480 Transactions. — Miscellaneous. 



therefore call seconds of time minutes of arc. Add one-half 

 the quantity and we have her hourly motion E., 28-5'. 



2. Her motion S. (8) is as easily got : for 10m. it is 141'^ 

 — that is, 14-1" for Im., or 14-1' for the hour. 



To avoid confusion we set these quantities off to the left of 

 the diagram, and draw the diagonal through the point of (j . 

 This diagonal, being measured on a narrow slip of paper, is 

 divided into 12 parts of 5m. each, and these divisions, set off 

 on the Moon's path in orbit, continued to the right as far as 

 necessary. We have the position of the Moon's centre at 

 these times. The elliptical quadrant being also so divided 

 where it is found necessary, we have the relative position of 

 the two bodies. 



Now, in the compasses (or on a slip of paper) measure the 

 semidiam. of the moon; add that of $ (15-20' + -11 = 15-31'), 

 and, laying it between the two paths, we shall find two points 

 wdiere it will just reach the same time on both. The first of 

 these, 3h. 30m., is the time of first contact ; the second, 3h. 59m., 

 that of last contact. To these times, if we add that of ? 

 meridian passage, 2h. 4-5m. (2h. 5m.), we get 5h. 35ni. and 

 61i. Im. as the New Zealand mean time of these phases. 



The south point of the Moon is that at its apex in the dia- 

 gram (Plate LIU.). Its vertex is on a line drawn through its 

 centre parallel with one joining Earth's centre and star. The 

 angles are measured in the usual way. In a solar eclipse the 

 Sun's hour- angle is the same as apparent time. 



EXPLANATION OF PLATE LIIL 



The semicircle represents the southern half of the Earth's disc, as 

 seen from the planet Venus, when © is Earth's centre, and the horizontal 

 line passing through ® the origin of co-ordinates. Any convenient scale 

 of equal parts may be used, but the larger the better, as enlarging the 

 time divisions. The divisions of the scale are taken as minutes of arc. 

 P. is Earth's radius as seen from IMoon's centre, ^u, is Moon's semi- 

 diameter seen from Earth's centre, and the two bodies bear the same 

 relative proportion when seen from Venus. We take the parallax of 

 Venus from that of the Earth so as to ascribe her slight motion to the 

 Earth, and leave her in one position during the occultation. Also, we 

 use the co-latitude of Wellington, because we measure from the pole and 

 not from the equator. At conjunction the centres of the three bodies are 

 in one plane, and while the Moon is moving eastward and southward iu 

 the line o£ her orbit Wellington is travelling along the curve of the ellipse, 

 the places of each being indicated by the time marked on the respective 

 lines. 



Fig. A. — Elements: ?. Hour-angle time rf, 21i. 45ni. P. Relative parallax, 5-.o'. 

 h. Declination of ? S., 10°. A. Diff. of declination of Bloon, 29-75' S. I. Wel- 

 lington reduced co-lat., 48^ 49'. B 's hourly motion E., 2S'5'. B 's liourly motion 

 S., 14-1'. jU-. Moon's semidiam., 15'2'. " ? 's semidiam., C'5". ^ -(- ? , 15-31'. 

 Besults : First contact, 3.o0 = 51i. 35m. N.Z. mean t. ; last contact, 3.59 = Cb. Im. 

 First contact, 120° E. of south point and 80° E. of vertex ; last contact, 173° E. 

 of south point and 126° E. of vertex. 



Fig. B. — Aiii)arcnt path of ? behind BIoou during the occultation on the evening 

 of the i3tb September, 1893. 



