IN PHYSICAL ASTRONOMY. 
339 
When the interval A v is indefinitely diminished, i A v is still equal to the 
variation of v between the epochs for which the quantities &c. 
are calculated, and 
S e = i A I. | (^) o + + 
-f 2 {A (rO.- A (r0 o } + ^-} 
If the radius be taken for unity, and i A v is the mth part of the circum- 
2 X 3'14159 
ference ; i A v = — — — , or, in other words, the resulting values of § e and 
§ a in the equations given above must be multiplied by 2 X 3.14159, and di- 
vided by 360° expressed in the same unit as i A v. 
n is equal to the angular circumference divided by the periodic time ex- 
pressed in the same unit as t ; so that if a degree be taken as the unity of 
angular circumference, n = 360° divided by the periodic time expressed in 
the same unit as t. 
In the elliptic movement or first approximation 
©,., + T {©,-©,} 
\ — n t z a series of sines of arcs multiples of n t &c. 
\ = w, t + z t + a series of sines of arcs multiples of n l t &c. 
~ — constant + a series of cosines. 
s = a series of sines. 
s i = a series of sines. 
These values being substituted in the equations of p. 334 give ^ and 
2 Y each equal to a series of sines without any constant quantity, and ^ 
and each equal to a series of cosines + a constant quantity. 
In the second approximation the values of X, r and s retain the same form ; 
and it is easy to see from the form of the expressions for &e. p. 334, 
that the form of the values of these quantities is not altered however far the 
approximation be carried. 
