other Four 20 Shillings, fo there remains juft 9 to myself.

It is eafy by the Help of this Theorem, to calculate in the Game of Dice, commonly called Hazard, what Mains are beft to fet on, and who has the Advantage, the Cafter or Setter. The Scheme of the Game, as I take it, is thus:

By an eafy Calculation you will find, if the Cafter has IV, and the Setter VII, there is due to the Cafter of the Stake; if he has

I need not tell the Reader, that IV is the fame with X, V with IX, and VI with VIII.

Suppofe then VII be the Main: To find the Proportion of the Hazard of the Cafter to that of the Setter.

By the Law of the Game, the Cafter, before he throws next, has Four Chances for nothing, viz. thefe II, III, XII; Eight Chances for the whole Stake, viz. thofe of VII, XI; Six Chances for, viz. those of IV, X; Eight Chances for 3, viz. those of V, IX; and Ten Chances for, viz. thofe of VI, VIII; fo his Hazard, by the preceding Theorem, is

4×0+8×1+6×}+8×}+10 × 1

36

Now to fave the Trouble of a tedious Reduction, fuppofe the Stake which they play for be 36, that is, the Setter had laid down 18; in that Cafe, every One of thefe Fractions are fo many Parts of an Unit, which being gathered into One Sum, give 174 to the Cafter, leaving 18 to the Setter; fo the Hazar d of the Caf ter is to that of the Setter 244, to 251.

55

Suppofe VI, or VIII, be the Main, then the Share of the Cafter is.

II.

III. VI. IV V.

XI. XII. X. IX. VIII. VII.

5×0+6x1+x63+8×÷+5×1+6×1=17328

39

leaving to the Setter 18167; fo the Hazard of the Cafter is to that of the Setter as 6961 to 7295.

Suppose V, or IX, be the Main, then the Share of the Cafter is

6×0+4×1+6×3+4×÷+10×3+6×3=17338

leaving to the Setter; fo the Hazard of the Cafter is to that of the Setter as 1396 to 1439.

It is plain, that in every Cafe the Cafter has the Difadvantage, and that V, or IX, are better Mains to to fet on than VII. because on this laft Caft, the Setter

N 3

has

has but 18 and 14. 84

559

or ; whereas, when V or IX

330

is the Main, he has 1886 likewife VI, or VIII, are

315;

better Mains than V, or IX, because 167 is a greater Fraction than 86

315

396

All thofe Problems fuppofe Chances, which are in an equal Probability to happen; if it fhould be fuppofed otherwife, there will arife Variety of Cafes of a quite different Nature, which, perhaps, it were not unpleasant to confider: I fhall add one Problem of that Kind, leaving the Solution to those who think it merits their Pains.

In Parallelipipedo cujus latera funt ad invicem in ratione a, b, c : Invenire quotâ vice quivis fufcipere poteft, ut datum quodvis planum, v. g. a b jaciat.

THE

THE

LONGITUDE

EX A MINE D..

A Short Epiftle to the Longitudinarians.

Gentlemen,

THE Books that are written about the Longitude

are fo acceptable to the Public, that the whole Edition is commonly fold off before any of them can reach our Northern Bookfellers; therefore I hope you will not refufe to admit me into your Number, though my Attempt is publifbed fo late; neither will you look upon me as your Enemy, if I overthrow all your Schemes to fet up mine; for, if you will believe me, I am in perfect Charity with you all: But Cuftom will prevail, and then I must fbew what I can do in the Beginning of my Book, that my Readers may enter upon the Defcription of my Engine with a good Opinion of my Skill; though the main Reafon is, that without Animadverfions upon the Attempts of others, I could not fwell this to a Six-penny Book, unlefs I had embellished the Recommendation of my Device with fine Metaphors, and clever Comparisons; quoting the Scripture in one Place, and the Poets in another; or filling up Voids with Paffages taken out of the Apoftolical

N 4

ftolical Conftitutions. But I never had the Knack of Speaking much, when I had but little to fay. I might, indeed, with the Printer's good Management, have made Four Pages of the Commiffioners Names in Capitals, and then have humbly fubmitted my Essay, and fubfcribed myself their devoted and obedient Servant in two Pages more; which, with the Copy of the Act of Parliament, and Title-Page, would have made up One Sheet: An Introduction of Aftronomical, Geographical, and Mechanical Definitions, to fhew that I was Somebody, might have filled the next Sheet; and the Devil is in it if I could not have made Sixteen Pages of my Movement; and fo by the Help of FINIS and ERRATA completed my Three Sheets. But then I confidered (fince I am fure of being right) that it was my best Way to go to Sea firft, and give the Mariners fuch ocular Demonftration of my Contrivance, that I shall have a fufficient Number of Witneffes of my Success, to vouch the Account which I fhall, at my Return, lay before the Commissioners, and fo carry off the Twenty thousand Pounds. As for the Introduction, I should have thought it very ill Manners to begin my Book, as if I meant to teach First Principles to thofe learned Philofophers by whom I am to stand or fall. If it be asked why I wrote the Book at all, I will frankly anfwer, That I wanted Money; and that if I had thought that the Commissioners would have been prevailed upon to have given me fome to carry on Experiments, I had never fet Pen to Paper. For this very Reafon I fhall not fay a Word about my New Inventon, till its proper Place. And if the Bookfeller does not cut open the Sheets, whoever has a Mind to know what I drive at, must buy the Book: Peeping in won't do; for I ball not begin a Paragraph with the Description of my Curiofities, or write the Names of any of my Machines in Italic Characters. All that I shall fay here, is, That I have tried all my Experiments at

Land