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. _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. [Illustration: _Plate 3. pag. 280._] 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.