VOL. LVII.] PHILOSOPHICAL TRANSACTIONS. 379 



the circumference of the circle cd/g, in the points e and f; draw the line sv, 

 and it will.be the axis of the shadow, and consequently will pass through c and 

 M, the centres of Jupiter and the section of the shadow; join om, /;m, fc, ec, 

 and the triangles abM, efc will be similar to each other, and therefore, aZ)M be- 

 ing wholly given, fee will likewise be known. Let adbg be the elliptic section 

 of Jupiter's body, and produce ew/both ways, till it meets the periphery of the 

 ellipsis in the points e and f; draw kf, Ae, and produce them till they meet with 

 ab, produced both ways, in n and n ; then will sn be the required duration of 

 the eclipse in the true shadow: now the triangles k/f, kan being similar, as are 

 also the triangles Ace, hbn, and the segments vf, eE being given, by the preced- 

 ing proposition, the required segments Ncr, bn will also become known, for they 

 will be to the former segments in the given ratio of sm to sc. 



It may be observed, that this method is equally applicable, whether the axis of 

 Jupiter is perpendicular to his orbit, or not; for if it is not, we can easily find, 

 by prop. 1 and 1, the sj)ecies and position of that elliptic section of Jupiter's 

 body, to which a right line connecting the centres of the sun and Jupiter is per- 

 pendicular; and this being obtained, every thing else will remain as before. 



As it would require more time than Mr. W. had to spare, to enter into a par- 

 ticular inquiry concerning the alterations, which this irregularity in the shadow 

 will occasion, in the present theory of Jupiter's satellites, he concludes with ob- 

 serving, that the errors in the semidurations of their eclipses, arising from this 

 cause, may sometimes amount to 20'' in the first; 50* in the second; 2*" 10» in 

 the third; and 1 1™ 14' in the fourth; which errors he deems sufficiently large to 

 merit the attention of astronomers. 



IF^. An Attempt to Account for the Universal Deluge. By Edward Kiw 

 Esq., of Lincoln s Inn, F. R. S. p. 44. 



Dr. Burnet, in his theory, has given such an account of the deluge, as Dr. 

 Keill has shown to be very improbable, and unphilosophical. He has first de- 

 scribed the primaeval earth so as to divest it of all beauty and elegance, and then 

 has ascribed the deluge to such causes, as are not only somewhat inconsistent 

 with that part of his theory where he supposes the earth to be well watered and 

 moistened with dew ; but are also insufficient to account for the waters flowing 

 over the tops of the mountains : since, on the breaking of his imaginary shell, 

 it is imjx)ssible to suppose that the waters of the abyss, even on such a concussion, 

 should flow up high enough on those parts that were left elevated, so as to cover 

 the mountains that now subsist. Mr. Whiston has called in the assistance of 

 another planetary body ; and has supposed the tail of a comet to be so greatly 

 condensed, as to afford a quantity of water sufiicient for this purpose. But, be- 

 sides the inconsistency of this theory with that of gravitation, it is no less dif- 



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