The Horizontal Parallax of the Moon, when she is in the Syzygys, at a mean distance from the Earth, I make to be 57 minutes, 30 seconds; and her Horary Motion, 33 minutes, 32 seconds, 32 thirds; and her apparent Diameter 31 minutes, 30 seconds. But in her Quadratures at a mean Distance from the Earth, I make the Horizontal Parallax of the Moon to be 59 minutes, 40 seconds, her Horary Motion 32 minutes, 12 seconds, 2 thirds, and her apparent Diameter, 31 minutes, 3 seconds. The Moon in an Octant to the Sun, and at a mean distance, hath her Centre distant from the Centre of the Earth about 602⁄9 of the Earth's Semi-diameters.
The Sun's Horizontal Parallax I make to be 10 seconds, and its apparent Diameter at a mean distance from the Earth, I make 32 minutes, 15 seconds.
The Atmosphere of the Earth, by dispersing and refracting the Sun's Light, casts a Shadow, as if it were an Opake Body, at least to the height of 40 or 50 Geographical Miles (by a Geographical Mile, I mean the sixtieth part of a Degree of a great Circle, on the Earth's Surface.) This Shadow falling upon the Moon in a Lunar Eclipse, makes the Earth's Shadow be the larger or broader. And to each Mile of the Earth's Atmosphere, is correspondent a Second in the Moon's Disk, so that the Semi-diameter of the Earth's shadow projected upon the Disk of the Moon, is to be increased about 50 seconds: Or, which is all one, in a Lunar Eclipse, the Horizontal Parallax of the Moon is to be increased in the Ratio of about 70 to 69.
Thus far the Theory of this Incomparable Mathematician. And if we had many Places of the Moon accurately observ'd, especially about her Quadratures, and these well compar'd with her Places, at the same time calculated according to this Theory; it would then appear, whether there yet remain any other sensible Equations; which when accounted for, might serve to improve and enlarge this Theory.
Plate 3. pag. 280.
An Estimate of the Degrees of the Mortality of Mankind, drawn from curious Tables of the Births and Funerals at the City of Breslaw; with an Attempt to ascertain the Price of Annuities upon Lives. By Mr. E. Halley, R. S. S.
THE Contemplation of the Mortality of Mankind, has besides the Moral, its Physical and Political Uses, both which have been some Years since most judiciously consider'd by the Curious Sir William Petty, in his Natural and Political Observations on the Bills of Mortality of London, own'd by Captain John Graunt: And since in a like Treatise on the Bills of Mortality of Dublin. But the Deduction from those Bills of Mortality seemed even to their Authors to be defective: First, In that the Number of the People was wanting. Secondly, That the Ages of the People dying was not to be had. And Lastly, That both London and Dublin, by reason of the great and casual Accession of Strangers who die therein, (as appeared in both, by the great Excess of the Funerals above the Births) rendred them incapable of being Standards for this purpose; which requires, if it were possible, that the People we treat of, should not at all be changed, but die where they were born, without any adventitious Increase from Abroad, or Decay by Migration elsewhere.
This Defect seems in a great measure to be satisfied by the late curious Tables of the Bills of Mortality at the City of Breslaw, lately communicated to this Honourable Society by Mr. Justell, wherein both the Ages and Sexes of all that die, are Monthly delivered, and compared with the number of the Births, for Five Years last past, viz. 1687, 88, 89, 90, 91, seeming to be done with all the Exactness and Sincerity possible.