of Purala in a Soc * Eclipse 17B १ oclipse more than the middle, nuld the middle more than the close: to the west of that 8ame point, on the other hand, it depresses the moon's disk away from the Sun's, but by an armount constantly increasing, 8o that it retirds the end of the elipse nmore than its middle, and its middle more than its beginning 'he cfoct of the parallax in longitude, then, upon each holf-duration of the eclipse, will be measureft by the difference between its retarting and accelerating efects upon contact १nd conjunction, and upon conjunction १nd separation, respective und the nnount of this difference will always be additive to the time of half-duration as otherwise determined . If, howevor, contact and conjunction, or conjunction and separation, take place upon opposite side of the point of no paralia in longitudethen the sum of the two parallacio effects, inst:nd of their difference, will be to be addea to the corresponding half-duration : since the one, on the east, will hasten the occurrence of the former phase, while the other, on the west, wil after the tecurr:ne of the latter phase. The amount of the parollnx in longitude for the middle of the eclipse has already been found; if, Tow, we farther determine its amountf-reckoned, it will be remembered, always in inme--for the moments of contact and separation, and add the difference or the sum of each of these and the paralax for the moment of conjunction to the corresponding half-duration as proviously determined, we shall have the true times of half-auratio. In order to find the prollax for contact and separation, we Zeneath the same process (see above, v, p3) by which that for cornjunction was found s we then started from the mornenk of true conjunction, and. by a gories of successive approximations, ascertained the time when the differonec of longitude would equal the paral]ax in longitude, so now we star frch to momen f6f nomoved from that of true conjunction by the equivalents in time of the two distances in longitude obtained by bhe last process, and, by a similar series of successive approximations, ascer tain the times when the differences of longitude, togethe: with the parallax, will equal those distances in longitude. In the process, as thus conducted, there is an evident inaccuracy. It is not enough to npply the whole correction for parallax in latitude, and then that for parallex in longitude, since, by reason of the change effected by the latter in the times of conduct and sepa¥ntion, a new calculation of the former becomes neesary, and them again a new enlculation of the latter, and so onuntilby series of doubly compounded approximations, . . a the true value of each is determined. This was doubtless known to the framers of the system , but passed over by them, on account of the excessive , ly laborious chazacter of the complete calculation, and beenuse the accuracy of such results as they could obtain was not sensibly affected by its negleet. The question naturally arisok, why the specifications of verse Is are made hypothetical instead of positive, and why, in the latter half of verse 16, a case is supposed which never arises. The commentator anticipakes the objection, and bakes much pains to remove it: it is not worth while to
