The scales of commerce and trade: ballancing betwixt the buyer and seller, artificer and manufacture, debitor and creditor, the most general questions, artificiall rules, and usefull conclusions incident to traffique: comprehended in two books. The first states the ponderates to equity and custome, all usuall rules, legall bargains and contracts, in wholesale ot [sic] retaile, with factorage, returnes, and exchanges of forraign coyn, of interest-money, both simple and compounded, with solutions from naturall and artificiall arithmetick. The second book treats of geometricall problems and arithmeticall solutions, in dimensions of lines, superficies and bodies, both solid and concave, viz. land, wainscot, hangings, board, timber, stone, gaging of casks, military propositions, merchants accounts by debitor and creditor; architectonice, or the art of building. / By Thomas Willsford Gent.

An ocular Demonstration in measuring of all tapering timber, whether round or square.

[illustration] diagram

The Pyramidal Segment here proposed for to be measured is A. whose length is 15 feet, the square at the greater basis is 9, and the lesser end 1 foot, as at A, and according to the last Probleme the mean square 3, the summe is 13, which multiply by ••/•• part of the length in this by 5, there will be produced 65 feet, the true solid content required;

which to prove, take the Segment A into pieces as B C and D, there would be 9 of them, and all of one length, but severall forms, viz. B a foot square taken from the middle of the Segment, then will there be 4 pieces like wedges a foot square at the base, and ending in a line at A, having no thick∣ness, as the four corner pieces are perfect Pyra∣mids, containing one foot square at the base, the other ending in a point, as D, each of whose di∣mensions, according to the last Probleme, must be 5 cubicall feet, being the length is 15, and con∣sequently 4 of these will contain 20 feet, and as for C, 2 such pieces turned end for end, will be equall to the figure B, containing 15 feet; then one of them is 7 ½ feet, and 4 of those will make 30, the totall of the 9 pieces in content is 65 cubical feet, equall as they are all together in the figure A, which is evidently proved, as was re∣quired.

But this Segment (according to common practise) is measur'd in the middle) by taking the Arithmeticall mean, that is by adding the sides of the two squares together, and taking the half of that for the common square, as in this, 1 and 3 makes 4, the half 2, whose square 4 multiplied into the length, 15, the product will be 60 feet, for the content, according to custome, which is apparently erroneous, and 5 feet too little in this piece, as before was demonstrated; divers other errours (in measuring of solid bodies) are crept in for want of Art, and having got possession of igno∣rant people, they plead prescription and custome

of the place, whereas Custome cannot establish a Law upon a bad Title, and a false ground nor Er∣rour prevail against Truth, nor Ignorance convince Reason, supported by Art upon Demonstration; but leaving the rough-hewn and cross-grain'd people to their own imaginations, although them∣selves confess a profit by some trees, and a disad∣vantage by others, but know not from whence, as in flat timber, which some call ill weighed; as for Cants, and multiangled figures, their bases may be measured by triangles according to the first Pro∣bleme of this Section: which found, their con∣tents will be discovered by some one species in the dimension of the 5 former figures, according to the precepts of Art. Yet I would not have any man for to exact upon the buyer, but wish him some advantage or allowance in every load of green timber, as in every 40 or 50 cubicall feet; and my reason is, because no green timber will hold measure when the bark is taken off, and some trees will shrink more then others, as I have found by experience, in a moneths time 2 feet in a load and more.

Here I have briefly delivered you the man∣ner and custome in measuring most kindes of solid bodies, whereby to understand what you doe, yet such exactnesse is not alwayes requi∣site in rough timber, especially where there is much to be measured, and therein to avoid confusion, mark the trees as you measure them with 1, 2, 3, &c. and enter them in a book with the year and day of the moneth, the owners

name, and the field or wood wherein they grow: this done, make 4 columns, one for the number of trees, secondly for their lengths, in the third co∣lumn their squares, and in the last their contents; by this means any tree will be quickly found, and if any mistake be you may correct it at your leisure; observing this course many abuses will be avoyded betwixt the buyer and seller, as in cutting any tree shorter, or altering their marks, &c. and will be ready for your own justification: and besides, it is necessary in some place of your book to enter the buyers name, with the conditions agreed upon for the price by the foot or load, with articles for mea∣suring, as in girting any tree more then once, and whether in the buyers or the sellers choice so to do, also what allowance to be abated for bark, as in Elmes, Ashes, &c. and sometimes in Oaks the bark will not run; besides a limited time should be agreed upon how long after the fell the trees must be measured, and the ground cleared; such things as these do often make cavils, when not a∣greed upon before; below the middle of any tree the buyer may girt it where he pleases, and this is general, divers other particular things there are for which I refer you to practise, and how the common Ruler is made for measuring of timber, observe this following Proposition.