earth, p that of Venus or Mercury, 

 Now that a transit may happen again at the same node, the earth mus't 

 perform a certain number of complete revolutions in the same- time tha* 

 the planet performs a certain number, for then they must come into 

 ronjunctioti again at the same point of the earth's orbit, or nearly in the 

 same position in respect to the node. Let the earth perform 'x revolti- 

 310 S3 



