HI 



ASTRONOMY. 



[SOLAR ECLIPSES. 



this eclipse, but for a different latitude and longitude. 

 The ratlins of pnj. . ' I: I 111), a tbe same in 

 this caw as in the last, being the difference of the linri- 

 znuUl parallaxes of tbe sun and moon ; C D is the meri- 

 dian or circle of tin-limit inn ; the ellipse represent* the 

 projection of the parallel of latitude ; L G N the moon's 

 apparrnt jath ; C Q the difference of dtcliiwtion of the 

 sun and moon at the conjunction in right ascension, and 

 C 12 the siue of the sun's zenith distance at noon. The 

 elements for the above eclipse, given in the \niitinil .11- 

 manaf, are as follows, and the place may be considered 

 a* situated 6' west of Greenwich, and at 52 41* of 

 north latitude : 



Greenwich mean time of conjunction in right ascension 



- March 15, Oh. 44m. 7s. <>, or March 15, Oh. 43m. 44s/2 

 of the mean time at the given place. 



The apparent time will be March 15, Oh. 34m. 37s. '8, 

 the equation of time being Oin. Cs. -4. The moon's 

 hourly motion in right ascension 30" 1C*'4 ; and the 

 sun's, y 17* '1 ; and the relative hourly motion of the 

 moon from the sun on right ascension 27' 59" 3, = which 

 must be reduced to the arc of a great circle by being 

 multiplied by the cosine of the declination, or 1 24' 21" -tf 



- 27 A 98. 



The radius A C=58'-0 as in the last case. 

 Hourly motion of moon from suu . . 27' "98 

 Moon's hourly motion from sun in declination * 15' 31* 

 Moon north of sun .... =42' 53* 

 Sum of semi-diameter of sun and moon =32' 1* 



Difference = ll*-9 



The semicircle A D B represents the northern half of 

 the earth's disc drawn with a radius, A C, equal to 58' 0, 

 as in the Lost case C I) is the axis of the earth. The 

 position of a point of 52 41' of north latitude, or 52 30' 

 of geocentric latitude, will be obtained in a similar 

 manner to the last, and its plnce on the axis of the earth 

 at noon and midnight will be 54 37' and 60 23' to the 

 north of the point where the sun is vertical. Obtain, by 

 means of a sector or graphically, the sines of those angles 

 to the radius C B, and set them off on the line C D from 

 C to 8. The position of the locality whose latitude is 

 52 30 7 at 6h. in the evening, will be obtained by taking 

 the cosine of the latitude, and marking it off on the line 

 T 6 T 6, perpendicular to C D on each side of T, that 

 point being the bisection of tho two points S 12. These 

 distances may likewise be obtained, and with more 

 exactness, liy multiplying the radius C B ~ 58' by tho 

 sines of 54 37', and 50 23', the former of which gives 

 the distance C 12, and the latter C B, the distance T 6 

 being obtained by multiplying 59' by the cosine of 

 52 W ; and those quantities may be marked off by 

 means of the same scale of equal parts, as adopted in the 

 radius B. The other times in path of the observer, 

 are determined as in the former instance. The moon's 

 path, according to right ascension and declination, is 

 laid down as before. Take the difference of the declina- 

 tions of the sun and moon = 42" 53", and set it off, 

 from C to G above tho line A C B, because the moon is 

 north of the sun. Take C () equal to tho hourly motion 

 of the moon from the sun in right ascension, reduced to 

 a great circle, and set it off from C to O. Make O K, 

 which is perpendicular to C B, equal to 15' 31", the 

 moon's hourly motion in declination from tho sun. The 

 line C K represents the hourly motion of the moon from 

 the sun in regard to right ascension and declination, and 

 the line L G N, drawn parallel to this, represents the 

 moon's path across the earth, the point G being the 

 position of tbe moon's centre, at the moment of conjunc- 

 tion in right ascension. The even hours may therefore 

 be marked off on this point, by taking the point G to be 

 34m. 38*. past noon on March 15th ; and the line C K to 

 l- the hourly motion of the moon, and the position of 

 tin) moon at noon will be found by tho proportion as 

 00m. : 34m. 38. : : C R : G XII. : : 31-6 : 182. The 

 hours on tho moon'* path should, if possible, be sub- 

 divided to minutes, and the same on the path of tho 

 spectator. Tho sum of the semi-diameters of the sun 

 and moon being taken on the adopted scale 32' ]*, 

 that duUnoe U taken in the compasses, and those are 



shifted backwards and forwards, as in the former caso, 

 until the mm times are found on the moon's path and 

 the path of the spectator, which are exactly at this dis- 

 tance apart. When tho loft leg of the compass is on tho 



i i's path, and tho right leg on that of the spectator, 



this will give the commencement of the eclipse ; and 

 when the riyht leg of the instrument is on the moon's 

 path, the left on that of the spectator, and the corre- 

 sponding times are again found at the same distance 

 apart, we obtain the end of the eclipse in tho same 

 manner. By applying the side of a small square to the 

 moon's path, and moving it along until the other side 

 cuts the same hour and minut,- on both lines, we obtain 

 the nearest approach to the centre of the sun and moon. 

 If the scale of the projection be made of sufficient dimen- 

 sions, the distance of those two points will show whether 

 the eclipse be total or annular; if le.is than the dilfei 

 of the semi-diameters of the sun and moon, it will be 

 annular at that locality. By describing a circle whose 

 radius is equal to that of the moon, and whose centre is 

 situated on tho moon's path at the time of the nearest 

 approach of the centres, we have a circle representing 

 the moon's disc. Taking the ratlins of tho sun in 

 the same manner, and the corresponding time on the 

 path of the spectator for a centre, we describe the posi- 

 tion of the solar disc, and their intersection will repre- 

 sent the phase of the eclipse at the moment of greatest 

 darkness. With the points of the compasses at a distance 

 apart, equal to the differences of the semi-diameters of 

 the sun and moon, tho times of the formation and rup- 

 ture of the annulus may be determined in a similar 

 manner, as the beginning and end of the eclipse. In the 

 present case we obtain for the beginning and end of the 

 eclipse at the given position llh. :!2m. A.M., and 2h. 8m. 

 P.M. of apparent time, which is equal to llh. 41m. and 

 2h. 16m. of mean time. The time of greatest obscura- 

 tion is 12h. 52m., found by taking the shortest distance 

 between the corresponding times on the paths of the 

 moon and spectator, answering to Ih. 1m. P.M. of mean 

 time as before. 



From the relative dimensions and positions of the sun 

 ami moon, it will be Keen that the eclipse is central and 

 annular at this locality viz., at O'O (of arc) of west 

 longitude and at 52 41' of north latitude, or at a point 

 which is a little to the oast of Peterborough. The line of 

 central eclipse passed across England from Bridport in 

 Dorsetshire (at 2 51' of west longitude, and 50" 43' of 

 north latitude) to the Wash, and a little to the north of 

 the towns of Sherborne, Marlborough, Oxford, Bucking- 

 ham, and Wisbeach. The diameter of tho moon so 

 closely approaches to that of the sun, that this eclipse 

 might be total in the vicinity of the island of Madeira 

 by the augmentation of the former value. At the sta- 

 tion for which the above calculation is made, theduratioii 

 of the annulus was only 12s. -3. 



Annular eclipses are more common than total eclipse*, 

 and the prediction of their times and duration shows more 

 palpably than anything else, the great accuracy to which 

 the tables of the sun anil moon have been carried ; but 

 astronomers still rely upon the careful observation of 

 those phenomena, in order to correct the places of those 

 bodies as given by theory ; and tho times of the eclipse 

 of March 15th, 1858, are liable to be slightly affected by 

 small errors in the tabular places of the sun and moon ; 

 whilst errors which are known to exist in the received 

 diameters of those bodies affect tho duration of the an- 

 nulus. These errors, however, only amount to a frac- 

 tional part of a second at moat. How different is this 

 from the prediction of the eclipse which was to have 

 h.-i] .peiied at Rome in 1684, which tho tables at that time 

 in uso predicted would be total, whilst in reality only 

 three-fourths of the sun disappeared. In the prediction 

 of the eclipse of 1706, the tables of La Hire were four 

 or five minutes in error. 



Annual Nvmher of Eclipsrs oj the Sun. Eclipses of 

 the sun on the earth generally are more frequent than 

 eclipses of tbe moon, in the proportion of three to two, 

 as it will be seen should follow from the following con- 

 siderations. In order that there be an eclipse of tho 



