ing in an equal probability to win; by this means I have two Chances to get 3 Shillings, four Chances to get 5 Shillings, and one Chance to get 9 Shillings, viz. when I win myfelf; for then out of the Stake, which makes 35 Shillings, I must give the firft two 6 Shillings, and the 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 call'd Hazard, what Mains are best to set 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

V against VII, 3 of the Stake.

VI against VII, of the Stake.

IV against VI,

V against VI, of the Stake.

IV against V,

of the Stake.

of the Stake.

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

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

By

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; fix Chances for, viz. those of IV, X; eight Chances for 3, viz. thofe 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 × 3+ 8 × 3 + 10 X TT

36

Now to fave the Trouble of a tedious Reduction, suppose the Stake which they play for be 36, that is, the Setter had laid down 18; in that Cafe, every one of these Fractions are fo many Parts of an Unit, which being gather'd into 17 to the Cafter, leaving 18 fo the Hazard of the Cafter is to 244,251.

one Sum, give to the Setter; that of the Setter

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.

220

5x0+6x1+x 63+ 8 ×$ + 5× 1+6× √19 = 1733%, leaving to the Setter 18167; fo the Hazard of the Cafter is to that of the Setter as 6961 to 7295.

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

6×0+4×1 +6 ×3 + 4 ×1⁄2 +10×8+6×3=17338,

86

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 fet on that VII, becaufe, in this laft Caft, the Setter has but 18 and 3, or; whereas, when V or IX is the Main, he has 18; likewife VI, or VIII, are better Mains than V, or IX, beeaufe is a greater Fraction than

86

All those 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 quota vice quivis fufci pere poteft, ut datum quodvis planum, v. g. ab jaciat.

THE

LONGITUDE

EX.A MIND.

A Short Epiftle to the Longitudinarians.

Gentlemen,

HE Books that are written about the Longi

tude, are fo acceptable to the Publick, that the whole Edition is commonly fold off, before any of them can reach our Northern Bookfellers; therefore I hope you will not refuse to admit me into your Number, tho' my Attempt is publish'd fo late; neither will you look upon me as your Enemy, if I overthrow all your Schemes, to fet up mine; for, if you'll believe me, I am in perfect Charity with you all: But Custom will prevail, and then I must fhew 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; tho' the main Reafon is, that, without Animadverfions upon the Attempts of others, I could not fwell this to a Six-penny Book, unless I had embellifi'd 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 Conftitutions. But I never had the Knack of Speaking

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 Capi tals, and then have humbly fubmitted my Eflay, and fubfcrib'd myself their devoted and obedient Ser vant 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 fill'd the next Sheet; and the Devil is in't if I could not have made fixteen Pages of my Movement; and fo, by the Help of FINIS and ERRATA, compleated my three Sheets. But then I confider'd, (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 of which I fhall, at my Return, lay before the Commiffioners, and fo carry off the twenty Thoufand Pounds. As for the Introduction, I fhould 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 ftand or fall. If it be afk'd, why I wrote the Book at all, I'll frankly anfwer, That I wanted Money; and that if I had thought that the Commiffioners 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 shan't say a Word about my New Inven tion, 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 shan't begin a Paragraph with the Defcription of my Curiofities, or write the Names of any of my Machines in Italick Characters. All that