OF FIXED STARS BY MOON. 19 



In the figure AB and AH are drawn at right angles to one another, each equal to 

 p cos '// = 0-V036. AP = 0-2385, AC = 0-6662. 



C is then the centre of the earth, and B and P the extremities of the major and minor 

 axes of the elliptic path of the observer. The star being above the equator, the part of the 

 ellipse below the line AB is taken. 



The aug-le HAH^ is made equal to 16'-3 to the east of AH, since the hour angle is 

 positive and the place is therefore east of the star. 



The angles HAH, HAH', H'AH", are each made equal to 15''-04. 



From i^i, H„, H', H" perpendiculars are drawn to AB, meeting it in A^, A^, A', A". 



The proportional compasses are now set to the ratio AH : AP, and the perpendiculars 

 from -ff„ &c, are divided in the points Pi P„ P' P" by means of the compasses in this ratio. 



These latter points are points on the ellipse. P„ represents the observer's position at 

 the time of Greocentric Conjunction, P; at one hour before, P' at one hour after, and P" at 

 two hours after. 



From the Ephemeris are found Y = + 0-3650, x' — 0-5686, y' = + 00358. 



CM(| is taken equal to -3659, Mg being above C, because Y is positive. 



Mt,D is drawn equal to 2/' = + 0-0358, still upwards because positive. 



D3I' is drawn at right angles equal to x' = '5686, always to the right, being always 

 positive. 



M„ is then the position of the moon's centre at conjunction, M' its position one hour 

 after. On 3I„M' produced take M,M, and M'3I" each equal to M,M'. Then M, is the 

 moon's position one hour before conjunction, and M" two hours after conjunton. 



Hence the points M„ M^, M, M" correspond to P„ P„ P', P" respectively. 



By measurement we find : — 



P,M, = -5944 P,M„ = -2130 



P'M' = -2096 P"M" =z -6264 



Hence the two points at which PM = -2*723, lie one betweeen Pj and P^, and the other be- 

 tween P' and P", and the time of immersion is found by : — 



2723 — 2130 „ . n^ . , 



r = ,g .-, .^ 01 an hoiu- = 9-6 minutes. 



and of emersion by 



^ 2723 — 2096 . , on • . ■ 



^^ ^9^4 onna °i ^" liour = 9-0 minutes. 



Hence we have for a first approximation : — 



Immersion at 9-6m before conjunction. 

 Emersion at Ih 090ni after conjunction. 

 For a closer ap^jroximation we may now plot in two points, one 10 minutes before 

 conjunction, and the other Ih 10m after conjunction, making the angles H^Ah, H'Ah' each 

 equal to 2|° and proceeding as before, p and p' being the corresponding points on the 

 ellipse, m and m' are the corresponding points on the moon's path, m M^ and m'M' being 

 each one-sixth of M„M'. 



Then we have by measurement : — 



M,P, = -2130 mp = -2750 



whence we get 



Tj = 9-6 minutes agreeing with the former result. M'P' = -2096, m'p' = -2776 

 whence r, = 9-2 minutes. 



