188 PHILOSOPHICAL TRANSACTIONS. [aNNO 1771. 



vature, which it really is; and as it differs not greatly from a straight line, an 

 arch of a circle may safely be used for it. But to form a computation in the 

 sphere on this principle, would require a process somewhat intricate; but all the 

 particulars usually inquired into in solar eclipses, may readily be assigned graphi- 

 cally with scale and compass after this manner. 



First, find the time nearly of the conjunction of the luminaries, without be- 

 ing solicitous to investigate the time with exactness. To this point of time as- 

 sign in some crude manner the moon's parallax in longitude, by which a time 

 may easily be assumed, not very distant from the visible conjunction. This may 

 very commodiously be performed instrumentally by the following proposition. 

 To this point of time compute the place of the sun and moon, also for an hour 

 before and after, or rather for such an interval of time as may include the whole 

 eclipse, and not too much exceed, of which an estimate may easily be made by 

 the forementioned proposition here subjoined. But all these places of the lumi- 

 naries may be deduced from the calculation for finding the true conjunction, by 

 means of the horary motions. In the next place, to each of these points of 

 time compute the. distance from the zenith, and the place in the ecliptic of the 

 nonagesime degree. Then from each position of the nonagesime degree, com- 

 pute, by the method described, the moon's parallax in longitude, her apparent 

 latitude, and apparent diameter. 



Fig. 7- After this, assuming on any straight line, as ab, the point c for the 

 sun, from it lay down, for the 3 points of the ecliptic for which the preceding 

 computations were made, the 3 distances cd, ce, cf, which shall be the mea- 

 sures in seconds, taken from a scale of equal parts sufficiently large, of the dis- 

 tances of the moon from the sun in each, compounded with their respective 

 parallaxes in longitude, so as to represent the respective apparent distances of 

 the moon from the sun in longitude. On these points erect the perpendiculars 

 DG, EH, Fi, for the moon's correspondent apparent latitudes, and describe through 

 these 3 points the arch of a circle, as representing the visible way of the moon 

 from the sun during the eclipse. 



Then if from c the line ck be drawn from the centre of this circle, k will be 

 the place of the moon at the greatest obscuration. The best method for assign- 

 ing this point k is to describe the arch of a circle with the centre c and any in- 

 terval by which it may cut the arch ghi, as in n and o ; for the point k bisects 

 the intercepted arch nko. Again, if cl, cm be applied from c to the arch ihg, 

 each equal to the sum of the semidiameter of the sun, and apparent semidia- 

 meter of the moon, l will be the place of the moon s centre at the beginning, 

 and M the same at the end of the eclipse. 



In the last place, for finding the time, when the moon shall be in each of the 

 points L, K, Mj measure the chords of the arches kg, hl, hm, hi, as not sen- 



