Methods of Astronomical Observation. 189 



stituted in formula (8) it becomes, 



A^ A* A^ 



(1-1+ -2--24- + 720- ^^'^ ^^"- ^,o, 

 tan. X = — — — (9) 



1 (-+-2- + ^ ~^^-&c.)tan.^t^ 



Now taking w = 23° 27' 40", tan. w = 0-4340056, and 

 tan. 2 w = 0*1883608. By introducing these values into 

 equation (9) it becomes, 



_ 0-2170028 A ^ — 0-0180836 a^ + 0-0006028a^ 



^°*^~'l-1883608-0-0941804 A 2 +0-0078483 a 4-0-0002616 a ^ 



tan.a;=0-18260684A2— 0-0007454 A 4— 0-00075777 A 6 &c. (10) 



in which A is the length of the circular arc to radius 

 unity. 



It is now only necessary to adopt the co-efficients of for- 

 mula (10) to degrees of arc or minutes of time, as these are 

 the terms in which the right ascension of the sun is 

 generally given, while tan. x may in like manner be con- 

 verted into seconds of arc. This is accomplished by applying 

 the logarithms of R,°, R", &c. to the logarithms of the 

 co-efficients of formula, (10) and they become those for A 

 expressed in degrees and decimals of a degree and x in 



seconds. 



I. II. III. 



Const, logs. 1-0596970, 5-154114, 1-64523. . (A) 



Similarly are obtained the logs, of the constants for 

 minutes of time when the right ascension is given in time, 

 and the distance from the solstice is known in minutes of 



time and decimals. 



I. II. III. 



Const, logs. 9-8555770, 2-745874, 8-03287* . (B) 



To render these co-efficients generally applicable, it is 

 necessary to find the variation of x corresponding to a 

 change of one second in w. 



For this purpose from formula (9) we get 



A2 tan. w 



2* 5 



tan. a: = j—-: ^ — = 77, A2 tan. ?^7 nearly, and thence, 



5 

 a:= y- A2 sin. 1" tan. m? . . ... (11) 



* 0"»7 170955 A2 — 0"-00,00000557024 A* — &c. 



