18 KING ON OCCULTATIONS 



In this manner we may find for difierent times, pairs of corresponding positions of 

 the moon's centre and the place of observation. If the measured distance between corres- 

 ponding points be exactly equal to the moon's radins, the star will then appear to the 

 observer to be on the edge of the moon's disk, and either the immersion or the emersion 

 takes place at that instant. 



If at a first trial such a pair of points be not found, two pairs, corresponding to two 

 instants near together, must be found such that at one the distance is greater, and at the 

 other less, than the radius of the moon. Then by proportion the instant at which the 

 distance is equal to the radius may be found with sufficient exactness. 



The intervals from geocentric conjunction haA'ing been thus found for immersion and 

 emersion, they must be subtracted from or added to the Washington M.T. of conjunction, 

 which is given in the Ephemeris, in order to obtain the Washington M. T. of the im- 

 mersion and emersion as seen from the place. Correcting them for longitude, we have 

 the local mean times at which the events will take place. 



By plotting, for the instant of immersion or emersion, the positions of the centre of the 

 moon and the observer, we can measure with a protractor the angle of the position of the 

 star on the moon's limb from the north point thereof, it being the angle between the 

 straight line or radius of the moon joining those two points and the direction of the axis 

 oîy. This angle is used for setting with an equatorially mounted telescope. 



For use with an altitude and azimuth instrument, the angle of position from the 

 highest point, or vertex of the moon's limb, is required. This is the angle, which may 

 also be measured with a protractor, between the same radius of the moon and the straight 

 line joining the centre of the earth with the observer's position, since this last straight 

 line is the projection of the vertical line of the observer, if the small difference of direction 

 of the vertical line and the central radius be neglected. 



The linear unit employed in the Ephemeris for the tabulated quantities Y, x', y\ is 

 the earth's equitorial radius. The moon's radius in terms of this unit is 0'2'723. 



The following example, with the figure, will indicate more clearly the practical use 

 of this method. The linear scale of the figure is one-sixtieth of an inch equal to "002 of 

 the equatorial radius, which is a convenient working scale. 



Required the time of immersion and emersion, and the angles of position, of the star 



68 Orionis, at Ottawa, January 2.5th, 1888. Latitude, 45" 23'. Longtitude, 5-4m. E. of 



Washington : — 



log cos p = 9-84659 log sin <^ = 9-85235 



From table in Appendix to \ ,„ ^ n.nnn7R i n ^ finoo? 



American Ephemeris 1'°^ ^ =0 00076 log G =0-00225 



log p cos <f> == 9-84735 log p sin 0' = 9-85010 



(! = + 19° 48'-8 log sin*<S = 9-53014 log cos & = 997350 



9-37749 9-82360 



■whence p cos <!>' = 0-7036 



pcosf sin é = 0-2385 

 P sin <p' cos à = 0-6662 



H. M. 



From Ephemeris :— Washington Hour Angle at Geocentric Conjunction + 59-9 

 Difference of Longitude, Washington to Ottawa — 5-4 



Ottawa Hour Angle at Geocentric Conjunction + 1 05-3 



= 16°-325 



