668 Proceedings of the Boyal Irish Academy. 



nodes, and this is evidently greatest in the position represented in the 

 figure, viz., that in which GT is parallel to the line of nodes. But P 

 is the position in the orbit corresponding to this position of p' : so we 

 see that the velocity in the line of sight is always a maximum when 

 the body is passing through the line of nodes. 



Therefore, to find when h is greatest, it is only necessary to have 

 a circle drawn on carefully-squared paper, such as papier millometriqiie, 

 of say 100 mm. radius. Take GF' equal to as many millometres as 

 there are units of the second decimal in the eccentricity. Draw the 

 line GT, making an angle equal to X with the line of apsides. Join 

 TF', and produce it to T'. Then measure the distance of F' from the 

 circumference of the circle at right angles to the line of apsides : this 



gives us -; also measure i^'r=-,andi^'J"=-,andZ.(3'Ti?"=^-(<A-X). 

 a a a ^ 



Then we have 



; i 



a . ,, ,, . la.F'B.QosGTF' . 



n r= — ^ sm (<^ - X) sm y = p-^7Y' — ^^^ y 



a 



I. a 



.. . , ,, . l.a.F'TmsGTF' . 

 = Y . sm ((^- X) sm y = p^T^g smy. 



' a 



For instance, in the case oi 6 p Eridani, I find in Houzeau's Vade 

 Mi'cum de P Asfronome the elements of the orbit to be — 



y = 44° 40', 

 X = 327° 15', 

 £ = 0-378, 

 a = 3"-82, 

 P= 117-51 ; 



and the periastron passage took place in 1817.51. I take GF'= 37-8miB. 

 Measuring the distance F'B above and below the focus, I find — 



P' 

 0-926 —=1-333 



a 



0-929 ^ = 0-642 



f-(c^-X) = 8°-8. 



^ = 0-9275 

 a 



