Section III, 1889. [ 57 ] Trans. Eoy. Soc. Canada. 



IX. — Compatation of Orcidtation and Eclipses for a (jiveu Jocality by Graphic 

 Comtruction. By N. F. Dupuis, Queen's College, Kiugstou. [Plate I.] 



(Read May 31, 1889.) 



At the meeting of this Soeiety last year a paper was read upou the predictiou of 

 eclipses by graphic construction. The method employed, as I uuderstau'd it, is the same 

 in principle as that given many years ago by James Ferguson, the celebrated " peasant 

 boy " astronomer of Scotland, in his work upon astronomy, and which is also given in 

 liobinson's " University Astronomy," published in 1850. How often the method has been 

 given, I do not know ; these are the only two works in which I have seen it. 



This method consists essentially in projecting, upou a plane through the earth's 

 centre, the earth and moon, from the sun in the case of an eclipse, or from the star in the 

 case of an occultation. The earth thus becomes a circular disc upon the plane of the 

 paper, and the moon a circular disc, a little more than one-fourth the diameter of the 

 former, and which, in the course of the eclipse or occultation, gradually moves across 

 and obscures more or less of the earth's disc. 



I need not here enter into the particularities of this method. "When certain kinds 

 of information are required, it offers advantages over any other graphic method. B^t 

 it has serious disadvantages, and when only local phases of the phenomenon are required, 

 the method becomes so tedious as to become of little practical utility. The earth, being 

 given in orthogonal projection upou the plane, the meridians and parallels of latitude 

 become, in general, ellipses ; and, as we have no simple instrument, like the compasses, 

 for constructing ellipses, these curves have to be constructed by points, and hence more 

 or less irregularly and inaccurately. Moreover, during the progress of the phenomenon, 

 any particular place on the earth's surface is carried forward, in the projection, along an 

 elliptic arc, while the moon's centre moves in a path which is in itself more or less 

 curved. 



A tentative measurement between two moving points thus becomes necessary in 

 order to determine the beginning or end of the jîhenomenon, and these are the things 

 usually sought in the construction. Also if the phenomenon takes place when the moon 

 is far out of the meridian of the plane of observation, the interspaces denoting equal fixed 

 spaces of time, as hours, on the path of the place of observation are very irregular. So 

 that equal parts of these interspaces cannot be determined by inspection or by mere 

 division, but must be obtained by careful and laborious construction. 



Having had to make a large number of approximate predictions of the times of 

 beginning and ending of occultations, the method referred to became so laborious that I 

 devised another method which I found to be much more convenient. This I here propose 

 to give. 



I reversed what I may here call Ferguson's method. Instead of projecting the earth 

 and moon from the star or sun, I project the moon and star, or in the case of an eclipse, 



Sec. Ill, 1889. 8. 



