VOL. XXII.]] PHILOSOPHICAL TRANSACTIONS. 505 



The equinoxes of this year, iGgg, according to the author's observations, 

 happened as follows: March gd. 20h. 35m. 27s. Sept. ]2d. JOh. 22m. 42s. 

 but by the author's tables, 9 20 40 30 12 10 32 52. 



Besides this observation, we have two others of very eminent men, viz. of 

 M. Godfred Tuber, Archdeacon of Ciza, and of M. Jacob Honold, pastor in 

 the village of Hervelsing, in the diocese of Ulm. The former was observed 

 at Ciza, the latter at Hervelsing near Ulm of Suevia. The former began at 

 9 o'clock, and ended at 1 ih. 35m. and increased to 1 ] digits. The latter began 

 at 8h. 55m. and ended at 1 ih. 31m. and its greatest defect was 10 digits. 



At Leipsic the moon was observed to enter the disc of the sun at gh. 1 Im. 

 (by the times corrected by altitudes taken of the sun) and to end at 12h. 3Sm. 

 30s. The greatest obscurity was 11,20 digits. It lasted from lOh. 1 6m. 45s. 

 for 6', 10 digits being obscured. 



The Dimension of the Solids generated by the Conversion of Hippocrates' s Lunula, 

 and of its Parts, about several Axes ; with the Surfaces generated by that Con- 

 version. By Ab. De Moivre, F. R. S. N° 265, p. 624. 

 Let BCA, fig. 15, pi. 12, be an isosceles triangle, right-angled at c. With 

 the centre c, and distance cb, describe the quadrant bfa ; on ba, as a diameter, 

 describe a semicircle bka ; the space comprehended between the quadrantal 

 arc BFA and the semicircumference bka, is called Hippocrates's lunula. 



If upon BC you take any two points d, e, and draw the perpendiculars dh, em, 

 meeting ba in i and l, and cutting off a portion fgmh of the lunula ; the solid 

 generated by the conversion of this portion about the axis bc, is equal to a prism 

 whose base is ilmh, and height the circumference of a circle whose diameter is 

 BC ; and the solid generated by the semicircle bka, is equal to a prism or semi- 

 cylinder, whose base is the semicircle bka, and height the circumference of a 

 circle whose diameter is bc. 



Having bisected ba in r, and bc in p, the surface generated by the conver- 

 sion of the arc hm about the axis bc, is equal to ; X bp X hm -\- bk X de, 

 supposing the ratio of the radius to the circumference to be as r to c ; and the 

 surface generated by the semicircumference bka is equal to a rectangle whose 

 base is the sum of that semicircumference and diameter ba, and height the cir- 

 cumference of a circle whose diameter is bc. As for the surface generated by 

 the arc gf, it is well known, that it is equal to a rectangle whose base is the 

 circumference of a circle whose radius is bc, and height de ; therefore the 

 surface generated by the conversion of the portion mhfg is known. 



If upon ba, fig. 16, you take any two points i, l, and draw in, lv, perpen- 

 dicular to it, cutting the quadrant in o and t, and the circumference in n and 

 VOL. IV. 3 T 



