Pearson — On the Computation of Occultations and Eclij^ses. 183 



XXXI. — Computation of Occijitation-s and Eclipses. By James 

 Pearson, M. A., F. E. A. S., late Scholar of Trinity College, 

 Cambridge, Yicar of Fleetwood. 



[Read, February 10, 1879.] 



Thj: methods of calculating the circumstances connected with the above 

 phenomena, as given by Mr. "VYoolhouse in the appendix to the Nautical 

 Almanac for 1836, or as contained in Admii'al Shadwell's work 

 on the subject, are confessedly so laborious and puzzling, that any 

 arrangement by means of which the same results might be obtained 

 with more facility must be esteemed desirable. The graphic process 

 delineated by Mr. Penrose in his valuable treatise is a step in this 

 direction, but it is capable of being so modified as that it can be easily 

 performed in about twenty minutes, and bring out the times of occur- 

 rence within thirty seconds. To explain the mode by which this is 

 accomplished is the object of the present communication. 



For ordinary use in these operations it is necessary first to con- 

 struct a series of concentric ellipses, having a common semi-axis major 

 ten inches in length. The semi-axes minor are in the same straight 

 line, but are of lengths 10 sin 2°, 10 sin 4°, 10 sin 6°, &c., up to 28°, 

 which is the extreme range of the moon's declination. Ordinates are 

 drawn to the semi-axis major, the abscissae of which are successively 

 10 sin 15°, 10 sin 30°, 10 sin 45°, &c., corresponding to the hours 

 I, n, HI, &c. The construction of this diagram will not be a matter 

 of much difficulty to those who are acquainted with the elements of 

 Conic Sections, and it must be treasured up for subsequent use, being 

 the only diagram required in the process. 



The next step is to construct a scale of equal parts, the length of 



ten divisions of which is represented by the number -=- =, where P 



^ ^ Pp cos I 



is the moon's reduced relative Horizontal Parallax, p the factor which 



deduces the Earth's radius at the proposed place from the equatorial 



radius, and I the geocentric latitude. Since this scale involves both the 



latitude and the parallax, it is called the latitude-parallax- scale, and 



the number referred to is to be taken from an ordinary inch-diagonal 



navigation scale. This done, the moon's reduced horary motion in 



right ascension, and given horary motion in declination, will enable 



us to lay down the moon's relative orbit by its aid, which orbit must 



be subdivided into hours and minutes by the compasses, commencing 



at the instant of the moon's true conjunction. The position of the 



centre of the projection of the parallel of latitude of the given place 



must be found by the number representing, 



{diff. dec. - Pp sin / cos S) , 



the notation being the same as before ; and it will be below or above 

 the moon's centre at conjunction according as the above quantity is 

 -f or - ; and this being ascertained, the ellipse-diagram will guide in 

 tracing out as much of the ellipse as is traversed during the progress 



