A book called the Treasure for travelers, divided into five books or parts, containing very necessary matters, for all sorts of travailers, either by Sea or by land, written by William Bourne. ¶ Imprinted at London for Thomas woodcock, dwelling in Paul's churchyard, at the sign of the black bear. 1578. VIRTUS IN ACTA ¶ To the Right worshipful Sir William Winter Knight, master of the Queen's majesties ordinance by Sea, Suruaior of her highness marine causes. etc. William Bourne wisheth increase of worship unto the state of honour and true felicity. WHat great commodity and profit Right worthy & worshipful Knight, hath always redownded unto the common weal, and govern ours of the same, which in martial affairs and warlike discipline, have chiefly delighted and taken great pains and care in the same, and unto what excellent fame and renown it hath always brought and exalted unto high dignity, those that have taken upon them, for their Prince and country's prosperity great exploits, rather putting themselves in danger of their lives, than their Prince and Country should be dishonoured. Then I may say without any objection or doubt, that your worship is one: For I myself can witness, and of my own knowledge, know, that no person in this Land hath such great judgement and knowledge in martial affairs by Sea, both touching the shipping, for that purpose, and also the provision for the same, as your worship hath: and as for your courage, valiantness, and wisdom, which is not unknown unto the world, whereas I being most simple have written this base and rude volume, which I do call a Treasure for travailers, am so bold to dedicate it unto your worship, not for that the book is worthy to be preferred unto so worthy a person, but for my bounden duties sake, to acknowledge my good will towards your worship, for that I have most largely tasted of your benevolence towards me, being as a poor Gunner, serving under your worthiness, hoping that your worship will take this simple work in good part: the which work is divided into five books, the first is geometry perspective, the second book is appertaining unto cosmography, the third book is geometry general, the fourth book is Statick, and the fifth and last book is appertaining unto natural philosophy, as the contents of the matter do appear in the Tables of the books, hoping that your worship will take this simple thing, as a true token of my good will towards you, although the thing itself be but rude & simple. And thus, I cease to trouble your worship any longer, at this time, beseeching the living God to prosper you in all your affairs, in perfect health, with all your children and family, Amen. By your worships at commandment, William Bourne. The Preface to the Reader. Considering with myself, gentle Reader, with how infinite pains and labour, divers heretofore, men of most excellent wits, and of passing knowledge, have compiled their books, and with what heed and circumspectness they have examined and perused their travails, and with what fear and wariness they have published the same. and not without good cause why, for thereby they have opened themselves, their name, and fame, to no small dangers and harzardes: namely to the view, judgement, and report of all men. For which cause, now seeing I have taken upon me at this time a hard enterprise, a burden too heavy for me to bear or sustain, who have at length showed myself so hardly, as to publish this little Treatise, I being altogether unlearned, and having no help of any other learned persons, being of myself altogether destitute both of knowledge and learning. Wherefore I desire thee, gentle Reader, to bear with my rudeness, and consider that it is the good will which I bear unto my native country, for to profit the common wealth, as much as lieth in me, although that it be not learned like, yet I pray thee hold me excused, being altogether ignorant, lacking the capacity both of knowledge and eperience (who having taken upon me) to publish this to the scanning and trying of so many touchestones, and dangerous crimes, that I being so simple, should enterprise so far to take upon me to open any Science. But notwithstanding, I do see, that it is so needful a matter to be known unto a number of persons, that do desire for to have instructions in those causes that are contained in this simple volume, the which book I do call A Treasure unto travailers, and is divided into five books. The first book. And the first book containeth the particular conclusions of the Skall Quardrant or astrolabe, and in the like manner the particular conclusion of the cross staff etc. Also the use of the horizontal or flat Sphere, whereby to draw or take the plat of any country. etc. The second book. The second book doth show unto you, if that you do know the Longitude and the Latitude of any place truly, then how to know the distance in miles from you, or any place assigned, and by what point of the compass that it is from you. And because that London is the most famous and the most principal place here in England, I have have named certain principal places here in Europe, and also in Africa, and in Asia, and also in America, with some of the principallest islands in the world, both their Longitude and Latitude, and their distance from the city of London, and by what point of the compass that it is from London, and also how much that the moon doth change rather or later, than it doth at the city of London, and what length their longest day is of. etc. The third book. The third book is as touching the measuring of Superficials and solid bodies, and how to augment them, or diminish them, unto what proportion or bigness you list, whether that it be the tonnage of any ship, or the bigness of any kaske. etc. The fourth book. The fourth book is as touching the Art Statical, as to know the weight of any ship swimming on the water, and such other like. etc. The fifth book. The fifth or the last book is as touching the natural causes of sand and rocks in the Sea, and divers such other like causes, as it doth appear in the table of the contents, of the books. etc. The which things, in my opinion, are very necessary for all manner of persons, and especially unto such as be travailers: which causeth me to give the book unto name, A Treasure unto travailers. For what thing can there be more better unto a travailer, either by Sea or by land, (gold & silver only excepted then to know the distances from place to place, and to have capacity to know the height and the lownes of any thing, & how to make a Plat or card for any country. etc. which is declared in the first book. And also how necessary a thing it is for a travailer to know unto what quarter of the world any place doth bear from him, & what the distance is thither, Geometric perspective. & what length the day is of, when he is there: as I have known a great number of persons that have travailed unto sundry places, & when they have come home, they have had no judgement at all, as touching that place that they have travailed unto, for that they have not known unto what quarter of the world the place is, that they have been at: neither in respect what the distance is thither. And these matters are showed in the second book. And also it is not hurtful, Cosmographia. but necessary for a travailer to know how to measure all manner of Superficalles, as land, pavements, board, and glass, and solid bodies, as timber and Stone, and the burden or tonnage of ships, and the bigness of any thing. And furthermore it is necessary for a travailer in like manner, Geometric general. to have a way to get the true weight of any thing that swimmerh on the water, & in like manner to know the weight of any thing that sinketh into the water, & what it weigheth in the water, to be lifted from the bottom unto the superficial part of the water, as it is declared in the fourth book. And furthermore, it is very necessary & convenient for travailers either by Sea or by land, Staticke. to have knowledge in the natural causes of sundry things that are to be seen in travailing, as the cause of sands & banks, as well in rivers as in the sea, Natural philosophy. and the cause of Marish ground and meadows, & the cause of cliffs on the sides of rivers, & on the sea coast, with such other like matters, as is declared in the fifth and last book. And now it is possible, that some persons will marvel, that I being so simple, and not learned, should take upon me to be a meddler in these causes, for that they be matters that do appertain unto learned men. And it is possible, that it will be dislyked of a number of people, as envy dwelleth generally in the hearts of most men, for that is the property of many people, to dislike all things that are not done by themselves, using to read books to no other end, but to find faults in them. Discouragement. And yet it is possible, that they will do nothing themselves, which were a cause of discouraging unto any person that doth write: yet notwithstanding it shall not discourage me, for that I am utterly unlearned, and therefore it shall not dislike me, if any learned man doth find any fault therein: for I being simple and unlearned, it is no discredit for me, either to be taught, or to have the faults showed unto me. For by that means I may reform the faults, either by them, or myself. And furthermore, I do not intend to make any book to teach them that are cunning & learned: But the only cause of my writing of this book is, to instruct or teach them that are simple and unlearned: And therefore notwithstanding, I shall the better like of it, Books are written to the intent to teach the unlearned. if any learned man should write or set out any book, as touching these causes, to reform this. And my opinion is this, if that any book be set forth unto the common people in the world, that then it is to the end, to teach the simplest sort of people that are not instructed in learned causes. But if that it be any high point in learned causes, than it is not for the common sort of people, but to be in learned men's Libraries, and therefore as it is not written by a learned man, so in like manner you must not look for fine or eloquent school terms, but even to take the substance of the matter rudely as it is, and more to regard the necessariness of the matter, whether it may do any good in the common wealth. etc. And yet notwithstanding my opinion is this, that no person is to be disliked of, that doth his good will and endeavour, No person is to be disliked that doth his good will to do good. to do good in the common wealth, howsoever that it proveth. But those persons are utterly to be dyslyked of, that do hurt willingly in the common wealth, as extortioners and usurers, and conuayers of corn and victuals, and other necessaries and commodities that his country doth lack or hath need of. And all those persons are not to be thought well of, Persons that are to be dislyked. that do desire to live easily, abusing the good benefits that God doth bless the earth with: as all licentious livers, as drunkards, banketters, whores, and whooremaysters, and such as do use an excess in apparel, much above their degree. And also those people are to be abhorred of all men, who do annoy the earth, that use quarrelling and fighting, robbing and stealing, caring not how they come by it, so that they may have it, with which this our country of England floweth at this day, (the more is the pity) for what wickedness is there that can be devised, but that it is used here in England amongst all degrees, which must needs procure the wrath of God to light upon us. And there is as great abuse amongst the clergy, which should be as lanterns to give us light, to lead us unto virtue. Abuses of England. But now in these days they be as lanterns to lead us unto vice. So that all degrees of people are given unto wickedness, although that we have the Gospel of Jesus Christ, preached daily unto us, yet wickedness doth abound, for what sin or wickedness is there, but that it is suffered and used, as witchcraft and sorcery, and magical enchantment, and coungering, which is the greatest and most abominable dishonouring of God, that may be. For in their magical enchantment and coungering, Magical enchantment is a great dishonouring of God. do they not observe hours in the making of Carecters, & set up pickturs of the rood, and Agnus Dei, and the doom, and a number of such other pickturs, painted, and gilded upon Virgin Parchment, as they call it. And then in like manner their cirkles must be perfumed, & inbalmed with sweet odours, and they must have a knave priest, made by the Pope's law, to hallow a certain portion, with a number of such vain Ceremonies. And when that they have the devil, whom they do serve, & do give him in some cases some thing for a sacrifice, and when that they do give the devil a charge to tell them any question that they would know, then are used a number of superstitious words, as in the name of the virginity of the Virgin Mary, and the head of John Baptist, and a number of vain saints more, besides a number of such detestable Ceremonies, to the great dishonouring of God. etc. And who is the cause and the procurement of these most odious and detestable matters, but a number of vain, & wicked people, yea some of them be of no small wealth nor calling, that do procure these matters: For if that they have lost any thing, them they must repair unto a conjuror, to know where that is again. And furthermore, there are some vain & foolish Gentlemen, which seek to live pleasantly and idly, that must live by gaming and play, and he must have a familiar in a ring, What manner of christian is he that desireth to be familiar with the devil. or such other like place. But what manner of Christian do you think him to be, that desireth to be familiar with the devil? So that a great number of people that are in the world, desire to live idly and pleasantly, caring not, so that they have their pleasure here, although their soul go unto hell, and there to be tormented in fire & Brimstone ever world without end. Wherefore God turn the hearts of those that are the cause of wickedness, and especially here in our native country, & realm of England, for that we have a most gracious and virtuous Queen reigning over us, and such a one as doth always study for the setting forth of the word of God and sacred Gospel of Jesus Christ, The virtuousness of the Queen's majesty is our preservation. and doth always study for peace & tranquillity. And considering the great wickedness that is used in England, the wrath of God would have lighted upon us long before this time, but only for the grace & virtuousness of the Queen's miaesty, that God hath spared us for her sake. Therefore let us all prey unto God for her long life and prosperity, that she may reign long over us. For surely my opinion is this, except we do repent and turn from our wickedness, the wrath of God will light upon us. For in these days every man is but for himself, the elder sort of people are given generally all unto excessive & huge covetousness, and the younger sort of people are given generally unto pride and whoredom, and other vain toys, The abuses of all degrees. as idleness and gaming, so that in respect few or none have the fear of God before their eyes. And if any persons do frame themselves to live virtuously, according unto the law of God, than they shallbe but derided both of the elder sort, & also of the younger: for the covetous rich persons will say, he is a fool, he can not make shift to live, he hath too precise a conscience: and the youngest, vain glorious proud fools, will say, He is a scriptured man, he will not have us to be meery nor go cleanly. Covetousness is called good husbandry. So that in these days, extortion & covetousness is called good husbandry: and the one of them will commend the other, saying, He is a wise fellow, he will live, how fraudulently soever he come by his goods. So what wickedness soever that it be, Pride is cleanliness, swearing lustiness, drunkenness, good fellowship. Whoredom, friendship 〈◊〉 a trick of youth. the same shallbe commended by them that use the like: as pride in these days is called cleanliness, and swearing lustiness, saying, he is a lusty fellow, and drunkenness, good fellowship, and whoredom a trick of youth or friendship, so that the one sort of people do heap up the goods on the earth unsatiably, and the other sort of people, spend it away most vainly and wanton, so that the good gifts or benefits of God, which are the riches of the world, are abused on every side, & not used as they ought to be, that is to say, to do good upon the earth with that, for it was created for the use of man to a good end, to take his portion of it, & the rest to use unto some good purposes at his discretion, for that God doth send it him, unto that end, and not to be heaped up, neither to throw it away wickedly, as a number do: Therefore men do not rightly consider, wherefore they were borne upon the face of the earth. The first cause that man is borne for, is to serve God. first he is borne to serve God, for that he hath created him, and all mankind, and hath created him a reasonable creature, and hath created all thing for his use: as first the earth, with all his minerals, as we do dig out of the earth, Gold, silver, and all other metals, and stones, to make us necessaries to serve man's use. And also the face of the earth, he hath created to bring forth Trees to make us Timber, and grass to feed cattle, to make us food and meat: corn to make us bread, with all his other benefits, which man receiveth from the face of the earth. The Sea with all other rivers, bringeth forth Fish of innumerable sorts, to make us food and meat, yea the very Sea is for man's use, too pass from country unto country. The air in like manner, wherein are multitudes of feathered fowls, for man's use, yea the very heavens are for man's use, as the sun, moon, and stars, are created for the use of man. And also he hath redeemed us from the original sin of Adam, by his precious blood sheedding. Wherefore we are first borne too serve God. The second cause that man is borne is to serve his country. And secondly, we are borne to serve our Prince, and native country, that is to say, to defend our territories, that no other ferreine Nations do spoil us of our labours, or our Prince of her dignity. Thirdly man is borne to labour to live And thirdly, we are borne to provide for our household, and our family and to see that they be trained up, to live in the fear of God, and to know their duty to their magistrates, and to train them up unto some faculty, whereby they may get them a living. etc. Wherefore I would wish all those persons, that it hath pleased God to bless upon the face of the earth, with any worldly revenues, or substance and living, to practise some thing, whereby they may do some good upon the face of the earth. And in like manner to train up their children in the nurture and fear of God. etc. Especially the noble men and gentlemen, and they themselves not to desire to live pleasantly and idly, The causes of all degrees. but to practise some virtuous thing, as martial affairs, or such other like causes, as their capacity will serve them. For there were two causes in the beginning of all degrees of the temporalty or laity, whereof all Noble men and Gentlemen had their original and beginning, and they are worthy to be had in honour unto the world's end, for their parentage, and the much the rather, if that they do follow the rule of their noble and worthy progenitors. The first cause was, for their noble acts and deeds in the defending of their Country against their enemies. etc. The first cause. So by that means, for their valiantness against their enemies, they were extolled and advanced unto high dignity, every person according unto his deserts, and had livings to maintain their state, and they to defend their Territories whilst the common people did manure and till the ground. And the second cause in degrees of nobility and gentlemen, The second cause. was to them that made good and wholesome laws for the good government of their common weals. Therefore I would wish all noble men and gentlemen to follow the noble race of their progenitors: and then they are the highlyer to be esteemed. But otherwise, what a shame and discredit, if that they do rightly consider of it, is it for them to be evil members in the common weal: considering how worthily their ancientrie did attain & come unto their calling. Good members in a common weal. therefore I would wish every gentleman, to practise something, that he may do good, either to defend the common weal, or else to profit it some otherway, and not to be idle and to seek to live easily, whereby the common weal may be the better maintained, the Prince the better served, and our country the better furnished, with such persons, as are able to defend the Prince, crown, and dignity, as well in their good counsel, and also in their acts and deeds. And also in my opinion, they are very necessary members in the common weal in divers respects, that are travailers into other Countries, and they are able to profit their own country in divers respects: for that he is able to give judgement by his own country of other, whether it be as touching the government of the common weal, in the executing of their laws of the manner of traffic, and in the usage and nature of the people, both in their Cities and towns, and in their country, and what manner of commodities they have, and of the situation of their towns, and in their fortifycation, and also of what strength and force other Princes and states are of, and of the order and manner of using themselves in martial affairs in the wars, and what their artillery is, and how they are weaponed and armed, and furnished in every respect, which is very necessary to be known unto the nobility, for that they may provide themselves, and their country for their better safety, and also they shall know what thing shall annoy their enemies most. Then it is a plain case, that travailers into other countries do much profit the common weal. For suppose this, that if we, or any Country did live in that order, that we did travail into no place or country, neither no nation unto us, then in process of time we should become barbarous and savage. Therefore the travailers are much to be commended in divers respects. Wherefore I will show you my opinion, what manner of people are meetest to be travailers. For a number of people have travailed, and when they have come home, they have had no judgement of their travail, but have been utterly ignorant of such things as were most meetest of a travailer to be noted, and partly some of them were not capable in those causes, What manner of persons are the meetest to be travailers. and some of them many times, their heads are occupied with other vain and foolish causes. etc. as this first: those people that are able to benefit their country by their travail, when they are come home, ought not to be to young: for commonly a young man his head is occupied with every vain and light cause, as with banqueting, and play, and game, & dancing, and dallying with women, and gazing upon vain toys. etc. So that his head is occupied with no other thing, but all pleasant matters. Therefore he that is sent to be a travailer, What a travailer should consider of. to the end to profit his Country, aught to be a man that hath a stayed & a modest head, and such a one as is capable, and hath a good wit with him, and learned. And if he be seen in the Mathematical Science, it is all the better: For than he shall the sooner conceive any matter. And also he ought not to be either to young nor to old, but between the age of .40. and 56. or 57 years. etc. And these be the principallest points, that a travailer should consider of. First, to consider what manner of Nation he is entered into, whether they be politic or wise, or civil people, or whether they be a rude or barbarous nation: and so in his travailing to frame his usage accordingly as near as he can, that the people may like well of him: for in so doing he should understand the better of the state and commodity of the Country, city, town or place: and when that you do come into any city or town, view of what manner of ground it standeth upon, and what it may be or is subject unto, and in like manner how it is fortified and provided, and how it is maintained, and whether it standeth upon any haven or river, that hath vent unto the Sea, or any water, that hath no vent or passage unto the Sea, but thorough or by some other city or town, before it cometh unto the Sea. And also under whom it is, and how it is governed, and what their laws and ordinances be: And what notable Monuments of buildings there be: and any other rare and notable thing that is not common: And also to learn what nation, Country, city or town that may most annoy them, and also what country, city or town doth most pleasure them, and what trade or merchandise they are principallest maintained by, and what commodities are most plentiest, and what commodities or things necessariest, are most scantest, and what the nature of the soil or ground is thereabouts, that is to say, what the ground is most aptest to bring forth, or most unapt, as touching corn, Trees, and such other like, whatsoever it be. And also what manner of Money and coin is used, both in silver and gold, and other base Money in Copper, if they have any. And also what the people hath most pleasure in, and what they do most abhor or hate, and whether the country be a plain and champion country, or hills and mountains, or low marsh or marish ground, and whether it be full of rivers or not, and also how the Princes or the other governors do levy their soldiers in the time of their wars, & how they do arm them, and weapon them, and furnish them in every respect, and what duties or customs, or tolls, or such like charges are paid, whether it be of themselves, or upon strangers, or any other kind of goods or merchandise, and what thing it is they make most store of, that they will not have pass out of their Countries, with all such other likeness, that for brevity I do omit. And now such persons as have noted these causes at their return home, are able to profit much the common weal in divers respects, and are persons of great valour unto their country, for that they are able to profit the state, and the common weal of their country in divers respects. For all those persons are of great valour and price, and are as special jewels unto their Country, What persons are of valour in the common weal. and in the common weal, that are politic, cunning, and valiant in martial affairs: for thereby their country is defended and preserved from the foreign enemies: For look what Country is rich and wealthy, than other Princes are desirous thereof, for to have the spoils, and the benifyts of it: wherefore by policy and manliness they must be defended. Therefore men expert in marshal affairs are very necessary in a common wealth. And furthermore, all those persons, that are wise and sober, and discreet in the good government of the common weal, such as do maintain virtue and suppress vice, are persons of great valour to their country, and also those persons are able by their wisdom and knowledge to benefit or profit their country, whether it be in the teaching of good arts and Sciences, or by any other means, so that the common weal be the better maintained, are persons of great valour, and are as jewels unto their country, and their country is beholding unto them. But contrariwise, all those persons that are not able to profit the common weal in any respect, and also desire to live pleasantly and wanton, and have great livings and riches, and do no good therewith: all those persons are more beholding unto their country, than their country is unto them. But if they have great store of riches, and do covet to heap more, caring not how they do come by it, so they may have it: such persons are the destruction, and are as caterpillars to the common weal of their country, for that they do annoy and hurt the prosperity and the state of their Country, for that they catch and heap up into their custody more than doth suffice themselves, by great quantities, whereas thousands do lack to serve their turns, that are better members in the Common weal than they are. And all such persons, the Common weal hath a good turn when they are delivered of such a one: For by that means is dispersed that heap of store unto a number of persons hands besides that which he would have heaped up more, if that he had continued longer. So that some of the richest sort of people are not the best members in the common weal, but the worst: and yet it behoveth some persons to be rich, and by their riches the common weal is the better maintained, as thus. The Prince of any country being godly and virtuous, the Common weal doth the better flourish, and is continually kept the safer from the foreign enemies: and the Noble men, and Gentlemen, that are virtuous, and given to practise the good government, & the preseruement of themselves, and the state of their Country. So then their riches do good, and also if the merchant be rich, so that he do not hurt his own Country, but winneth his riches out of other foreign Countries, or any other good and virtuous subject, by his riches he may do good, if he do use that he hath to the furtherance of the common weal: So that it is necessary that there should be rich persons in the common weal, for a number of causes, so that those rich persons be virtuously bend, but otherwise they may do hurt. And thus gentle Reader, I do make an end, desiring you that you will take this simple book in good part, and if there be any faults committed by me, either by ignorance or negligence, I pray you let me gently understand thereof, for man cannot be so precise, but that he may err. And thus I betake you unto almighty God, the Creator of all things. By yours, William Bourne. ¶ A brief note, taken out of M. Dees Mathematical Preface that goeth before Euclides elements now extant in our English tongue, as touching what the Mathematical Sciences are, that is to say, all those arts that order number, measure, or weight, and time, without the which, in respect, we can do nothing. For what can be done in any respect, but we must use number, which is arithmetic? or what can be done, but we must use measure or weight, which is geometry? or what can there be done, but that we must use time, which doth appertain unto astronomy? for by number we know how many or few there are: and by measure we know whether it be inches, feet, yards, scores, miles, leagues, pounds, ounces, galloes, quarts, or tons: and by time, we know whether it be minutes, hours, days, weeks, months, years. etc. Whereof two are principal, arithmetic and geometry, whereof all these compounded scientes are sprung of these two Simples. ☞ things done by hand geometrical. 1 Mecometrie. Is the measuring of the length anything whatsoever. 2 Embadometrie. Is the measuring the contents of all flat things, as Land, board, glass. 3 stereometry. Is the measuring of all solid bodies, as Timber, Stone, Kaske, & such like. ☞ things measured that have distance from you. 4 Apomecometrie. Is how far any thing is from you, whether it be on land or on water. 5 Hipsomettie. Is how high or deep any thing seen, is from the level, whether it be on land or water. etc. 6 Platometrie. How broad any thing is. etc. 7 Geodesie. Is the surveying or measuring of lands, woods, or water, having distance from you by instrument or otherwise. 8 geography. Is the description of Countries, or kingdoms. 9 Cherographie or Typographie. Is the description of a part of a Country or kingdom. etc. 10 hydrography. Is the description of the Seas, with the islands and rocks, and dangers and lines, and Courses. etc. 11 Stratarithmetrie. Is the view or measuring of a battle of men, to know the number of them not coming near them. etc. 12 perspective. Demonstrateth the manner and property of all radiations direct, broken, and reflected. 13 astronomy. Is the moving of the lights and Planets. etc. 14 music. Teacheth the diversyty of sounds. etc. 15 cosmography. Is the description of the whole earth, and the parallel of the heavens answering thereunto etc. 16 astrology. Is to give judgement by the signs, lights and planets. etc. 17 Statick. Is an art that doth order and deal with heaviness and lightness. etc. 18 Anthropographie. Is of things appertaining to the body of man, to show them. etc. 19 trochilic. Doth appertain unto the turning of wheels, this art is necessary for Clockmakers, & Crane makers, and mills, & all other sciences, that do deal with wheels. 20 Helicosophie. Is an art to draw hylical or Spheral or winding lines, and is very necessary for Skrewe makers, & divers other things. 21 Pneumatithmie. This art is necessary for all them that do make pumps or great Bellows, for that it teacheth all those things that go by wind and water. etc. 22 Menadrie. Is an art, that teacheth the making of all ingenes, as things to pull to, or thrust fro, or lifting up, or pressing down. etc. 23 Hypogeiodie. Is that art that doth appertain unto miners in the ground. etc. 24 Hydrogogie. Is that art to bring water unto any place assigned. etc. 25 Horometrie, or Horologiographie. Is the making of dials of all sorts. etc. 26 Zographie. Is the art of a cunning Painter. etc. 27 Althalmasat. The art of graving. 28 Archetectur. Is a cunning Mason or Carpenter. etc. 29 navigation. Is sailing on the Sea. etc. 30 Thauruaturaike. Is that which doth make strange works, as those that made the brazen head seem to speak, the brazen Serpent to hiss, the dove of wood to fly, the Eagle made by art to fly. etc. 31 Archemastrie. This art teacheth to bring to actual experience sensible all worthy conclusions, by all the arts Mathematical, etc. FINIS. To the Reader of the first book, ¶ The first book of the treasure for travelers, containing the particular conclusion of the scall for to know the hieght of any Tower, Steeple, or Hill, or wall, and the distance unto them, and the particular conclusions of the cross staff, and to know the things before rehearsed after the plainest order of teaching, & also there is the conclusion of the horizontal or flat Sphere how to take the plat of any country, after the plainest order, with such other like, very necessary for all sorts of travelers either by sea or by Land, written by William Bourne. To the Reader of the first part. GEntle Reader, there is contained in this first book, the particular conclusions of the Skal, as touching the knowing of heigthes, both by right shadow, and contrary shadow: and also how to know any distance by the Skalle. And although that M. Thomas Dygges hath set out a book called Pantometria, which is extant in print, as touching the conclusions of the Skall, which is very learnedly done. Yet notwithstanding I do not think it hurtful to show it particularly and plainly, whereby they may do it in most causes, without arithmetic. For the Skall being put but into .12. Parts, it may be counted by the head, without arithmetic: but if the Skal be put into many parts, than it must of force require the aid of arithmetic. And also there is the particular conclusions of the cross staff, as to take the wideness between any two marks, and the length of any wall, and the distance unto any place, with other necessary matters to be done with the plain cross staff. etc. And also there is the Conclusion of the horizontal or flat Sphere, how to take the plat of any country, after the plainest order of teaching, that is to say, by the point, and parts of points of the compass: For it is all one matter, whether that the Instrument be divided into degrees, or parts of points: and that same may be done by plain lines of opposition, without any Instrument or circle, which I do omit at this time to speak of. And although gentle readers, that it seemeth not unto you, to be learned like done, yet notwithstanding it is possible, that there is some thing that is not common in those books that are extant, that may do you pleasure. For the learned sorts of books (it may be) are not most necessary to be common, and yet it would do well, that the common sort of people should have some instructions. FOr that it is sufficiently declared in divers books now extant in our English tongue, wherefore I do think it superfluous for to show what a prick is, or what a line is, or what a Plat or Superficial is, or what Angles be, and what a sholded body is, as it is sufficiently declared in all these books: as in Euclides elements, and in M. Thomas Dygges book called Pantometay, and also in M. Leonarde Dygges book called Tectonicon. etc. A Circle. A Centre. A Circumference. A diameter A Circle is that which is drawn round with a pair of Compasses, a Centre is the middle prick, Circumference is the compass, Diameter is the breadth of a Circle. etc. And furthermore, for that in this first part there is the conclusions of the scall, and the cross staff, showing by them how for to know the distance unto any place assigned: Therefore it is very necessary for to know the parts of measure, as it is not unknown unto all men, what a foot is, and that .12. inches maketh a foot, so .3. Foot is a yard, and .5. A foot. A yard. A pace Geometrical. foot is apace geometrical: but some persons have been of that opinion, that .3. Foot is apace, which is a yard, but it is but a simple step, A simple stop of yard. and few men are able to endure to pace a yard any long time together: but any person may endure to step two foot and a half, all a day long together. Therefore apace Geometrical, is two reasonable steps, and that is five foot: and so any man may endure all a day together, A race is two steps. and twelve paces maketh a score, 12. paces is a score, that is, 20. yards. A mile is a 1000 paces, that is .5000. Foot, or 1666. yards, and 3. A Rod is .16. Foot .2. of land measure, and 18. foot is a Rod of wood measure .6. Foot is a fathom, and .833 fathom is a mile. and that is twenty yards, and that maketh .60. Foot: and a mile containeth .1000. Geometrical paces, and that is .5000. Foot, and that maketh 1666. yards. ⅔. and that is .2. Foot, and that containeth 83. score. ⅓. and that is .20. Foot. etc. and a Rod is .16. Foot and a half, of land measure, and .18. Foot is a Rod of wood measure, according to our English account: and .303. rod and .1/33. that is half a foot, is a mile of land measure, and .277. rod, and .7/9. that is .14. Foot of wood measure, is a mile, and a fathom is .6. Foot, and that is .2. Yards: and .10. Fathom is a score, and a mile containeth .833. Fathom, and. ⅓. part, that is 2. foot. etc. And thus much have I said as touching our English account, as concerning the measuring of the length, or the distances unto any place assigned. etc. ¶ The first Chapter of the first book containing the making of the Quadrant with the Skall, whereby you may know the height or lowness of any thing. etc. Now beginneth the first part of this book, called A Treasure for travailers, showing the conclusions of the Skall, whereby you may know the height of any Tower, Steeple, or Wall, or the height of a hill, and the distances unto any mark assigned by the Conclusions of the Skall. And also in this first part there is the Conclusions of the cross staff: showing how to know the length of the Corten of a wall, and the distance thereof, or any town more plainer then is showed in M. Leonarde Dygges book called Tectonicon. And also there is the making and the use of an Instrument, that may be called an Horizontal Sphere, to draw the plat of any country set out upon the face of the whole earth: and how to know how to place the longitude and the latitude of any town, with other necessary things. etc. very necessary and profitable for all travailers and serviteurs, either by sea, or by land, as Gonners and captains, and leaders of men. And now shall follow the making of a Quadrant, The making of the Quadrant, with the Skal with the Skal divided but into. xii-partes, although some will have it divided into .60. Parts, and some into 48. parts, and some into more parts, and some into less parts, according unto the fantasy of sundry authors. But I do think it best to be divided into .12. Parts: for that divers people are desirous to know the use of the Skall, that are not seen in arithmetic, and yet the use of the Skal is very necessary and profitable for them to know, and the Skal divided but into .12. Parts, any reasonable man may have the use thereof. But if it be divided into .48. or .60. Parts, than it doth require arithmetic, which is not in many persons: wherefore I do think the Skall that is divided into .12. Parts, to be most necessary and profitable for all sorts of people. And although that M. Thomas Dygges in his book called Pantometria, hath written thereof generally, yet I do think it very necessary, to write of it particularly. etc. And now for the marking of the Quadrant, do this: first take a piece of well seasoned wood, that is bard, and fine grained, as box, or such other like, or else you may make it in metal, as in brass, or Latin. etc. and then being well plained or polished, and the larger, the better. For in a small Instrument you may commit an error, sooner than in a large: then be sure that one of the corners have a square or right angle, and then there set the one of the feet of your compases, and with the other foot of the compases make a quarter of a circle, for that it is called a Quadrant, it is the .4. Part of a Circle, and no .4. cornered thing. And that being done, then divide the edge thereof into .9. equal parts: and every one of those parts divide into .10. equal parts: so that then there will be in all .90. equal parts: and every one of those divisions or parts, are called a degree. & a degree is no other thing but a whole circle divided into .360. Equal parts, and then at every .10. or .5. degrees you may make them, as thus .5. and .10. and .15. and .20. or else as this .10. The use of the degrees. and .20.30. and so forth unto .90. for that the quadrants is divided into ·90. Equal parts, and the use of these divisions or parts called degrees, is to know the height of the sun, or any star above the horizon, whereby they may know the altitude or height of the pole of the world above the horizon, as I do more at large declare in my book that is extant in print called The Regiment for the sea. etc. and also the degrees are very necessary for gunner's, to know what ground that any piece of exdenance doth cast or convey the shot at the mont of every degree, as I do more at large declare in my book called the Art of shooting in great ordinance. etc. And now furthermore, for the making of the Scal upon the Quadrant, do this, at the right angle or corner make a square in such sort, that the other corner right against it doth stand just upon .45. degrees, & look that it be a right or square angule in like manner, and so from that to the two sides there will be .4. square or right angule, and then divide two of those sides, that is to say, the two sides that is from the corner where that the Plummet shall hang towards the parts of the degrees, divide each of them into .12. equal parts, and then mark .12. at .45. degrees, and then make two sights upon one of the sides of the Quadrant: and those divisions, or parts of that, or next unto the two sights, are the parts of right shadow, and then the other divisions are the parts of contrary shadow. And here doth follow the demonstration of the Quadrant, with the Seal. etc. Now followeth the form of the backside of the astrolabe. etc. ¶ The second Chapter is of upright shadow, that is to say, to know the height of all things taken within the length of the thing. Now follow the conclusions of the scall, both of the Quadrant, and also of the astrolabe, but the astrolabe is the better. And first, for line of level called of Gonners the point blank, turn the other side C. right with the line of level G. and H. then put your thumb thorough the ridge D. then hold up your hand that you may look thorough both the sight A. and B. them all things that you see thorough is level with the sight of your eye, neither higher nor lower. Now if that you will know, the height of any town or upright wall, do thus turn the Athelida C. to the corner of the scall, and set it upon the part 12. What to observe in taking of height with the Skall. then go forwards or backwards, till that you do see the top of the wall thorough the two sights A. and B. then measure how many foot it is from the middle of your foot to the hard wall, so many foot the wall is high. and as much as it is from your eye, down to your feet, and that you must add to in all your heights, & look that the ground be level, and be sure that you stand upright, and wink with the one eye. Now furthermore being an upright wall, set the Athelida C. upon the part one, of upright shadow: Upright shadow at on station. then doing as before is rehearsed, than meet the ground to the wall .12 times the measure shallbe the height of the wall, than the Athelida upon the part 2. then six times the measure to the wall, shall be the height of the wall the Athelida upon the part 3. then 4. times the measure shall be the height of the wall. then upon the part 4. then 3. times the height shall be the measure of the height of the wall, the Athelida upon the part 6. then meet to the wall double, the measure shallbe the height of the wall. Always provided, that you add to the measure the length of your body, from your eye to your feet, now shall you have a way to get the height of a steeple or wall that hath a ditch: but than you must have two standings: and still for upright shadow, set your Athelida upon the part 12. then looking thorough the sights, holding it upon your thumb as afore is rehearsed, then with the middle of your foot set a mark, then turn the Athelida to the part 6. of upright shadow, and there make an other mark, then meet how many feet it is, betwixt the 2. standings, then double that measure shall be the height of the steeple or wall, the first standing upon the part 12. then turn the Athelida to the part 8. of right shadow, then measure the ground 3. times: that distance shall be the height of the steeple or wall, the first upon the part 12. and the second upon the part 9 then 4. times the measure shall be the height of the steeple, the first standing upon the part 12. the next on the part 10. then the measure between the two stand shall be the 6. part of the height, the first standing on the part 12. the next on the part 11. the measure between the standings shall be the 12. part of the height. yet furthermore for upright shadow, first set the Athelida upon the part 9 of right shadow, then doing as afore is said, set a mark with the middle of your feet: then turn the Athelida to the part 3. of right shadow, and there set a mark, then measure those two standings, and then double that measure that shall be the height of the Steeple or wall, or the first standing upon the part 8. & the next upon the part 4. them doing as before is said, 3. times the measure shallbe the height of the steeple or wall, and the first standing upon the part 10. and the next upon the part 6. of upright shadow, then doing as afore is said measuring the distances 3. times, that measure shallbe the height of the steeple or wall. Or the first standing upon the part 7. & the next upon the part 6. of upright shadow, then doing as before is rehearsed mesuring the distance 12. times, that measure shallbe the height of the wall. Or the first standing upon the part 7. & the next upon the part 5. then measure the distance 6. times: that measure shall be the height of the wall. Thus much have I said for upright shadow, & upright shadow is this, all things whose height is taken within the compass of the length of any thing measured, as for ensample this, by the figure following. By a tower or Steeple being 65. Ensample. foot high of all those questions of upright shadow afore rehearsed the first was the Athelida upon the part 12. and to the wall the measure of the ground was 60. foot, & then from mine eye to the ground was 5. foot: so that 60. foot and 5. foot, make, 65. foot. So I conclude the whole height of the tower to be 65. foot. The next is the Athelida upon the part 1. and the ground to the wall 5. foot, so 12. times 5. is 60. then the next was upon the part 2. and the measure 10 foot, and six times 10 is 60. the next upon the part 3. and the measure to the wall 15. foot, than 4 times 15. is 60. the next was upon the part 4. and to the wall 20. foot, and three times 20. is 60. the last upon the part 6. and to the wall 30. foot, and 2. times 30. is 60. Ensamples of two fashions or standings. Now all the other have two stations or standings, therefore you do not measure to the wall, but the measure between the 2. standyngs, the first standing upon the part 12. the next upon the part 6 and the measure between the 2. standyngs is 30. foot, than 2. times 30. is 60. then between the part 12. and the part 8. was 20. foot, and 3. times 20. is 60. then between the part 12. and the part 9 was 15. foot. and 4. times 15. is 60. then between the part 12. and the part 10. was 10. foot. and 6. times 10. is 60. then between the part 12. and the part 11. was 5. foot. and 12. times .5. is 60. And now furthermore where you could not go so far back as the part 12. the one standing upon the part 9 and the other upon the part 3. the measure of ground was 30. foot. then 2. times 30. is 60. the one standing upon the part 8. and the other upon the part 4. the measure was 20. foot. and 3 times 20. is 60, than the one upon the part 10. and the next upon the part 6. the measure was 20 foot. and 3. times 20. is 60. then the first standing upon the part 7. and the next upon the part 6. the ground between the 2. standings was 5. foot. and 12. times 5. is 60. the one standing upon the part 7. and the other upon the part 5. the measure between the 2. standings was 10. foot. then 6. times 10. is 60 So you may see that every way the whole height to be 65. foot. adding unto it as before is said the length of your body being 5. foot, thus much have I said of upright shadow, and now followeth contrary shadow. The 3. Chapter showeth how to know the height of any thing with the scall by contrary shadow (that is to say) without the length of any thing so taken. NOw followeth contrary shadow, & contrary shadow is this, that when soever any height is taken without the height or length of any thing, as followeth: first, doing as before is said, in all points, putting his thumb thorough the ring of the astrolabe, set the Athelida unto the part 12. then with the middle of your foot, make a mark, them turn the Athelida to the part 6. of contrary shadow: them go bakwards till you may see the top of the steeple or tower thorough both the sights of your astrolabe, being sure that it is hanging plumb upright. Then at the middle of your foot there make another mark, then measure how many foot there is between your .2. Stand, so many foot is the height of the Steeple or tower. Then in like manner at the first standing, the Athelida upon the part .6. then turn the Athelida to the part .4. of contrary shadow. Then meeting the ground between the .2. Stand, it shallbe the height of the Steeple or tower. Then in like manner the Athelida at the one standing upon the part .4. and the other upon the part .3. and then measuring the ground between the .2. standings, shallbe the height of the Steeple or tower, then at the one standing the Athelida at the part .3. and the other standing the Athelida upon the part .2. then measuring the ground between the .2. Stand, half that measure shallbe the height of the tower, Steeple, or Wall. Furthermore the one standing the Athelida on the part .2. & the next standing, the Althelida upon the part one: then measure how many paces or foot was between the two stand: the .6. part of that measure shallbe the height of the steeple or tower, but you must be sure that the ground be plain & level, or else it may err. Now for your better ensample, by this figure here under made, by a Steeple that is from the top down to the ground .120. Ensample of contrary shadow. foot hyth from the foot to the top of the shaft or spear, and now by the height is known the distance, as you shall know by all the questions before rehearsed. First the Athelida at the first standing was on the part .12. and at the next standing, at the part .6. and the measure between the .2. Stand was .120. Foot. Now I do conclude that the height of the said Steeple is .120. Foot from the ground to the top, and the distance to the said Steeple is .240. Foot, that is .48. paces: & the height of the Steeple .24. Pace. Then from the part .6. to the part .4. in like manner once the height of the Steeple, and the distance to the Steeple, is .3. Times the height, that is .360. Foot to the Steeple, that is .72. Pace: then from the part .4. to the part .3. is once the height of the Steeple: and the distance to the Steeple is .4. Times the height, that is .480. Foot to the Steeple, that is .96. Pace. Then from the part .3. to the part .2. is twice the height of the Steeple, and the distance to the Steeple is .720. Foot, that is in pace .144. Pace. Then from the part .2. to the part .1. the distance of ground is between the .2. Stand .720. Foot, that is .6. Times the height of the Steeple: and the whole distance to the Steeple is .12. times the whole height of the wall, that is .1440. Foot. The sum of the whole distance from the part one, to the Steeple, and that same in pace is .288. which maketh .24. score: and at the part .2. the distance of scores is .12. then at the part .3. it is to the Steeple .8. score, at the part .4. it is to the Steeple .6. score: at the part .6. it is to the Steeple .4. score, then at the part .12. it is the just height of the Steeple, being .120. Foot, that is .2. score, adding as before is said, so much to the height of the Steeple, as from your eye to your feet, which you shall do in this sort. And specially if the distance be far from the Steeple at every station, if you will work exactly, when you have taken the height, turn your astrolabe (the Athelida standing as before) not removing your foot from that standing, then looking thorough the sights, turning your face directly from the Steeple, then whereas your eye doth rest, there set a mark: then there is no doubts but that you shall take the true height and distance, doing this at every standing, your ground being plain and level. ¶ The fourth Chapter showeth how for to take the part of any height as the length of a window or such like. NOw furthermore to take the part of a height, you may in like manner, doing as afore is rehearsed in all points, and also you may with the Scal of the astrolabe take the length of a pinnacle or a window or windows, the one above the other, you may take the measure between them as thus. Set your Athelida to the part .12. then go backwards or forwards, till that your sights do agree with that thing that you would take measure of, letting your Athelida stand still at the part .12. Then in like manner take the other end of that thing whose length you do mean to take, then take your sight agreeing with the other end of the pinnacle, then measure the ground between the .2. Stand: that shallbe the length of the pinnacle, window, or cross, as by this figure it may more plainly appear, as for ensample this. First I did set the Athelida upon the part .12. and doing as before is said: and took the upperside of the window, and at my foot made a mark, Ensample in the taking of the point of a height. than I went nearer the Steeple, and took the lower end of the window as you may see at the letter. A. then I measured the ground between the .2. Stand, and found it 20. foot, so I do conclude the window to be .20. Foot long. Then in like manner I took the pinnacle, doing as afore is rehearsed, first at the top, and then at the foot, the Athelida standing still on the part .12. and found the measure between the .2. Stand .15. Foot, the just length of the pinnacle, as by the .2. Lines B. it doth appear, then between the .2. crosses, doing as before is said, and found the distance between the .2. Stand .10. Foot; the length between the .2. Stand as by the .2. Lines C, it doth appear, and so do by all other small parts. ¶ The fifth Chapter showeth how to know the distance of many things that is from you, and also whether any other tower be higher or lower than the tower that you be upon. YEt furthermore by the Scal of the astrolabe, you may know when you be on the top of a tower, or top of a Castle, how far many things be from you, and in like manner the height of an other tower that shall stand near unto you. And also how much that one tower is higher than another, with divers profitable things more, as this: First if you know not the height of the tower that you be on, then take a line, hanging a Plomet of lead or some other such thing, then let it down over the wall to the ground. Then by the length of the line you shall know the height of the tower or wall that you be upon, then when you know the true height of the wall or tower, then take your astrolabe, hanging it upon your thumb by the ring, as afore is declared, then looking thorough the sights in order, as afore is rehearsed. So shall you find the distance, as this: first, at the part .12. How to know distance by the shadow. look what the height of the wall is from the ground, so far it is to the mark that you do see thorough the sights of the Athelida, turning your astrolabe that the sights may go downwards, than the Athelida on the part .6. of contrary shadow, the thing that you shall see thorough the sights shallbe .2. times the height of the tower or wall: then on the part .4. of contrary shadow, that thing that you do see thorough the sights shallbe 3. times the height of the tower of Castle, then on the part .3. it shallbe .4. Times the height of the wall to that thing that you shall see thorough the sights. Then on the part .2. that thing that you shall see thorough the sights, shallbe .6. Times the whole height of the tower or Wall. Then the Athelida on the part one, that thing that you shall see thorough the sights, the distance will be 12. times the whole height of the tower or Castle, or wall, as for an ensample by this figure following. By a tower being found to be .60. Foot high, at the part 12. the shadow to run downwards, it is .60. Foot of, An ensample. at the part .6. the sights did show you that thing that was 120. foot of, that is .2. score, at the part .4, 180. foot of, that is .3. score, at the part .3. the sights show you .240. Foot of, that is 4. score, at the part .2. all things seem from the top of the tower thorough the sights, as .360. Foot of, that is, 6. score of. Then at the part one, all things seen thorough the sights from the top of the tower shall be .12. Times so far from the wall, as the wall or tower is in height, that is .720. Foot from the Wall, and that maketh .12. score. Now if that there were another tower or Wall near unto you, you may know how many foot that it is higher than that which you be on, as thus. First doing as afore is declared, you shall know how many foot that the tower is high, thus by this afore rehearsed, you shall know how far that the other is from you. Then set your Athelida to the line of level, so shall you see whether that the other tower be higher than that which you be on, then to know how much that the other tower is higher than that you be on, do this: First look how many parts that there is from the foot or base of that tower that you would know how much that the one is higher than the other, to the right line called the line of level, then turn the Athelida till that you do see the top agree with the .2. Sights, holding the astrolabe by the ring upon your thumb, as before is rehearsed, as this: The foot of the next tower seen thorough the sights at the part .12. To know how much the one tower is higher or lower than another. than you shall divide that height of the tower that you be on, into .12. Parts. Then look how many feet that there cometh unto a part, then turn your Athelida till that you may see the top of the next tower, and look how many that cometh unto, add so many foot of the measure of your own tower, to the other tower. Then at the part .10. if you do see the foot of the next tower, divide the height of the tower that you be on, into .10. Parts, then look how many parts, that the other tower is higher than yours, add so many foot more to the height of the other tower as the parts of feet doth answer of your own tower, then in like manner, if you see the foot of the tower at the part .6. Divide the height of your own tower into .6. Equal parts: then look how many parts that the other tower is higher than yours that you be on, add so many foot to the height as those parts doth come unto: and if you do see the foot of the other tower, at the part .3. then divide the height of that tower that you be on into .3. Equal parts. Then look how many parts that the other tower is higher than your tower, add so many foot as those parts doth come unto the other tower, as this for an ensample, by a tower that is 60. foot high. Then I took my astrolabe and turned the Athelida to the part .4. Then I did see the base or foot of the other tower, than that tower that I was on, the top being .60. Foot high, I did divide it into .4. Equal parts, and that did answer to .15. Foot a part: for this I am assured of, that when I did set the Athelida to the line of level, that it was just the height of my tower, that place which I did see upon the other Castle. Then I did turn the Athelida still about, Ensamples. seeking where I might see the top of the Castle: then at the part one and a half, I might see it justly with both the sights, than did I add .15. Foot and a half .15. that is .7. and a half, and those .2. Sums make .22. Foot and a half, and then put .22. Foot and a half, to .60. Foot, maketh .82. Foot, and. ½. the whole height of the other tower or Castle. Yet for more plainness, lie another tower of .50. Foot high which I was upon, I took my astrolabe, and did as afore is said, and I saw the base or foot of the other tower at the part .10. Than I did divide the height of the tower that I was on, into .10. Equal parts, being .50. Foot high, and every one of those parts came to .5. Foot. Then I did take the astrolabe and turned the Athelida, till that I could see the very top of the other tower thorough both the sights: and then at the part .4. I saw that it was true. Then I did add .4. of those parts, which was, 5. foot, to a part, and that came to .20. Foot. So that the one tower was higher than the other by .20. Foot: so I did add .20. Foot to .50. Foot, which maketh .70. Foot. So I do conclude the whole height of the higher tower to be .70. Foot just. Yet another emsample of .2. Towers: first, that tower that I was on to be .40. Foot high, and I saw the base or foot of the other tower at the part .2. of contrary shadow. Then I did divide that tower that I was on, into .2. Equal parts, and that did answer to .20. Foot a part. Then I turned my astrolabe, and removed the Athelida to the part one. Then I saw the top of the other tower thorough the .2. sights. Then did I add one of these parts being .20. Foot, to the height of the other tower, which maketh in all .60. Foot high, the true height of the other tower, as by these .2. figures you may perceive. Now furthermore in like manner, if you be on the higher tower, To know how much any Tower is lower than that you be on. you may know how much the lower tower is shorter than the other. As this: first, knowing the height of your tower that you be on: then take the foot, or base of the shorter tower with your astrolabe (as before is said,) then look how many parts it cometh unto, divide the height of your tower that you be on, as you did before: then turn the Athelida, till that you may see the top of the shorter tower, then look at what part you may see the top of the shorter tower: take so much away from the height of your own tower, as the parts do come unto: then that which shall remain, shall be the height of the shorter tower, as for ensample thus: By a tower that you were on, being 63. foot high, Ensample. and you saw the foot of the other tower, thorough the sights at the part 9 of contrary shadow, then divide the whole height of your tower that you be on, into 9 equal parts, and every one of these parts cometh to 7. foot. Then turn the Athelida, till you may see the top of the shorter tower agree with both the sights, then at the part 2. you did see them, the one of those parts being 7. then 2. times 7. maketh 14. So that the lower Tower is 14. foot shorter than the other. Then pull 14. out of 63. foot, there remaineth but 49. foot, so you may see the whole height of the lower Tower to be 49. foot, and thus do by all other Towers, Castles, Steeples, or walls. The 6. Chapter showeth how for to know the height of a Hill, and also the distance unto the top of any Hill with the scall. NOw furthermore, by the scall of the astrolabe, you may take the height of any hill, and also of the distance unto the top of the hill, by the line Hypothenasall, as though there were a line made fast to the top of the Hill, as hereafter followeth. First that hill that you do require to know the height of it, or to know the number of the pace, or feet, that is above the ground that you be on: then seek a plain ground near about the hill, there where you may see the top of the hill, then doing thus. First turn your Athelida, till that you may see the top of the hill thorough both the sights, your astrolabe hanging upright, the Ring being upon your thumb, then look at what part that the Athelida standeth on, then accordingly as you did see before, by the taking of the height of Steeples, Towers, or walls, meating the ground between the 2. standings, to be the height of the hill, as you may know by this ensample. To know the height of a hill. First I seeking out my ground meet for my purpose, to be as plain as I can find it, first, at the part 6. I set the Athelida, and so did I see the top of the hill, for nearer I could not see it: then I did turn the Athelida too the part 4. and then where I saw it agree with the sights of the astrolabe, there I began for to meet how many pace, that it was between the part 6. and the part 4. the measure of ground was 100 pace: so I did conclude that the height of the hill was 100 pace high, that is 500, foot. and then I must needs say, that from the part 4. to the centre or top of the hill, if there were a perpendicular line let down as low thorough the middle of the hill till that it were level with the sight of mine eye, than it were to the end of the perpendicular line 300. pace just. Then for to know the just distance to the top of the hill, by a right line, as though there were a line stretched from the top of the hill to mine eye, which is the line hypothenusal: Then must I be perfect in the second part of Arithmetyke, To know the length of the Hipothenusall line by the extracting of the root. (that is to say) the extraction of roots, and there will I do thus: I must multiply the whole distance in itself, which is 300. times 300 pace, and of that multiplication cometh 90000. Then in like manner I multiply the height in itself, which is 100 times 100 and of that multiplication cometh 10000: then I do add both those numbers together, & that maketh in number 100000. then this being done, I do extract the square root of both these numbers added together (that is to say) 100000, and then there will stand in the quantity line .316. and will remain 144. which is 18/79. Therefore I do conclude that the line should be stretched from the top of the hill down tyo the sights of mine eye which is the line Hypothenusal, to be 316 pace, and one foot and better, the just length of the hypothenusal line, as by this Ensample it doth more plainly appear. So by this hill you may see that the height of the hill was above the ground, that it was taken upon 100 pace: that is 500 foot, and that maketh 8. score, and 20. foot: & the distance to the centre, or perpendicular, or plumb line imagined into the Hil to be 300. pace, & that is 1500. foot, which maketh 25 score, and the Hipothenusall line, from the top of the Hill to the standing, at the part 4. is 316. pace, & near 2. foot, which is in feet 1582. and in scores, 26. and 22. foot, as the figure afore made doth represent. And thus do by all other hills, whether that it be a part of a Hill or a whole Hill, all is one matter. The 7. Chapter showeth you by the Skall of the astrolabe, to know the true wideness of any water, or how far that any ship is of from you, or to take any great distance by laying the astrolabe flat before you with the scall upwards. YEt furthermore, by the scall of the astrolabe you may know the wideness of Waters, and the distance from place too place all along the water side, and also how far that any ship doth ride from the shore side, and also how far the ship is from you: whereby you may make a perfect shot, very profitable for Gonners to have the use of, as hereafter followeth. To know the wideness of waters. first, take your astrolabe, and set the same upon some steady thing, laying that flat with the scall upwards: Then turn the astrolabe till that the line of level doth stand as the shore side, as those that you should set the Athelida with the line of level, to look all alongst the water's side: then shall the plumb line of the astrolabe stand directly cross the water, than all things seen right with that line to be right over the water: then your astrolabe lying still, turn the Athelida to the part 12. then look what mark or bank that you see hard to the waters side, through the sight of the Athelida, mark it: then take your astrolabe going directly by the water's side, till you come directly right against the mark taken upon the other side of the water, setting your astrolabe as before is rehearsed. Then if the perpendicular line do directly point to the mark afore taken, than the measure between the two standings, shallbe the true breadth of the water. Furthermore, the astrolabe standing as afore is rehearsed, setting the Athelida upon the part .6. of the right shadow, then double that measure between the .2. standings, that shallbe the breadth of the water, than the Athelida upon the part .4. of right shadow, the astrolabe set as afore is rehearsed, than the measure between the .2. standings, shallbe the .3. part of the breadth of the water, and so forth to the part .3. to the mark right over the water, shallbe the one quarter of the breadth of the water, than .4. Times the whole measure shallbe the breadth of the water: for to take the breadth of waters with the Skal of the astrolabe, is no other thing in the doing of it, but as you do take the height of walls or towers in all points, saving that in the taking of heigthes, you do hang your astrolabe by the ring upon your thumb: and for to take the breadth of waters, you must lay your astrolabe steady afore you, and the line of level to stand all along the waters side, as circumspectly as you may or can: than you must make your measure all alongst by the water's side, as by this ensample following, of a water that is measured, and is .36. score over it. An ensample. First I take my astrolabe, and come to the waters side, and lay my astrolabe upon some steedye thing, and lay the line of level all alongst by the water's side, than the thwart line of the astrolabe pointed just thwart or cross the water's side, near to the Church end: then I turned the Athelida to the part .12. so I saw a polled tree through the sights: Then I took up my astrolabe, and began to go, measuring the ground by pace, two steps to apace, and that made .5. Foot, which is a Geometrical pace: and .12. of those paces make a score: And then I came right against the tree, proving it with my astrolabe, and found that the measure was from my first standing, till I came right against it, 432. paces, and that maketh .36. score. So I did conclude the breadth of the water to be .36. score, from bank to bank. Then furthermore I turned the Athelida to the part .6. and then I saw a polled tree at the house end: then I went measuring the ground, and found that the ground was .216. paces, and then I was right against the mark, and that was .18. score: then two times .18. is .36. Then I turned the Athelida to the part .4. of right shadow, and measured the ground, till I came right against the mark taken through the sights of the Athelida, and found the measure between the first standing, and the next, one hundred forty and four paces, that is, twelve score: then three times twelve score, is thirty six score. Then the Athelida standing upon the part .3. I measured the ground between the two standings, and found it to be .80. paces, that is .9. score, and the fourth part of the breadth of the water, for four times 9 is .36. Then the Athelida upon the part .2. Always provided that you do as before is rehearsed, measuring the ground till you come directly against the mark taken, shallbe three score and twelve paces, that is, six score: then six times six, is .36. For upon the part .2. the ground between both the standings, is but the sixth part of the wideness of the water. Then at the part one, the ground between the two standings, shallbe but the twelfth part of the breadth of the water, that is .36. paces, and that maketh three score: then .12. Times three, is .36. Now furthermore, if you will know the length of any of the Hypothenusal or slope lines, then extracting the root, To know the length of the slope line, by the extract of the root. the length of that line shall appear: so that with the Skal of the astrolabe, you may know any distance, being sure that you do make a square Angle, by laying the astrolabe flat afore you, even according unto the Conclusions, when that you do hang the astrolabe. And also you may take a greater distance, and also a larger station, whereby you may work more exactly, by laying it, then by hanging of it. For that there is seldom any ground, but that it is higher or lower in one place, than it is in another, & that may breed a notable error, if it be not well considered of. But if you do lay the Skall flat before you, considering well the conclusions, you may commit no great error, being sure, that in your removing, you do make a square Angle, and then measure the distance of ground truly, for thence are many fold notable conclusions to be done with the Skal, as by this you may know how far of that any ship doth ride at an ancore in the Sea, or in any bay, or river: you may know certainly how far she is from you, so that she be not movable: And also you being besieged in a town, may know how far any thing is from you: And also if you be without any town, you may know by the scale of the Quadrant or astrolabe, how far any tower, Balwarke, or Steeple is of from you. etc. The eight Chapter showeth unto you, if that you do know the distance, than you may know whether that it be higher ground or lower ground than the place that you are upon, and how much, both By the parts of the Scal, and by the degrees: and also you may know whether that one ship be higher than an other etc. And furthermore, you knowing the distance unto any place assigned, than you may know the height of any hill or steeple or tower, or the deepness of any valley by the parts of the Scal, as this: The distance being known, if that it be higher or lower by one of the parts & the scall to be divided 12. To know how much any place is higher or lower than the placeth it you are on, whether that it be on tower, Steeple, hill, cliff, of valley. etc. parts: then the thing is higher or lower by the .12. parts of the distance, & if it be higher or lower by two of those parts, than the thing is higher or lower than the place that you do stand upon by the sixth part of the distance. And if the thing be higher or lower by .3. of those parts, than the thing so taken, shall he higher or lower by the .4. Part of the distance: and if that it be higher or lower by the .4. part, than the thing shallbe higher or lower by the third part of the distance: and if that the thing be higher or lower by the .6. part of the Scal, than the hill or valley shall be higher or lower by half the distance. etc. As for an ensample this: I laying the Skall flat, took a mark upon the top of a hill, or in the bottom of a valley: and so working as is declared in the Chapter going before, and found the distance to be .24. score from me, and then I desire to know how much that the hill was higher ground, or the valley lower ground, than the place that I stood upon. And then I took the astrolabe and hung it upon my thumb, and so I saw that the hill was higher by the one part. Therefore I did conclude that it was .2. score higher, that is .120. foot higher ground than the place that I stood upon, for that the distance is .24. score: and the .12. An ensample. part of 24. is .2. Wherefore if that it were a valley, than it were .120. Foot lower than the ground that I stood upon. etc. And then if that it were higher or lower by the .2. part of the Skall, than it should be higher or lower than the place that you stood upon, by the .6. part of the distance, that is .4. score, and that maketh .240. Foot. And furthermore, if that it were higher or lower by .3. of the parts of the scall: then the ground should be higher or lower by a quarter of the distance, that is .6. score: and that containeth 360. foot. And furthermore, if that it were higher or lower by .4. of the parts of the Scal, than it should be higher or lower by the third part of the distance, that is .8. score: and that containeth .480. Foot, etc. And this I do take to be sufficient for an ensample. And now furthermore, if that the distance were very far, and also the Scal divided but into .12. Parts, yet you might know the height of a hill, or the deepness of a valley, To know how much any place is higher, or lower by degrees. An ensample of ships on the water. by the degrees of your astrolabe, or Quadrant, as this: the distance being known unto any mark upon a hill, or in any valley, if that it were one degree higher or lower than the place that you do stand upon, than the thing should be higher or lower ground by the .60. part of the distance. If .2. degrees, than it should be higher or lower by the .30. part of the distance: if .3. Degrees, higher or lower, than the ground should be higher or lower by the .20. part of the distance: if .4. Degrees, than the ground should be higher or lower by the .15. Parts of the distance: if .5. degrees, than the ground should be higher or lower by the .12. part of the distance: and thus far the degrees will serve exactly enough, but not unto many more degrees, for that they be the divisor of a circle. But unto .5. or .6. degrees they will serve the the turn very well. And now for your better understanding, I will make an ensample unto .5. degrees according unto the distance before rehearsed, An ensample. that is, at, 24. score from you, the ground being higher or lower by one degree, the thing is higher or lower by the .60. part of the distance, that is .24. Foot, whether that it be any mark upon a hill or valley, or the height of any tower or Steeple. etc. if that it be .2. degrees higher or lower, than the mark shall be higher or lower than the ground that you do stand upon, by the .30. part of the distance: and the distance being .28. score, the mark shall be higher or lower by .48. Foot. And Furthermore, if that the mark be higher or lower by. 3. degrees, than the thing shall be higher or lower than the ground that you do stand upon, by the .20. part of the distance: that is .72. Foot. And Furthermore, if that the mark be higher or lower by .4. degrees, than the thing shall be higher or lower by the .5. part of the distance, that is .96. Foot. And further more, if the thing be higher or lower by .5. degrees, than the thing so taken, shall be higher or lower than the ground that you stand upon by the .12. part of the distance: that is .120. Foot. etc. And furthermore, by this means or order, you may know the distance unto any ship upon the sea, or riding in any haven or Harborowe you knowing the height of any tower or cliff, or any hill upon the sea coast, how many foot that is higher than the water: and you may know it either by the parts of the Skall, or else by the degrees, as for an ensample, the tower or Hil, or cliff to be .60. Foot higher than the superficial of the water, and the .60. Foot is one score. An ensample of ships on the water. And if you do see the ship at one degree lower than the horizon than it shall be .60. score unto the ship: and if at .2. degrees, than it shallbe .30. score unto the ship, if at .3. degrees, than it shall be .20. score unto the ship, if at .4 degrees, than it shall be .15 score unto the ship: if .5. degrees than it shallbe .12. score unto the ship: if .6. degrees, than it shall be .10. score unto the ship: but if the ship be nearer, the degrees will serve no turn, but will be erroneous. Wherefore you must use the parts of the scall, as .5. degrees and the part one is all of like distance: for the height of the tower, cliff, or hill being .60. Foot in height above the ship, that is just one score: at .5. degrees, the distance unto the ship is .12. score. And also at the part one, the distance is .12. score in like manner etc. and at the part .2. the distance unto the ship is .6. score: and at the part .3. the distance unto the ship shallbe .4. score: and at the part .6. but .2. score: and at the part .12. the distance from the foot of the cliff or tower, unto the ship, shallbe but one score, that is just the height of the tower or cliff. etc. Furthermore you may know, if that you be on the sea, whither that one ship be higher or lower of board, To know whether my ship be higher or lower of board, than another, and whether the one doth overtop the other, and how. than the other ship, and how much: and also whither the one ship doth overtoppe the other ship, you may know how much: so that she be not above a mile from you, as this, by the line of the horizon lack, what place so ever that you do see just with the horizon, is equal in height with your eye, neither higher nor lower, whither that you be one the Sea, or upon the land: and then you being in a ship on the Sea, and you do desire for too know whither that the other ship be higher or lower of board than that ship that you are in, then look upon the other shpppe, at what place that the horizon quoteth: and if you do see the horizon over the other ship, than your ship is higher of board than the other ship: and if that you would know how much, then go too a lower place in your own ship, until such time that you do see the Horizon just with that part that you do desire to know the height of, and then standing still, look what part of your own ship that the Horizon quoateth, that part of the ship is just equal with the other ship, neither higher nor lower: then to know whether that the other ships top of her Mast be higher or lower than your ships, then go up, or send one to the top, and if that the other ships top be higher than the Horizon, than the other ships top is higher by so much as you do see above the Horizon: but if that you do see the Horizon over the top of the other ship, than your ship is the higher: and then to know how much, come down lower, until you do bring the other ships top unto the Horizon, then at the just height of your eye, is the true height of the other ships top, neither higher nor lower: and then look how much it is higher than your eye unto the top, so much your top is higher than the other ships top. etc. And also you being on the land, you may know whether one ship be higher of board then the other, and also whether the one ship doth overtop the other ship, as this, by the quoting of the Horizon upon both the ships, as this, If you be either in a tower, or any high house, near the sea coast, or else at the foot of any hill either. Then if that you desire for to know which of the ships be the higher of board, or else the higher topped, then ascend or descend, until that you do see the horizon just with the higher part of the ship, and then look upon the other ship, and then if that the other ship be higher than the Horizon, than that ship is so much higher of board from the quoting of the Horizon upwards, and then if that you would know how many foot, then ascend upwards until that you do see the upper part of the ship just with the horizon, then look how many foot and inches that you were higher than you were before, and so many foot the Ship is higher than the other ship just. To know how much one house, ship, tower, or hill is higher than the other. And by this order you may know how much one ship is higher topped than the other. And by this order you may know whether one tower is higher than another, or one house higher than an other: And also whether that one hill be higher than another. etc. And furthermore, by this means you do know whether that one ship doth overtop the other: than you may know how many foot it is from the top of any ship, unto the water, by the height of your own ships top, and the height being known, than you may know the distance unto any ship sailing on the sea, so that she be not too far of, by the parts of the Skal, and also by the degrees, as before is rehearsed, going so low as you can in your own ship, and then to consider how much that you are above the water, etc. And thus I do end the conclusion of the Scal, and now doth follow the conclusion of the cross staff. The ninth Chapter showeth the making of the cross staff, that in some cases is better than the Skall of the astrolabe, or Quadrant. etc. Now furthermore as concerning the making of a cross staff, that serveth the town in divers respects, much better than the Skal of the backside of the astrolabe, and specially for to take the length of the Cortane of the wall of a town, or the distance between two towns, or any two marks standing directly against them, very profitable for all servitors, or other, for to have the use of. And now followeth the making of a cross staff, as much as shall serve landmens' turns. First take a piece of good, fine, and well seasoned wood, and let it be well plained, and very straight, of five foot long, and then let it be divided into .60. equal parts or inches, and then you may grave in it .1.2.3. and .4. and so till you do come to the end at .60. And be sure that you make every inch or part note, the one to be bigger or lesser than the other. Then if you will, you may make at the end of every .12. inches, a roundel or circle, and at the end of every .6. inches, half a circle: The making of the cross staff. then at every .3. inches, some mark or cross, and then your long staff is finished. Then in like manner you shall make an other short staff, called a Transuastorie, of two foot long, and in the very middle of it you shall make a square hole, such a one as shall go close to the longer staff without any swerving, and then shall you make .2. wings or plates of brass, one for the one end, and the other for the other end, then shall you make a chase or rygall on the one side of the safe, that the wings may be removed at your discretion: & then at .6. inches from both the ends you shall make a mark: And then there will be .12. inches between the 2. marks. Then in like manner, you shall make .2. other marks 9 inches from both the ends, and there will be .6. inches between the .2. Marks. And then in like manner, you shall divide the rest of the middle of the Transuastorie into inches equal parts, and then it is finished, saving that in the middle of the Transuastory you shall put a little piece of brass into the hole or socket that the longer staff doth go thorough, and then you shall make a little vice or worm, to the end that you may make the Transuastory to stand fast at your discretion: as these .2. figures do represent both the staff and the Transuastorie, and the uppermost, the longest staff ¶ The tenth Chapter showeth how for to use the cross staff, for to know the length of any Wall, or the distance between any two marks, and also the distance from you, unto any Wal or Mark. Now when so ever you list for to take the length of any curtain of a Wall, or the wideness between two marks, or any other thing what soever it be, then shall you take the longer staff, set out with equal parts, and put the Transuastorie upon it, through the hole in the middle of the Transuastorie: and then if you would know the wideness between any two marks, or the length of the curtain of any Wall, How to use the cross staff to take the widnes and the distance of any thing. and the distance unto them: then shall you do thus: first, set the end of the longer staff, hard under one of your eyes, winking with the other eye. Than your Transuastorie standing at .24. inches from the end of your long staff, which is the whole length of your Transuastorie: Then go forwards or backwards, standing upright with your body, and head, and both your feet together: then go forwards or backwards, looking toward your mark, till both the ends of your Transuastorye do agree with your two marks justly. If it be a Wall, measure the ground just to the middle of the Wall, and that shallbe the true length of the Wal. But if there be a ditch between you and the Wal, then remove your Transuastorie at the second standing, his whole length further forwards, that is, two foot: and then go backwards, till that you may see again, both the ends of the wall agree with the two ends of the Transuastorie. Then measure the ground between the two standings, and that shallbe the just length of the wall. And then the distance unto the wall, shallbe twice the length of the wall. Then if that the distance be further than the transitory will take, and the wall too short: then remove the plats or wings of the transitory, to the marks, six inches from both the ends of the transitory: and then the two plats or rings will be but twelve inches asunder. Then take the wideness between the two marks, or the two ends of any wall justly with the outsydes of the two plats or rings: then with the middle of your foot, there make a mark: then remove your transitory forwards or backwards, the length that the plats or rings be asunder, as you have ground: and then go forwards and backwards, till that your two plats or rings do agree again with both the ends of the wall: and then there make an other mark at your feet. Then measuring the ground between the two standings, it shallbe the length of the wall. And then for to know the distance unto the wall, you shall do thus: look how many times that the transitory is from the end next towards you, and especially the distance between the two plats or rings: so many times the length of the wall, shallbe the distance unto the mark: as for ensample thus, By the wall of a curtain of a town between two turrets, and my desire is to know the length of the curtain of the wall: and then I having the transitory upon the long staff, I could not come so near the town as I would. Then I removed the Plates or wings of the transitory, to the division of six inches from both ends, that was, twelve inches asunder: then I going forward, till that I did see both the turrets with the two Plates or wings of the transitory: and then at my feet I made a mark, and then in like manner I removed my transitory twelve inches forward, and then I went backwards, till that the two ends of the wall did agree again with the two Plates or wings of the transitory, and there is made an other mark. Then I measured the ground between the two standings, and found it ten score: then I did conclude, that the length of the Cortayne of the wall, was ten score from the one tower to the other. And now I knowing the length of the wall, I may easily know the distance unto the wall, as thus: now I do look how many times twelve inches that the transitory was from the end next unto me, and it was four and a half: that is, 54. inches. And now, because that the Plates or wings of the transitory were twelve inches asunder, and .54. maketh four times and a half twelve, and the length of the wall, ten score. Therefore I do conclude, the distance unto the wall, from the place of the last standing, to be four times and a half ten score: that is, forty and five score: as by the ensample of the figure following it is declared. Now furthermore, if the distance be further, than the two Plates or wings may be removed nyene inches from the two ends, that is, but six inches asunder: Then in like manner if that be too wide, you may remove the two plates or wings ten inches from both the ends, and that is but four inches asunder. Then in like manner, if that the distance be very far of, and the length of the wall be short, then may you remove the Plates or wings of the Transuastorie, eleven inches from both the ends: that is, but two inches asunder: And then, doing as before is rehearsed, to take two standings, that shallbe the mydenesse between any two marks. Provided always, that you remove the Transuastorie at the second standing, either forwards or backwards, so many inches, as the two Plates or wings be asunder, justly, and no more, and then you shall know the distance unto any mark or wall. When you do know the length of the wall, (and that is known, as afore is said, by the measure between the two standings) than look how many inches that the Transuastorie is from the end of the long staff next to your eye: then look how many inches that the Plates or wings of the Transuastorie are asunder, so many times the length of the wall shallbe the distance unto the wall. As for ensample thus: By the curtain of the wall afore named, being ten score long, & the Transuastorie to be set at .48. another ensample. inches from the end. First, the two wings stood at the very utter end of the Transuastorie, that is .24. inches asunder: then the measure unto the wall, shallbe twice ten score, and that maketh .20. score, because there is twice .24. in .48. Then in like manner the Plates or wings were set .12. inches asunder, and the Transuastorie .48. inches from the end. Then there is four times .12. in .48. Than you may conclude, that that is four times ten score unto the wall of the town, that maketh .40. score. Then in like manner the Plates or wings being set but six inches asunder, then there is eight times six in .48. which maketh eight times ten score: that is .80. score. Furthermore, if that the wings were but four inches asunder, the transitory being .48. inches from the end, there is .12. Times four in .48. So the distance unto the wall is .12. Times .10. score. that is .120. score. Then furthermore, the wings standing but .2. inches a sunder, but than it is an hard matter for to take it perfect: then there is .24. Times .2. in .48. so that maketh .24. Times .10 score: which maketh .240. score. Now furthermore, in like manner if that it fall not right just measure, then if that there be but half the measure between the wings, then for that, take half the length of the wall, and add it unto the rest of the measure: and if that it be three quarters, than three quarters of the measure, and for a quarter, one quarter. etc. The eleventh Chapter showeth you how for to take the length of a wall, when that you have not ground large enough for your two stations or standings. Now furthermore, if that you have not ground for to go forwards or backwards, so much as that the quantity of the wideness of the curtain, or the distance between any two marks shall come unto, there is a remedy for that, as this: look at what length you have set the distance between the two Plates or wings: then remove the trancevastory of the long staff, but half the length between the two Plates or wings, at the second standing, and then the ground between the two standings shallbe but half the length of the wall, or distance between your two marks: then double the measure that shallbe the length of the wall: then having not so much ground, remove the transitory but the third part of the measure between the two wings of the transitory, and then the ground between the two standings, shallbe but the third part of the length of the wall, and three times that measure, shall be the whole length of the curtain of the wall. Then having not so much ground, then remove the transitory but one quarter of the measure of 2. plates or wings, and then the measure between the 2. standings shall be but one quarter of the length of the Wall: and then 4. times that measure shall be the whole length. Then in like manner you may remove the Transatory but the 6. part of the measure & there Transitory the between the 2. standyngs shall be but the 6. part of the length of the Wall: and so forth to the 12. part or more, as you have ground or room. But here is one thing by the way, never take a short station between the 2. marks, as long as you may have a large: for that a little error often times multiplied, becometh a great and miraculous error in the end, yea an untolerable fault. Ensample. And now for your better Ensample of all those questions afore rehearsed of the length of a Brickwall 12. score long, first I took my cross staff, and sought out my ground right against the middle of the Wall: and because I could not come so near as I would, I removed the 2. plats or wings 6. inches from the 2. ends of the transatorye that was 12. inches asunder, and set the transatorye 36. inches from me: and then there where the 2. Plates or wings did agree with the two ends of the Wall, there at my feet I made a mark: then I had not ground enough neither for to go forwards nor backwards: therefore I removed my Transitory but 6. inches forwards, that is at 42. inches, and then I went backwards till that the 2. plats or wings did agree again with the end of the Wall, and there I made another mark. Then I measured the ground between the 2. standings, and found it but 6. score: then that being half the length of the Wall, 2. times 6. score maketh 12. score. Then I having not so much ground, removed the Transitory the third part but 4. inches forward, that is, at 40. inches. Then measuring the ground between the 2. standings, was 4. score: then three times 4. score maketh 12. score: then having not so much ground, remove the Transitory but one quarter forwards, that is 3. inches forwards, that maketh 39 inches: and then the ground between your two standings shall be but three score: and four times three score maketh twelve score. Then in like case if that you have not so much ground, you may remove the Transuastorye but the sixth part of the measure between the two Plates or wings, that is two inches forwards, and that maketh .38. inches: & then the measure between the two standings is but two score: and six times two score maketh twelve score, and so forth to the twelve part of the measure between the two Plates or wings of the Transuastorye, as by this Example. The 12. Chapter showeth you how to know the distance unto any two marks, or to the two ends of any wall by the extracting of the square root. Now furthermore, whensoever you have taken the wideness between any two marks, than you do know the just wideness, but not the true distance, except it were a Wall, you do know the true distance unto the middle, but not to the end. To know the distance unto any two marks by the extracting of the square root. Now therefore whensoever you would know the distance unto the ends of any Wall, or unto a church, and a Tree, or whatsoever that you have taken the wideness between them, than how far so ever that they be asunder, divide the measure into 2. equal parts. Then take the line of the distance unto the middle of the mark, and first multiply the distance in itself: then in like manner multiply the half wideness in itself: then part both the numbers of the multiplication, and add them both together: then extract the root of both the numbers, and it shall be the distance of both the ends of the Wall, or any other 2. marks, as now for example thus: by a Church and a bulwark. And my desire is to know the wideness between them, and first I take my cross staff and set the trancevastorye 24. inches from the end: and the 2. plaits or wings stood at the hard end: and then I took my first standing, as afore is declared, holding the long staff hard under the side of mine eye, and then I seeing the bulwark & the church agreeing with the 2. ends of the trancevastory, there at my first standing I made a mark, and then I removed the trancevastory 24. inches forwards, and that maketh 48. inches, and there where the two marks did agree again at the 2. ends of the trancevastorye going backwards, there I made an other mark, and then I measured the ground between the 2. standyngs, and found it 24. score. Then I did conclude the wideness between the Church and the bulwark, was .24. score: than it must needs be said, that the distance to the middle way between the bulwark and the church at the first standing to be .24. score: because that the transitory was once his whole length from the end next unto me, and then at the second standing the distance must needs be 48. score, because that the transitory was twice his whole length from the end next unto me, being .24. inches. And now for to know the distance unto either the bulwark or the church, then shall you do this: and for the nearest standing, when that the transitory was once his whole length from the end, and the distance unto the middle .24. score, than I did multiply .24. Times .24. and that maketh .576. And then from the middle between the bulwark and the church, was .12. score to the bulwark, and .12. score to the church. And then .12. score multiply squarely, that is to say, 12 times .12. and that maketh .144▪ Then add both your numbers together, that is to say, 576. and .144. and that maketh .720. Then extract the root of the number, and then there will stand in the quantity line .26. and .44. Will remain over. So that you may conclude, that from the nearest standing, to the bulwark or to the church, it is .26. score, and 11/13. part of a score, that is more near .51. Foot: and now from the furthest standing, and the distance unto the middle .48. score. Now multiply .48. Times .48. and that maketh .2304. Then multiply .12. Times .12. for the half wideness, that is .144. and that added unto .2304. maketh .2448. so extracting the root, there will stand in the quantity line .49. and then will remain over .4. which maketh .47/98. part, that is, near half a score, being .29. Foot. So I do conclude, that from the further standing to either the church or bulwark, it is .49. score, and near 29. foot. The thirteenth Chapter showeth how to know the distance unto any mark with the cross staff, without the extracting of the root, and also how to take the height of any thing with the cross staff. Now furthermore for your more ease, whensoever that you would know how far it were to any mark or place by the help of two marks, To know the distance unto any mark with the cross staff without the extracting of the root. with not knowing the length of the slope line, then shall you do thus: First, stand right against the mark that you do desire to know the distance unto, then seek out your mark, and be sure that the other mark make a square Angle unto that mark that you desire for to know the just distance unto: then remove one of the plates or wings of the Transuastorie to the very middle of the Transuastorye: then when soever you list to know the distance, first at your first standing, then make a mark: then for your next standing, remove the Transuastorye, but so much as the distance is between the .2. plates or wings, being sure that you take the mark that you do desire the distance unto, with that plate or wing of the middle of the Transuastorye: then (as afore is declared) look how many inches that the .2. plates or wings be the one from the other, so many times the measure that the distance is between the .2. Marks, shall be the distance unto that thing that you have taken with the middle of the Transuastorie. And so forth in all points as afore is rehearsed: as for ensample thus, by a tower that I do require the distance unto, An ensample. and then I standing with my face right against the tower, than I sought a tree that stood right beside the tower, that made a perfect square Angle to the tower and unto me: then because that the distance was somewhat far of, and the tree somewhat near unto the tower, therefore I set one of the plates or wings .6. inches from the end, and the other wing right with the middle of the Transuastorie. Then I set the end of the long staff hard under one of mine eyes, and took the measure true between the tree and the tower, with the plates or wings of the Transuastorie, the Transuastorie standing .48. inches from the end. And then I removed the Transuastorie .6. inches forwards, because that the .2. plates or wings were but .6. inches asunder, and that made .54. inches: and then I went backwards and made my second standing, and then I measured the ground between the .2. Stand, and found the ground .4. score, than I knew that the tree was .4. score from the tower. And then I looked how many inches that the transitory was from the end, and found it .54: then in like manner I looked how many times .6. there was in .54. and found .9. times .6. Then I must needs conclude, the distance unto the tower to be .9. Times .4. score, that is, 36. score: as by ensample of these figures following. The whole distance unto the tower is .36. score. Now furthermore, you may take the height of any wall, or tower, or Steeple, or any other thing, so that you set one of your plates or wings with the very middle of your transitory, As touching the taking of heights with the crossestaffe. & with the middle plate be sure to take the foot or base of the tower, Steeple, Wall, or tree: or else you may commit error. And by the staff you may know the wideness of waters, with divers other most necessary things, as this: When that you be in a town, for to know the distance of any place whose length or wideness that you do know, as by the length of a pike, or the wideness or distance between .2. Bushes or .2. stones, or any other thing, being sure that you take your sight true upon your marks holding your hands steedie till you may see your .2. Marks, end with your 2. plates or .2. Ends of your transitory, setting the end of your long staff close to the utter part of your eye, winking with your other eye, standing upright with your neck and head: and this doing, you shall not fail of the truth. For if that you err, the fault shall be in yourself, for that you have not taken it truly. Therefore that is very good to have a rest to lay your long staff on, & for to take a heythe, you must turn the Transuastorie one end upwards, and the other end downwards, and then you must hold the end of the long staff close to the corner of your eye. ¶ The fourteenth Chapter showeth unto you, how that you shall know the distance of any ship from you, and you being in another ship, and both the ships under sail, and going by the cross staff. etc. ANd furthermore, by the cross staff you may know the distance unto any ship sailing on the Sea, very exactly, you being in another ship sailing after them, or before them, or beside them: although that divers men are not of that opinion, for that both the marks are movable, whereby they cannot get any certain station or standing, as this is declared in the eight Chapter going before, how to know whether that one ship doth over top the other, by the sending of one up unto the top of the ship, to look how the Horizon cutteth upon the top of the other ship: and by that he doth know whether that the other ship doth overtoppe or undertoppe the ship that he is in: and then you knowing how many foot that your own ships top is in height from the top down unto the water, than you may know by that how many foot the other ships top is in height in like manner from the water very exactly. As touching the knowing the height of any ships top. But if that you do not know the just height of your own ships top unto the water, than you may know it thus, by sending one up unto the top, with a lead or a Plomet made fast unto a line, and so let down unto the superficial part of the water: and then measuring the line, you may see the height of the ships top that you are in, down unto the water: and then by the height of your own ships top, you may justly know the true height of the other. etc. And now to know the distance unto the other ship with the cross staff, you must do this: How to know the distance unto any ship. take your cross staff, and remove the two plates or wings of the Transuastorie unto the middle of the staff, and set them at a known distance between the two wings or plates, as at an inch or half an inch a sunder at your discretion, and that being done, then set the long staff hard unto the corner of your eye, wynking with your other eye, & then removing the Transuastorie forwards or backwards until that you may see and serve it truly, the top of the ship just with the upper plate, and the lower part of the ship hard unto the water with the edge of the lower wing or plate: and that done, then look how many times the wideness between the two plates that the transuastorie is from the end next unto your eye, so many times the height of the top down unto the water as that cometh unto, shall be the true distance between the two ships: which you shall work in this manner: First, the number of feet that the other ship is from the top unto the water being known, then look how many times the distance of the two wings or plates be a sunder, then look how many times that quantity the Transuastorie is from the end next unto your eye, then do thus multiply the number of feet from the top unto the water, by the number of the distance between the two plates or wings from the end next your eye: and then look what that number cometh unto, and then divide that by .60. and so many scores the two ships be a sunder justly. An ensample. As for an ensample thus: by a ship that was found by the order before rehearsed, to be .65. Foot from the top of the top mat unto the water, and the two wings or plates were set just an inch asunder. And then in the observing the Transuastorie was removing forwards and backwards until that he die see the top of the mast, and the lower part of the ship hard unto the two plates or wings: and that done, than he looked how many inches the Transuastorie was from the end next unto his eye, and found it .54. inches just. Wherefore he multiplied .65. by .54. for that .65. Foot was the height of the top unto the water, and the plates or wings were just one inch asunder, and the Transuastorie .54. inches from the end: and of that multiplication there cometh 3510. Wherefore divide that .3510. by .60. and that will show unto you the number of scores, and that .3510. Divided by .60. there will stand in the quantive line .58. and .30. Remaineth over. So that you may conclude, the distance between the two ships to be just 58. score and. ½. and by this order you may know the true distance between any two ships. etc. And yet for your better understanding, I will give a second ensample more easier to be understood, Another ensample. by a ship that was just .60. Foot from the top unto the water, that being a just score and no more, the two wings or plates being just one inch a sunder, and the ship being observed and was found to be where as the two plates did agree with the top and the lower part, that the Transuastorie was .40. inches from the end. Therefore they may conclude that the distance between the two ships was just .40. score, for that the top of the mast unto the water was just one score: that is .60. Foot, and the two plates or wings just one inch a sunder, and the Transuasitorie .40. inches from the end. etc. And also by this order you may know the distance of any ship from the land. etc. And thus I do end the conclusions of the cross staff. etc. ¶ The fifteenth Chapter showeth unto you, how you shall make an instrument whereby you may describe a Region or country, which you may call an horizontal Sphere: and also how to take the plat of any ground. etc. Then resort to your Paper, and look upon the instrument at what point and degree the Athelida is standing on, then upon the point and degree of the Circle write the name of the town, or Village, or hill, then turn the Athelida to the next mark: and so forth, till you have taken all the towns and Villages round about the country or coasts that be within the Angle of sight, and write the names of all those towns at the point and degree that the Athelida doth stand upon, at the time of the taking of them with the 2. sights. And furthermore, writ in the paper the 4. principal winds, as East, West, north, and south. Even as the coast of the country doth stand: and then draw right lines from the centre of the Circle too the Circumference, to the place where the names of the towns were written, and so passing right to the edge of the Paper. And thus do by every town written on the edge of the Circle, and then that station is finished. And then furthermore, look to what place that you do mean for to go unto for to make your second station, being one of those that you have observed afore. For the first observation is to no purpose: so that you must of force have 2. And then upon that line that the name of the town or hill that you do mean to go unto, set one of the feet of the compasses, and with the other foot of the compasses make an other circle in like manner: then draw an other Meridian line, and be sure that both the Meridian lines do agree the one with the other, and so divide that circle into 32. equal parts, as the other was in all points: and then go up unto some high place that was the mark before, and then lay your instrument afore you again, setting it by the needle due South and North, and so let the instrument stand. The second observation. And then turning the Athelida to such towns as were taken before, looking thorough both the sights were where the Athelida doth stand, and write the names of those towns again upon the edge of that circle at the point and degree that the Athelida doth stand upon: and do thus till that you have taken all the towns that were observed at the first standings: and then draw right lines from the centre of that Circle, by the edge of the Circle, to the names of those towns that were written, and so the lines for to run right to the sides of the Paper. Then look where that the lines do cross, there make a mark: for there standeth the town or place that you have observed. And now in like manner, if you list, you may know the distance from one town to an other, as thus: first, you must measure the distance between any one town to another: & that ground being measured, To know the distance unto any place. you must make a Scal or trunk of measure on the side of the paper, and then measure the distance between those 2. Towns in the paper: then according to that proportion of measure make your miles in the scall or trunk of the card or map: and that being done, you may know the distance with a pair of Compasses between any one town or towns to the other, by the scall of the card: and then this being done, you may make that fair in an other thing without lines, and bewtyfye that at your pleasure, as for example thus, by the parts or country about Grauesende. first, I took the Instrument, and then in like manner I made a Circle in a sheet of paper: then I drew a Meridian line, An Ensample. that is to say, a line from the South to the North: and I divided the Circle into 52. equal parts, and then I wrote the 4. principal winds in the four sides of the paper: that is to say, the East, West, North, and South: and then I went up to a hill that standeth beside Grauesende, called Ruggon hill, and there beside the mill I made my first standing: and then I observed all those towns and places following: first cliff Church, and that I took North-east and by East, and the sixth part of a point to the eastward: the next was West Tilbrye church, North, and ¾. of a point to the eastwards, and then I took the bulwark of West Tilbrye, North, and ¼. of a point to the westwards: and then I took bravesende church steeple, North and by West, and ⅔. Parts of a point to the westward: and then I took little Thurrock, Norwest and by North, and the 6. part of a point to the westward: then I took Gray's Thurrock Northwest, and the 6. part of a point to the westward: & then I took saint Clement's church, West, Northwest, and ¼. to the northwards: then I took North fleet Church, West and ●/4;. Parts of a point to the Northwards: then I took Swankam church, due West: then in like manner I took the Vinyard Mill, West, Northwest, and ¼. Part of a point to the westwards: then I took Mappam Church south-west, and ⅕. part of a point to the westwards: then I took Cobbam church, Southeast, and by South, and ⅕. Part of a point to the southwards: then I took shorn mill, East, and by South, and ⅖. Parts of a point to the southward: Then I took Chaulke church, East, and ⅖. of a point to the southwards: and so I make an end of that standing. And now I chose out for my second standing, West Tillary church, & I did draw a line from the centre of the Circle to the Circumference of the Circle, to the title of Tilberye church being North, and ¾. of a point to the eastward. the line passing right to the edge of the paper. And then I took a pair of compasses, and set the one foot of the compasses upon that Line, and with the other foot I made a Circle: and then I made an other Meridian line by the other in the other Circle, so that the one did agree with the other: and then I divided the Circle into 32. equal parts, and then I went over the water to West Tilbery Church, and then I laid my instrument before me, and set it due North and South, and there I observed all the towns and places before named: as cliff, East and 1/●. Part to the North: shorn mill, and Chaulk Church, South East & by South, and ½. parts to the Southward. Cobbam church, South and by East, and ⅙. part to the Southwards. Ruggon Hill, the mill South, ● ¾. to the Westwards. Mepham Church, South and by West, and ½. to the westward. Tilberye Bulwark and Gravesend, South, south-west, and ½. to the southwards. north fleet church: south-west, and ¼. to the South. Swanskam church, south-west, and ¾. to the westward. Saint Clement's church, west, and by South, and ⅛. Part to the West. Gray's thurrock, West, and ⅔. Parts to the South. Little Thurock, West, and ⅖. Parts to the southward. The vinyeard Mill, West, and ⅕. part to the southward. And so I make an end. And then I drew lines from the centre of the Circle to the Circumference, to the title of the names of the towns, and so I passed by the right lines to the furthest parts of the paper, first upon the one Circle, then upon the other, till that I had drawn so many Lines as that there were towns in both Circles: and there where that the lines did cross the one the other, I made a mark: For there standeth the town, as by this Ensample it doth appear. The .16. chapter showeth you how for to make a Trouke or skalle of measure in a map or card, whereby you may know the distance in miles that it is from one town to an other. Now this being done, you may know the distance from any one town to an other. For as many towns as you have observed, and if you list you may go from place to place, till that you have observed and taken all the towns in a whole region or country, as thus: first measure the distance in miles from any one town to another, than that distance being known, make a trunk or Skall of measure with a pare of compasses, according to the distance taken with the compasses between those .2. How to make a tronck or Skal of measure to know the distance from any one town unto another. towns in the paper. Then that being truly divided into miles and half miles, and quarters of miles, than you may know the distance from one town to an other thorough all a whole region or country, by the replying it with a pair of compasses, as you may perceive by the rule or Skall made upon the other side of the paper: and the roundles with the pricks in the middle, be miles: and the pricks measured between them, is one quarter of a mile: as ensample, for the making of a trunk or Skall. First, I measured the distance between Northfleete Church & Gravesend Church, & found the measure upon the right line a mile and half a quarter: and then I made a trunk of Skall in the card, as thus: then I took a pair of compasses, and measured the distance from the crossing of the .2. Lines of the .2. circles of the title of Grauesende, and the title of Northefleete: and then I finding the measure to be a mile and. ⅛. Parts of a mile, I did rebate the .8. part of a mile: and then that which did remain was just a mile: and then according to that proportion of measure, I made a Skall or trunk of measure on the side of the .2. Circles, and divided it into .4. Equal parts, and every one of these parts to be one quarter of a mile, as by the demonstration afore made, it doth appear. Now whensoever that you do desire for to know the distance from any one town to an other, An ensample how to reply a pair of compasses to know the distance unto any town assigned in any card or Map. then take your compasses, and open the compasses to the wideness between the .2. Towns, that the one foot might stand upon the one town and the other upon the other. Then set your compasses to the Skall or trunk of measure: there shall you see the distance of miles open with half miles and quarters of miles: as for ensample this, by certain places afore named, which is (cliff Church, and the vineyard mylle,) and the third to be Grauesende. And the vinearde mill, and cliff church, the one beareth from the other by a right line East & west. cliff Church a quarter and half a point to the north of the East, and the vineyard mill a quarter of a point to the South, of the west, and the distance between them by a right line, over the water and the land .8. Miles and. ⅖. Parts of a mile: and cliff church bears from Grauesende, East, north-east, and to the North: and the distance over the water and the land by a right line, 4. miles and ⅙. part of a mile. Then the vineyard mill bare from Grauesende, West and by North, and part of a point to the North: and the distance to the mill from Gravesend .4. Mile and. ¾. Parts of a mile: as by this ensample it doth appear. And now you knowing the distance unto any place assigned, you may know the height of any hill, or the deepness of any valley, by the order declared in the Chapter there by the scall, or else by the degrees. etc. The vineyard mill. The .17. Chapter showeth unto you how you may make a card or map for any country, placing in it the true Longitude and the true Latitude: And also how for to know the true longitude and the true latitude. NOw furthermore, if that you list, you may make a card, & beautify it at your pleasure, & make it fairer, & you may draw the longitude and the latitude of every place, as thus: first, you may take the distance of every town and Village, and Hill, or any other notable mark whatsoever it be, and then make a mark for the name of such a town, according to the observation that you have observed afore: both the distance, and towards what cost of the country the town doth decline, according to the crossing of the .2. Lines, placing in it the principal rivers or waters: and then in the very middle of the map or card make a Meridian line, to the intent for to rule all the rest of the work. And then in the margin of the card, from the South to the North, How to make a card or plad Typography and to place the longitude and the latitude in it. upon both of the edges of the map or card, place the latitude of the country, (that is to say) at how many degrees that the pole artic is lifted above your Horizon, as you may know it by your astrolabe, by the altitude of the same upon the Merydian line, knowing what declination, the Sun hath upon that day of the month that you take the height of the sun. How to take the latitude of any place. And then if that the sun hath North declination, you must subtract or pull away the sun's declination with degrees and minutes: & if South declination, you must add or put to the suns declination with degrees and minutes: and then that which shall remain shall be the altitude of the Equinoctial. Then pull that sum out of .90. degrees, with degrees and minutes: the remainder shallbe the height of the North pole artic above the Horizon. And furthermore, you may know the latitude of any town or country by the stars of the South, or stars of the North, knowing there just declination from the Equinoctial, doing by them as you do by the suns declination in all points. And then if that they be Northern stars, you must know the distance from the pole, and then if that the star be above the pole than you must pull that sum away with degrees and minutes. And if the stars at the time of your taking of them, be under the North pole, then put to that which is the distance of the star from the pole, unto the height of the star: and that in like manner shall show unto you the true height of the North pole artic above the Horizon. And then in the margin of the map of the East side and of the West side, you may write the latitude directly, in that East and west line of that place which you have observed the latitude of the North pole: and then that being truly known, you may know the true latitude of all the towns in a whole country or Region, knowing the distance to every town or place, as thus. Every .60. miles going directly South and North, doth answer unto one degree. And then further, if that you would place the longitude, and that you cannot get without a globe, or else a card Cosmographye, or else you must follow some author who hath written thereof, and because you cannot get the longitude with no instrument, for that the whole frame of the firmament with all the lights thereof be carried round about in 24. hours, so that there remaineth no mark nor light that standeth still, but only the two poles of the world: therefore I will show unto you how that you may get the longitude with a globe or card Cosmographye, so that it be truly placed in it. How to know the longitude. First you must measure the longitude from the Meridian of the canary islands, or other wise called the fortunate islands, and so take the number of degrees from that place unto any other that hath that same Meridian that your town or place hath: and that shallbe the number of the degrees for your place. And then you having one place true, you may find the just longitude in a whole region or country. But there is one special thing to be noted, and that is this: The degrees of longitude be not so many miles in length as the degrees of latitude. For as those places that be to the south parts of this side or under the equinoctial be as long as the degrees of latitude, so that to any of the 2. poles shorter & shorter, as I have declared in the .16. Chapter of my book called the Regiment for the Sea, as by this Ensample it doth appear, by the realm of England. Now whensoever that you do desire to know the longitude and the latitude of any town or place in a card, after that the map or card is drawn, then do this: First, by the ensample afore made, hold a line or a string, How to know the longitude & the latitude in a card or map. the Map lying flat & plain upon a table before you. And first for the latitude, hold the line East and West right over the town and place, then by the ensample afore made, you do see the latitudes be upon the East side, and upon the West side: then by the line you shall know how many degrees and parts of degrees, the Pole is raised above the Horizon. And then in like manner for to know the longitude of any town in a map or card, then hold the line due South and North right over the town or place whose longitude you do desire for to know: and for to hold it due South and North, which is called your Meridian line, you must do this: For that the degrees be shorter to the North parts, than they be to the south side or parts of the map or card, therefore you must seek the number of degrees both at the South side and at the north side all at one time: holding the line proportionable right over the town: that is to say, half degree for half degree, and quarter for quarter, and so forth to the least part of a degree. The eighteenth Chapter showeth unto you how you may place all the principal rivers or waters truly in any card or map. NOw furthermore, as it is sufficiently declared before, how for to describe or draw a Map or Card, for a whole region or Country, and also how to find the distance from one town to an other: therefore for that it is one of the special matters, in like manner to draw or describe the principal rivers or waters within a Region or country into a map or card: therefore after that you have observed all the notable towns and places worthy of memory, then if you can take a boat and so go all the whole length of the water or river in the very middle between both the lands, and then with a mariners compass you may see how that the river doth trent or turn: than you having the observation about you, than you may know how long that the water doth trent by that point, or wind by the marks of the land, How to place the rivers or waters in a card or Map which you have afore observed: and then so often as the water doth turn or compass about, you shall see by your Sea man's compass, and how much: and still you shall know the length by the mark upon the shore. And then you must draw a crooked line into the Paper that you have noted those towns and places, in the Region where that the principal places be, according to the crossing of the 2. lines, in every place the crooked line to be made according to the trentinge of the river or Water, and every treminge to be according unto that point or wind that the compass did show to you: and this being done, you may know the wideness of the Water by the observation afore taken, and then you may draw your Plates, and so bewtifye it at your pleasure, taking the crooked line from the very middle of the Water. ❧ A Table of the Contents of the first part of this book called a treasure for travailers. FIrst to the Reader of this first part. The first Chapter of the first part containing the making of the Quadrant with the Skall, whereby you may know the height or lowness of any thing. The second Chapter is of upright shadow, that is to say, to know the height of all things taken within the length of the thing. The third Chapter showeth how for too know the height of any thing with the Skall by contrary shadow, that is to say, without the length of any thing so taken. The Fourth Chapter showeth how to take the part of any height, as the length of a window or such like. The fifth Chapter showeth how for to know the distance of many things that is from you, and also whether any other tower be higher or lower than the Tower that you be upon. The sixth Chapter showeth how for to know the height of a Hill, and also the distance unto the top of any hill with the Skall. The seventh Chapter showeth you by the Skall of the astrolabe to know the true wideness of any Water, or how far that any ship is of from you, or to take any great distance by laying the astrolabe flat before you with the Skall upwards. The Eight Chapter showeth unto you if that you do know the distance, than you may know whether it be higher ground or lower than the place that you are upon, & how much, both by the parts of the Skall, and by the degrees, and also you may know whether that one Ship be higher than another. The ninth Chapter showeth the making of a cross-staff that in some cases is better than the Skall of the astrolabe or Quadrant. The tenth Chapter showeth how for to use the crossestaffe, for to know the length of any wall or the distance between any 2. marks, and also the distance from you unto any wall or mark. The eleventh Chapter showeth you how for to take the length of a wall when that you have not ground large enough for your .2. stations or standings. The twelve Chapter showeth you how for to know the distance unto any 2. marks, or to the 2. ends of any wall, by the extracting of the square root. The thirteenth Chapter showeth how for to know the distance unto any mark with the Crossestaffe, without the extracting of the root, and also how for to take the height of any thing with the Crossestaffe. The fourteenth Chapter showeth unto you how that you shall know the distance of any ship from you, and you being in another ship, and both the ships under sail and going, by the cross staff. The fifteenth Chapter showeth unto you, how that you shall make an instrument whereby that you you may describe a region or country which you may call a horizontal, and also how for to take the plat of any ground. The sixteenth Chapter showeth you how to make a Trounke or Skall of measure in a map or card, whereby you may know the distance in miles that it is from one town to another. The seventeenth Chapter showeth unto you how you may make a card or map for any country, placing in it the true longitude, and the true latitude, and also how for to know the true longitude, and the true latitude. The eighteenth Chapter showeth unto you, how you may place all the principal rivers or waters truly in any card or map. Finis. The Argument of the second book, of the Treasure for travailers. The second book of the Treasure for travailers, showing how by the longitude and latitude of any city, town or place, for to know the distance in miles unto them, and also by what point or wind of the compass they be from you. And also there is showed in this book, how divers notable cities, towns or places, do bear from the city of London, both in Europe, Africa, Asia and America, with sundry principal islands in the sea, both by what distance they be in miles from London, and what wind or point of the compass they are from London, & also their longest day, & the diversity aspect, that is to say, how much the moon shall change rather or later, than it doth at the city of London: being very necessary for all sorts of travalers' either by Sea or by land: Written by william Bourne. ¶ To the courteous Reader. friendly Reader, there is contained in this second book, how by the longitude and the Latitude, to know the distance unto what quarter of the world that any place assigned is from you: that is to say how many miles, (according unto our english account) and by what point of the compass any city or town, or any other notable Place is from you wheresoever you be, upon the face of the whole Earth. And for that the city of LONDON is the most notable, & the famousest place here in England, therefore I have thought it good, to assign the city of London to be the place appointed, how far sundry notable Cities and towns, and other places worthy of memory are from the city of London, both their distance in miles, & unto what quarter of the world they do bear from the city of London, according to their longitude and latirude, accordingly as sundry authors have set down their longitude and latitude: and also there is contained in this second book, the diversity aspect, that is to say, how much that the moon shall change rather or later, than it doth at London, according unto the Longitude of the places that are mentioned in this second book: and also the length of the longest summer day at the places named in this second book, according unto the latitudes of the places set down in this second book. And for that there is no person that hath travailed generally through the face of the whole earth, therefore they must needs of force follow such authors, as have written thereof, whether they be true or not: and therefore you must needs take them as they be, for otherwise I know not how it is possible for to do it, but only to follow the best and most Learned authors that have written in those causes. And yet the learned men that have been afore time, must of force follow those that have given unto them the notes of the longitude and the Latitudes of any places that they have not been at themselves, whether they be true or not. And there be a number of persons, who if they do find but a small fault in any book, then by that means they will go about to discredit the whole matter, often repeating the matter, if they do find any error in it: as who should say, what a cunning man he is, although in all the rest of the whole book, he is not able to say any thing thereunto. And it may be possible, that he may have no judgement in the rest of the causes how necessary so ever the rest of the substance of the matter is. Wherefore (gentle Readers) if you do find any fault in this book, then gently give me warning thereof: and if you do amend the faults therein contained, than I shall be the more beholding unto you etc. For as touching the longitude and the latitude of places, men must credit those that have been there, for the truth of the matter: and yet every man that hath been at any place, cannot do it, for the .100. person that hath travailed unto places, is not able to take the true latitude, but much less the longitude of any place. And furthermore, as touching the true distance unto any place assigned, that cannot be by any one point of the compass, as is declared in this book. etc. And thus (gentle Readers) I betake you unto the almighty God for evermore. ¶ The second book of the treasure for travailers. The first Chapter of the Second book, showing you how for to know the distance unto any town upon the face of the earth, and what is to be considered in the doing thereof. etc. Now beginneth the second book, showing by longitude and by latitude the distance unto any town, or city, or place upon the face of the earth, keeping one point or wind over the Sea and land, although that it be not the very nearest way, for the very nearest way over the Sea and Land can not be by one point of the compass, except it be upon the Meridian line, that is, due South or due North from you: or being under the Equinoctial, to be due East or West. But if it be in any other place from under the equinoctial, although it be due East or West, The nearest way over the Sea and Land is not by any one point of the compass. both the places to be under one parallel: yet in the going due East and West, is not the nearest way over the Sea and Land, but the next way over the Sea and land is, by divers winds or points of the compass: and the further from the Equinoctial to either of the two poles, the greater changing of the points of the compass. For the next way over the Sea and the Land, unto any place, is to go by the great circle which is equal unto the equinoctial or the Meridian circle, which will not be according unto any one point of the compass, but unto divers: as for proof thereof you shall have this for an ensample thus: An ensample. that in the latitude of .60. degrees that there were two towns or places in that parallel, the one being opposite or right against the other, that is .180. degrees, and a degree in that parallel doth contain .30. Miles. And now to go just East or West in that parallel, to come unto the place assigned, it is .5400 miles: as for proof thereof, multiply .180. Times .30. but that is not the next way unto the place assigned: but the next way is to go by the Merydian line, that is to say, to go due North, until you do come right under the pole, and then to go by that Merydian, due South, till you have that latitude again: and then it is but .3600. Miles, as you may know by plain multiplication, as it is from the latitude of .90. degrees, unto the pole, to go due North .30. degrees, and from the pole, Southward again, other .30. degrees, that is in all .60. degrees: and then to multiply .60. Times .60. it showeth the true distance, which is but .3600. Miles. And to go by the parallel line, that is due East or West, than it is .5400. Miles, that is half so much more, as by plain proof you may know. But if the two places be both underneath one parallel, & be shorter than 180. degrees asunder, than it requireth to go by divers points of the compass, and not by the Meridian, The greatest compass of the earth, 21600 miles according unto the passing of the great circle, which doth contain in circumference 21600. miles, which is the greatest compass of the earth, and not according unto more parallels than one, which is the Equinoctial, neither unto no one point of the compass: for any point of the compass will bring you unto the poles of the world, or very near, except those that be pararel, which is East or West, All the points of the compass will bring you unto the pole of the world except the East or West. as all right lines draw being extended, excepting lines parallel, will cross the other in the end: so all the points of the compass do wind until they do come unto the poles or very near the poles of the world, as they be all hilical or Spherall lines. Wherefore there is no one point or wind, that can be prescribed to be the next way by that point unto any place assigned, but only the Meridyan line or lines: and to go East and West, then to be under the equinoctial, for the next way else is by sundry points of the compass etc. Wherefore I omit to say any more thereof, but only to show unto you, how for to know the distance unto any town or place situated upon the lace of the whole earth, by any one assigned point of the compass, then for to know the true distance over the Sea and the land. And I do show it this way, You cannot pass the nearest way for it is thorough the frozen zones. for two causes, the first is this, for that it is not possible to pass the next way, by the means of the frozen Zone. Wherefore it is supposed, that it is not navigable in those Seas, neither passageable by land in those countries: and the second cause is this, as before is declared, in the going the next way, it doth require to go by sundry points of the compass, which would be but a confused matter, for the most part of those persons that do desire to know the distance unto any place assigned, neither shall he know so readily which way it standeth, or beareth from him. A confused matter to say a place doth stand by divers points of the compass. And furthermore, in the knowing the distance unto any place assigned, and by what point of the compass it beareth, this is to be considered, that the Longitude doth begin at the Meridian of the canary island, and so to follow unto the eastwards, and so ending at .360. Again at the canary islands, as I do show in my book called the Regiment for the Sea. The second Chapter showeth unto you, how you may know the distance unto any town situate upon the face of the whole earth, so that you do know the true Longitude and the true Latitude of them. NOw furthermore, if that you do know the Longitude and the Latitude of any town or towns, situate upon the earth, you may know the distance unto them, as before is declared, as thus: If that the town be just East or West from you, that is to say, that your town or place is under the parallel that the other town is, To know the distance of any town from you, if that both the places are in one parallel. that is to say, that the Pole arctic of that town or place is so many degrees above the Horizon as your town is, both in degrees and minutes: then shall you seek how many degrees of Longitude, the other town doth differ from yours: than you shall seek how many miles that one degree shall answer unto it, in that parallel, and then you shall multiply the one by the other, that is to say, the degrees by the miles: and that sum which cometh of that multiplication, shallbe the distance between the two towns: as for ensample, thus: by the city of London & Answerpe in Brabant, which differeth but .4. An ensample. minutes in Latitude: for at London, the Pole is raised .51. degrees & .32. minutes, and at the city of Antwerp, the Pole is raised .51. degrees .28. minutes, therefore we be both under one parallel. Now the Longitude of London is from the Cannarie islands .19. degrees, and .54. minutes, and Antwerp's Longitude is .26. degrees & .36. minutes, so that Antwerp standeth East from London .6. degrees .42. minutes. Now must I know how many miles a degree containeth in that parallel, (and of that I do make mention in my book called The Regiment for the Sea, in the .16. Chapter) and that I do find to be .37. Miles to one degree. Then I multiply .6. times .37. because that it is .6. degrees & .37. Miles to one degree: and of that multiplication there cometh .222. Then there is .42. minutes more, and that .42. minutes containeth near .26. Miles: so that the whole sum of miles from London to Antwerp, by a right East line over the Sea, and the land, is .248. Miles. Now furthermore, if that town or place have that Longitude that your town hath, and hath another Latitude, To know the distance if that both the places are in one Merydian. that is to say, that it doth stand due South or North from you, having all one Meridian line, then must you look how many degrees the other town is south or north from your town: and then you knowing that, you may know the distance to any town or place that standeth underneath your Meridian, allowing .60. Miles for every degree of Latitude, as for ensample thus: by the city of London, and Roan in Normandy, An ensample. which hath in manner all one Longitude, as the city of London hath .19. degrees .54. minutes of Longitude, as afore is declared: so hath the town of Roan .20. degrees .3. minutes, which differeth 6. miles to the eastwards of the Meridian of the city of London, and as it is afore rehearsed, that the latitude of London is .51. degrees and .32. minutes, the Latitude of Roan is 49. degrees and .10. minutes: so that Roan standeth .2. degrees & .22. minutes to the southwards of the city of London. And then multiply .2. Times .60 which maketh .120. and then there is .22. minutes more, then that cometh to .22. Miles, so that .120. Miles, and .22. Miles, maketh in all .142. Miles, the distance between the city of London and Roan, over the sea & land, by a right line between them. Now furthermore, if so be that any town or country hath an other longitude and an other latitude, then yours hath, then to knew the distance between them, you must work thus: First, look what latitude that your town hath, and then look the latitude of the other town that you would know the distance unto, How to know the distance, if that both the places doth differ both in longitude and in latitude, that is to say, that is neither under your parallel nor Meridian. then that being known, you must seek the longitude of the other town how much it doth differ from yours: then look how many miles of the latitude will answer to one degree: then that number being multiplied, the number of degrees by the miles, and that showeth how many miles that it is from the Meridian of your town to the Meridian of the other town. Then the other town hath an other latitude than yours hath, and if the town be to the northwards of your town, than the degrees of that parallel, shall be shorter than the degrees of your parallel, and if the latitude of the town be to the South parts of your town, then shall the degrees of the parallel be longer than the degrees of the parallel of your town. Then in like manner as you have multiplied the number of miles by the degrees of your town, so in like manner you shall seek how many miles will annsweare unto one degree in that parallel: Then multiply the degrees by the miles, and it will show unto you the distance of miles from the other town too the Meridian of your town: then the distance of the Southermost town, from the Meridian, is more miles than the other town is. Therefore you shall add or pull both your numbers together, and then take half that for your East and West line, then shall you multiply the number of miles in itself, and keep it in memory: than you knowing the number of miles of Latitude, that the one town doth differ from the other, then in like manner you shall multiply that number in itself, than the multiplication of both the numbers you shall add together, than you shall by extraction of roots, seek the square root: that being known, shall be the just distance by that point or right line over the Sea and the land, from the one town to the other: as for ensample thus: By the city of London, An Ensample by Jerusalem and the city of London. and the city of Jerusalem now being destroyed, which was sometime the most famous city on earth, and the Latitude of London, as afore is declared, being 51. degrees 32. minutes, and every degree of our parallel is 37. miles: and the Latitude of Jerusalem is 31. degrees, and 22. minutes, then for every degree in that parallel, shall be 51. miles. Then I knowing the Longtitude of the city of London for to be 19 degrees and 54. minutes, than I do seek the Langtitude of Jerusalem, and I find it for to be 65. degrees, and 45. minutes. Then I do pull away 19 degrees 54. minutes, out of 65. degrees 45. minutes, and then remaineth 45. degrees 51. minutes, and so many degrees and minutes is Jerusalem east from the city of London. Then first I do multiply the miles in a degree of our parallel, as this: being 45. degrees and 37. miles to one degree. Therefore I do multiply the one by the other, that is 45. times 37. and of that multiplication cometh 1665. then 51. minutes more, and that cometh near unto 32. miles: then put 32. unto 1665. that maketh 1697. and so many miles it is from the city of London unto the Meridian line of Jerusalem. And now you must multiply the number of degrees into miles for the latitude of Jerusalem, which is 51. miles to one degree in that parallel, and the degrees be in number 45. degrees 51. minutes: therefore I do multiply 45. by 51. and of that multyplycation there cometh 2295. Then there is 51. minutes more, and that cometh near unto 44. miles: and put 44. unto 2295. and that maketh 2339. and so many miles it is between Jerusalem and the Meridian line of the city of London. Then this being done, I do add both the numbers together, that is to say, the number of miles in the parallel of London between both the Meridian's, the one being .1697. and the other for to be 2339. then adding both these numbers together, maketh 4036. then take half that number for your true East and West line, which will be 2018. miles: then I do seek the diversity beeweene the 2. parallels as thus. The pole artic of London is raised 51. degrees and 32. minutes, and the pole artic of Jerusalem is raised 31. degrees and 22. minutes. Then I do subtract 31. degrees 22. minutes, out of 51. degrees 32. minutes, the remainder is 20. degrees 10. minutes: then I do multiply the number of degrees by miles, 60. miles to one degree, because that they be degrees of Latitude, thus .20. times 60. & of that multiplication cometh .1200. and then there is 10. minutes more, and those 10. minutes cometh to 10. miles: so that the whole sum of miles from the parallel of London to the parallel of Jerusalem, is 1210. miles. And now for to find the true distance over the Sea and the land by a point or line: you must do thus by the exctactions of roots. first, you must multiply the Longitude and the number of miles in itself, as it is afore rehearsed: the half of the miles of the distance between the 2. Meridian's of both the Latitudes added together, that is to say, as afore is rehearsed .2018. times 2018. and of that there cometh 4072324. Then multiply the distance between the 2. parallels in itself, that is to say, 1210. times 1210. & of that multyplycation there cometh .1264100. Then I must add or put both these numbers together, and these 2. numbers being both together, From Hierusalem unto London 2352. miles. and 25 26. are 5536424. This being done, you must extract the square root of this number, and the square root of 5536424. maketh 2352. And 4520/4704. part, and that doth contain in miles from Jerusalem to London by a right line over the Sea and the Land 2352 miles, and near 25/26. parts of a mile, the just distance between Jerusalem and the city of London. A second Ensample by Venice and London. So that the longitudes and the latituds be true. Yet furthermore, for your better Ensample, by the city of Venice, as the longitude of London is 19 degrees and 54. minutes, the longitude of Venice is 35. degrees 30. minutes. Therefore subtract or draw 19 degrees 54. minutes out of 35. degrees .30. minutes, the residue shallbe 15. degrees, 36. minutes. Then Venice is 15. degrees .36. minutes, to the eastward of London, than the latitude of London being 51. degrees and 32. minutes, the latitude of Venice is 44. degrees and 45. minutes. Then take 44. degrees 45. minutes out of 51. degrees 32. minutes, the remnant shall be 6. degrees 47. minutes. So that Venice is 6. degrees 47. minutes to the South part of London. Then you shall multiply the number of degrees of longitude into miles, and first for the parallel of London, as afore is declared .37. Miles to one degree: and the degrees of longitude being .15. degrees .36. minutes, you shall multiply 15. times 37. and that cometh to 555. Then there is 36. minutes more, and that cometh to 22. miles more. Then put .22. Unto .555. and that maketh .577. Miles, the distance between London, and the Meridian of Venice. Then you must seek how many miles will answer to one degree in the parallel of Venice, that cometh to 43. miles to a degree. Then multiply the degrees of longitude by the number of miles in that parallel, that is 15. times 43. and that cometh to 645 then the 36 minutes more cometh unto near 26. miles. Then put .26. Unto .645. and that maketh .671. so that it is .671. miles from Venice unto the Meridian of London. Then put both these numbers together, that is to say, the distance between the Meridian of London and the Meridian of Venice, in the parallel of London, and the parallel of Venice, the one being 577. miles, and the other 671. miles: and those 2. numbers being both together, maketh 1246. Then take half that number for your East and West line, & that cometh unto 623. And now I do conclude, that Venice is East from London 623. miles. Then you must multiply the degrees of latitude into miles 60. miles to one degree, and the Latitude of Venice being 6. degrees to the South part of London: therefore I multiply .6. times .60. and that cometh unto .360, then there is 47. minutes more, and that maketh .47. miles: then put 47. unto 360. then it will be 407. This being done, multiply the miles of longitude in itself, as 623. times 623. and that cometh unto 388129. Then multiply the latitude in itself, that is to say, 407. times 407. and that cometh unto 165649. then add or put both these numbers together, that is to say, 388129. and 165649. and that maketh 553778. And now you must seek the square root of both these numbers added together by extracting of roots, & that will be 744 & ●2/744. part, and that it is near ⅙. part of a mile. So I do conclude that the distance from Venice to London, by a right line over the Sea and land, is 744. miles, and ⅙. part of a mile: so that the longitude and the latitude be truly taken. And thus may you do by all other towns and places situate upon the face of the whole earth, whether that the distance be much or little: so that you may know the true longitude and the true latitude, and so resort to the true length of the parallel as afore is declared. The third Chapter showeth how for to know unto what quarter of the World any place doth stand from you, that is to say, by what point of the compass, you knowing the true Longitude and the true Latitude etc. ANd furthermore, you knowing the true longitude and the true latitude of any town upon the face of the whole earth, than you may know unto what quarter of the world it doth bear or stand from you: that is to say, by what point of the compass, as this: If a-that any two places have both one longitude, that is to say, one Meridyan line, & hath an other latitude, that is to say, that the North pole is raised more degrees than yours is, than it is North from you: if few degrees, then that beareth South from you. And also if that it hath your longitude, and have the South pole, North or South. above the Horizon, then in like manner the place is due South from you etc. And furthermore, if any two places have all one latitude, and hath another longitude, being both in one parallel, and if that it have more degrees in longitude, than your town hath, than that city, town or place, is unto the eastwards of you. If fewer degrees in longitude, than your town hath, East or West. than it is West, from your city, town, or place, as in the Chapter going before is declared. If that it be more degrees in longitude then your city, town, or place hath, by .180. degrees, than that place is West from you, although both the places have one latitude, that is to say, in one parallel. And then to know how many miles, you must first note the degrees of longitude that it hath from the Meridian of the Canary island: Note. and then rebate that out of .360. and then add or put unto that number of the longitude of your own place: and so multiply the number of miles in that parallel, & that shall show unto you the number of miles, that the city, town, or place is unto the westward of your place, and the reason thereof is this, for that the circumference of the earth is to go from the East unto the West, is .360. degrees: and half that number is .180. degrees. And then if that it be more degrees than it is westwards from you, 360. degrees is the compass of the earth. and if that it be but just 180. degrees, than it is opposite or right against your place that is neither East nor West, nor no point of the compass else, if that both the places were under the equinoctial, or else if that the one have the North pole, and the other have the South pole, both of one altitude, or height above the Horizon. For then the one should be Antipodies the one unto the other, that is to say, What Antipedies are, that go foot unto foot. the one to go foot unto the foot of the other, the one of the one side of earth, and the other on the other side of the whole earth, & to have the whole thickness of the earth between them. etc. And furthermore for to know by what other point or wind of the compass that any place doth bears, then that is thus known: the two towns or places to differ both in longitude and in latitude, then as in the Chapter going before is declared, it is known, by this order following. If that it have fewer degrees in longitude then your place hath, and fewer degrees in latitude in like manner, than it is according unto the degrees, and especially unto the number of miles, as thus: If the place be short in longitude, and also in latitude, and both in like quantity, that is to say, in the just number of miles, that it be no more miles from the Meridyan of the two places then that it is from the parallel of the two places, In the south-west quarter. than that place is south-west from you just. And furthermore, if that the distance in miles between the two parallels be .5. times the distance between the two Meridian's, than that place is South and by West. And furthermore if the distance in miles, between the two parallels of any place assigned, be two times & a half so many miles, that is to say, ⅖. part of the distance between the two Meridian's, than that place is south-west from your places. And if that the distance between the two Meridian's be .3. quarters of the numbers of miles between the two parallels, than that place is south-west & by South from your place. And if that the distance between the two parallels, be but .3. quarters of the number of miles between the two Meridian's, than that place is south-west & by West from your place. etc. And furthermore, if that the number of miles between the two parallels be but. ⅖. Parts of the number of miles between the two Meridian's, than that place is West south-west from your place. And furthermore, if the distance between the two parallels of any place assigned, be but the .5. Part of the number of miles between the two Meridian's, that is to say, that the number of miles be .5. times that number of miles between the two parallels, than that place is West & by South from your place. etc. And furthermore, if that any Cities, towns, or places, be more degrees in longitude than your city's towns or place is, & fewer degrees in latitude, than all those places shallbe in the Southeast corner, as all the other before rehearsed, were in the south-west corner, In the Southeast quarts. as thus: The degrees multiplied into miles, both the longitude & the latitude, as in the chapter going before is rehearsed, then if that the number of miles of the distance between the two parallels be equal unto the number of miles between the two Meridian's, than that place shallbe just Southeast from your place. And furthermore, if that the distance of miles between the two Meridian's, be but the .5. part of the number of miles between the two parallels, than that place is South & by East from your city, town, or place. etc. And if to .5. Parts, that is to say, that the number of miles between the two parallels is more than the number of miles between the two Meridian's, by double & half so much more, than that place is South, Southeast from your place. etc. And furthermore, if that the number of miles between the two Meridian's be but .3. quarters of the number of miles between the two parallels, than that place is Southeast & by South from your place. etc. But if that the number of miles between the two parallels be but .3. quarters of the number of miles between the two Meridian's, than that place is Southeast & by East from your place. etc. And if that the number of miles between the two parallels be but. ⅖. parts of the number of miles between the two Meridian's, than that place is east, Southeast from your city, town, or place: etc. If but. ⅕. part of the number of miles between the two Meridian's, than that place is East and by South from your place. etc. And furthermore, if that any place be more degrees in longitude, & also in latitude, than your place is, than those city's towns or places are in the North-east quarter. In the North-east quarter. And (as before is rehearsed) if that the numbers of miles, be equal both between the two parallels, & the two Meridian's, than that place is North-east from you. And also if that the number of miles between the two Meridian's be but the .5. part of the number of miles between the two parallels, than that place is North & by East: if ⅖. parts, than North north-east: if ¾. then North-east & by North. etc. And if the number of miles between the two Meridian's be more than the number of miles between the two parallels, that is to say, the number of miles to be but. ⅓. part, than that place is East and by North: if. ⅖. Parts, than East north-east: if. ¾. then North-east and by East from your place. etc. And furthermore, if any place hath more degrees in latitude and fewer degrees in longitude then your place, than those places be in the Northwest quarter. In the Northwest quarter, And (as before is rehearsed) if the number of miles be equal both between the Merydians and the parallels, then that is but Northwest: and if the number of miles be less between the Meridian's, than it is between the parallels, than (as before is said) if it be but. ⅕. Part, than it is north and by West: if. ⅖. Parts, North Northwest. If. ●/4. parts, Northwest and by North. But if it be not so many miles between the two parallels, as it is between the two Meridian's, if. ⅕. Parts, that place is West and by North: if. ⅖. Parts, West Northwest: if ¾. An ensample by Rome and London. then Northwest and by West from your place. etc. And for your better instruction, you shall have ensample by the city of London and Rome: and as before is declared, in the Chapter going before, that the latitude of London is .51. degrees .32. minutes, and the longitude .19. degrees .54. minutes, and the latitude of Rome 42 degrees just, and the longitude .36. degrees .40 minutes. And (as in the Chapter going before is showed) in the knowing of the distance is to rebate the less from the more: wherefore rebate the longitude of London out to of the longitude of Rome, as thus: Rome being .36. degrees 40 minutes, in longitude: so London is .19. degrees .54. minutes. So that there is .16. degrees .46. minutes, between the Meridian's of Rome and London. etc. And the latitude of London being .51. degrees .32. minutes; the latitude of Rome is .42. degrees just. Wherefore rebate .42. degrees just, from .51. degrees .32. minutes: then .9. degrees .32. minutes remaineth: so that there is just .9. degrees .32. minutes between the two parallels. And now to know by what point of the compass, do this: Rome is to the East wards of London .16. degrees .46. mi. for that it is more degrees in longitude. Wherefore you most seek how many miles that it is, first in your parallel, and here at London .37. miles doth answer unto one degree: therefore multiply .16. times .37. and that cometh unto .592. and then there is .46. minutes more, and that cometh unto .28. miles, and better. Then put .28. Unto .592. and that maketh .620. so that you may conclude that it is .620. Miles from London unto the Meridian of Rome in the parallel of London. And now the latitude of Rome is .42. degrees, and then .44. miles maketh a degree in that parallel. Wherefore multiply .16. times .44. and that maketh .704. and then there is .46. minutes more, and that maketh .33. Miles and better. Wherefore add .33. Unto .704. & there it will be .737. so that you may conclude that it is from Rome unto the Meridian of London .737. Miles. Wherefore add or put both these two numbers together, that is to say, 620. and .737. and that maketh .1357. And now take half this number, and that will show unto you how many miles that Rome is to the eastwards of London, and that is .678. Miles and a half: and now there is .9. degrees .32. minutes between the two parallels, and 60 miles make a degree. Therefore multiply .9. times .60. and that maketh .540. and then take .32. Miles more for the .32. minutes, & .32. put unto .540. maketh .572. so that Rome is .572. miles unto the southwards of London, and now for that Rome is more degrees in longitude than London, and fewer degrees in latitude than London, therefore than Rome must needs be in the Southeast quarter: and to know just by what point, then look what both the numbers be, as thus: Rome is unto the Eastwards of London 678. miles and ½. and unto the southwards of London .572 miles, then viewing the two numbers .572. is more than ¾. of 678. Therefore you may conclude, that Rome doth stand from London, Southeast and by East, and somewhat declining or leaning more unto the southwards: and if that the numbers had been equal, than it had been due Southeast. etc. And to know how many miles by that point of the compass, that is showed in the Chapter going before, and by this order you shall know by what point of the compass that any place doth bear from you. etc. ¶ The fourth Chapter showeth the Longitude and the Latitude, and by what point of the compass, that sundry places within England and Scotland, and Ireland, and also of certain islands, near unto them, doth bear from the city of London, and what distance of miles that they are from London, by the point of the compass over the water and over the land. And also there is showed how much that the moon shall change, rather or later than it doth at London, and also it doth show the length of the longest summers day, for as many places as be named. Now furthermore, in so much as I have showed unto you how by the longitude and by the latitude, you may know by what point of the compass that any place assigned beareth from you, and also at any place assigned for to know the distance by that point of the compass, that is to say, how many miles that it is from you: so in like manner I think it good for to show the longitude and the latitude of sundry principal places upon the face of the whole earth, according unto divers authors that have written thereof, and also for that the city of London is the principal and most famous place here in England, London is the principallest and the most famous place of England. I will declare or show unto you, by what point of the compass that any of those places do bear or decline unto, from the city of London, and also how many miles by that point over the Sea and London by that right line or point of the compass. And also I do think it good for to show unto you the diversity aspect of all those places by the city of London, The diversity aspect at London. that is to say, how much that the moon shall change rather or later then that it shall do at the city of London, whereby may be known the time of any Eclipse either of the moon or sun, and also the aspects of the moon with the other planets, you knowing at what hour or time that it will happen or be at London. And also I do think it good for to show unto you the length of the longest summer day in all those places that shall be named according unto the longitude and latitude, The length of the day. and then the length of the shortest winter day is soon known: and the day is meant to be, from the sun rising unto the sun setting. For the latitude of places doth alter the length of the day, and the longitude doth alter the times of the Eclipses either of the sun or of the moon, with all the other aspects, that the moon hath with the sun or any other of the Planets. etc. And now shall follow the longitude and latitude and the other things before rehearsed, of certain places, and first for England, and scotland, and Ireland, with some islands belonging thereunto. And for that London is the assigned place the longitude thereof from the canary island being 19 degrees 54. minutes, London the assigned place. and the latitude or elevation of the Pole being 51. degrees 32 minutes: S Michaelmount in Cornwall. and first this S. Michael's muount in Cornwall hath longitude .14. degrees .20. minutes, and latitude 30. degrees 40. minutes, and is West and by South from the city of London .210. miles, and the moon shall change rather than at London by .25. minutes, and the longest summer day is .16. Hours .20. minutes long. etc. Donor in Kent, the longitude .21. degrees .15. minutes, Donor in Kent. the Latitude .51. degrees .20. minutes, and is East and by South from the city of London .49. Miles, and the moon shall change later than at London .5. minutes, and the longest day in summer is .16. Hours .25. minutes. etc. Barwick, the Northermost part of England, Barwick. standing upon the edge of Scotland, the longitude .20. degrees .24. minutes, the latitude .55. degrees .58. minutes, and is North and a little declining unto the eastwards .267. miles, and the moon shall change later than it doth at London .2. minutes: and the longest summer day is .17. Hours .24. minutes long. etc. The city of York hath longitude .20. degrees, The city of York. and latitude 54. degrees .2. minutes, and is in manner due North from the city of London .150. Miles, and the moon changeth later than at London .7/5. part of a minute, and the longest summer day is near 17. hours long. etc. Carlell in Cumberland, the longitude .17. degrees .48. Minutes, Carlell. the latitude .55. degrees .2. minutes, and is north, Northwest, 224. miles from the city of London, and the moon changeth rather than it doth at London .9. minutes, and the longest day in summer is .17. Hours long. etc. Edenborowe in Scotland. Edenborowe in scotland, the longitude is .19. degrees .50. minutes, and the latitude is .57. degrees just, and is due north from the city of London .328. miles, and the moon changeth near about that time that it doth at London, and the length of the longest summer day is .17. Hours .40. minutes long. Catnes point. Catnes point the Northermost part of Scotland, the longitude .20. degrees the latitude 62. degrees, and is in manner due north from the city of London .628. Miles, and the moon changeth near about that time that it doth at London, and the longest summer day is 19 hours .25. minutes. The south-west part of Ireland. The south-west part of Ireland hath longitude .6. degrees, and latitude 52 degrees, and is West and somewhat unto the Northward from the city of London .518. Miles, & the moon changeth rather then at London .55. minutes, and the longest summer day is .16. Hours .30. minutes. The North-part of Ireland. The Northermostpart of Ireland hath longitude 13. degrees, and latitude .58. degrees 10. minutes, and is Northwest and by North, & to the northwards 462. miles, and the moon changeth rather then at London .27. minutes, and the longest summer day is .17. Hours .55. minutes. The city of develinge. The city of develing in Ireland, hath longitude .12. degrees .40. minutes, and latitude 54. degrees .40. minutes, and is Northwest and by West .296. miles, and the moon changeth rather then at London .29. minutes, and the longest summer day is .17. Hours .15. minutes long. Saint Patrick'S porcatorye. Saint Patrick's Porcatorie hath longitude .8. degrees .42. minutes, and latitude .56. degrees .50 minutes, and is Northwest and by West .415. Miles, and the moon doth change rather than at London .45. minutes, and the longest summer day is 17. hours and .4. minutes long. The I'll of man.. The I'll of Man hath longitude .15. degrees, and Latitude 56. degrees .4. minutes, and is north Northwest, and somewhat declining unto the West .358. Miles, and the moon changeth rather then at London by .20. Minutes, and the longest summer day is, 17. hours 30. minutes. The islands called Sylley, hath longitude .12. degrees .24. The islands called Silley. minutes, and the Latitude 50. degrees 54. minutes, and is West and by South from the city of London .278. Miles, and the moon changeth rather then at London .30. minutes, and the longest Summer day is 16. hours long 20. minutes. etc. The fifth Chapter showeth the longitude and the latitude and the other things before rehearsed of certain of the principallest places in Europe, as in Spain and Portugal, and France, and Italy and Germany. etc. ANd now shall follow the longitude and the latitude with the other things before rehearsed, of Europa, as Portugal, Spain and France, and Italy, and Germany. etc. And first Lyshborne in Portugal: Lyshborne in Portugal. and that hath longitude 5. degrees, and latitude 38. degrees 50. minutes, and is South south-west 985. miles, and the moon shall change. rather than at the city of London near an hour, and the longest Summer day is 14. hours 45. minutes. Cape Saint Vincent in Portugal, the longitude .4. degrees 58. Cape saint Vincent. minutes, the latitude 35. degrees 36. minutes, & is South south-west .1092. Miles from the city of London, and the moon changeth rather then at London, one hour: and the longest Summer day is .14. Hours .30. minutes. etc. Cape Saint Mary, the longitude is 5. degrees .10. minutes, Cape saint Mary. the latitude .36. degrees .45. minutes, and is South south-west 1089. miles from London, and the moon changeth rather then at London .58. minutes, and the longest Summer day is .14. Hours 30. minutes. etc. Cape Finester in Galeza, the longitude 4. degrees 50. minutes, Cape Finester. the latitude .43. degrees .10. minutes, and is south-west and by South .788. miles, and the moon changeth rather then at London one hour, and the longest Summers day is .15. Hours 20. minutes. Bayone. Bayone in Galeza, the longitude is 5. degrees 40. minutes, the Latitude .42. degrees .40. minutes, and is south-west and by South 800. miles from the city of London, & the moon changeth rather then at London 57 minutes. S. james. saint James of Compostella, the longitude 7. degrees, the latitude 42. degrees 15. minutes, and is south-west and by South 810. miles, and the moon changeth rather then at London .56. minutes, and the longest Summers day is 15. hours 4. minutes. etc. Bylbow. Bylbow in Bysley, the longitude .11. Degrees .45. minutes, the latitude .43. degrees .35. minutes, and is South south-west .578. Miles, and the moon changeth rather than it doth at London .33. minutes, and the longest Summer day is .15. Hours .30. minutes long. S. Sebastins in Byskey. S. Sebastian's in Byskey, the longitude is 15. degrees, the latitude .43. degrees, 30 minutes, and is South and by West .572. Miles from the city of London, and the moon changeth rather then at London 18. minutes, and the longest Summer day is 15. Hours 30. minutes. Toledo in castle. Toledo in castle, the longitude 10. degrees .49. minutes, the latitude 37. degrees, and is South and by West 934. miles from London, and the moon changeth rather then at London 36. minutes, and the longest Summer day is 14. hours .36. minutes etc. The city of civil. The city of civil in Andelazia, the longitude 7. degrees, the latitude 38. degrees .5. minutes, and is South & by west .950. Miles, and the moon changeth rather then at London 52. minutes, and the longest Summer day is 14. hours 40 minutes. Gibaraltarre. Gibaraltarre, the longitude .7. degrees .30 minutes, the latitude 36. degrees 4. minutes, and is South and by West 1066. miles from London, and the moon changeth rather then at London 49. minutes, and the longest Summer day is 14. hours .25. minutes. Granmaliga, hath longitude 8. degrees .50. minutes, Granmaliga the latitude 37. degrees 30. minutes, and is South and by West 960. miles from London, and the moon changeth rather then at LONDON .35. minutes, and the longest Summer day is .14. Hours .4. minutes. The city of Granado hath longitude .9. degrees .5. minutes, Granado. and latitude .38. degrees .20. minutes, and is South and by West .911. Miles from London, and the moon changeth rather then at London 45. minutes, and the longest Summer day is 14. hours 43. minutes. Bordeaux in France, the longitude .17. degrees .54. minutes, Bordeaux in France. the Latitude 45. degrees .45. minutes, and is South and somewhat to the West 36. miles from London, and the moon changeth rather then at London .8. minutes, and the longest Summer day is .15. Hours 25. minutes. Paris in France, the longitude is 23. degrees .30. minutes, Paris in France. the latitude is 48. degrees 40. minutes, and is South Southeast, .215. Miles, and the moon changeth later than at London .13. minutes, and the longest Summer day is .15. Hours .57. minutes. Roan in Normandye, the longitude 20. degrees 30. minutes, Roan. the latitude .49. degrees .10. minutes, and is South and a little to the East 142. miles, and the moon changeth later a little then at London, and the longest Summer day is .16. Hours 4. minutes. etc. Calyce in France, the longitude .22. degrees .15. minutes, Calais. the latitude .51. degrees .15. minutes, and is East and by South 86. miles from the city of London, and the moon changeth later than at London 9 minutes, and the longest Summer day is 16. hours 25. minutes. bridges in Flaunders, hath longitude .24. degrees .30. Bridge● in Flaunders. minutes, the latitude .51. degrees 20. minutes, and is East .162. Miles, and the moon changeth later than at LONDON 16. minutes, and the longest day is .16. Hours .16. minutes. etc. Gaunt. Gaunt in Flaunders, the longitude .25. degrees .30. minutes, the latitude 51. degrees 15. minutes, and is East 209 miles, the moon changeth later than at London 20 minutes, and the longest day is 16. hours 13. minutes. etc. Midleborow. Midleborow in Walkerlande, one of the islands of Zelande, the longitude 25. degrees 26. minutes, the latitude 51. degrees 48. minutes, and is East 205. miles, and the moon changeth later than at London 20. minutes, and the longest day is 16. hours 30 minutes, etc. Antwerp in Braband. Antwerp in Braband, the longitude is .26. degrees 36. minutes, and the latitude 51. degrees 28. minutes, and is East, and somewhat bending unto the South 248. miles from London, and the moon changeth later than at London 24. minutes, and the longest Summers day is 16. hours 28. minutes. etc. Amsterdam in Holland. Amsterdam in Holland, the longitude 27. degrees 5. minutes, the latitude .52. degrees .20. minutes, and is East and by North 266. miles from London, and the moon changeth later than at London 28. minutes, and the Longest day is .16. Hours .40. minutes. etc. luck. Lucke, the longitude 29. degrees .30 minutes, the latitude 50. degrees, and is East 333. miles from London, and the moon changeth later than at London 30. minutes, and the longest day is 16. hours etc. Gulder. The city of Gulder in Gulderlande, the longitude 27. degrees 48. minutes, the latitude 51. degrees .42. minutes, and is East 296. miles, the moon changeth later than at London .28. minutes, and the longest day is 16. hours 30. minutes. etc. Cleve. Cleve in Cleveland, the longitude is .28. degrees .6. minutes, the latitude is 52. degrees, and is East 303 miles from London, and the moon changeth later than at London .32. minutes, and the longest day is 16. hours 30. minutes. etc. Collyne. Colline hath longitude 29. degrees 45. minutes, the latitude 52. degrees, & is East and by North 360. miles, and the moon changeth later than at London 39 minutes, and the longest day is 16. hours 34. minutes. etc. The city of Mentz in high germany, the longitude .31. degrees 15. minutes, the latitude 50. degrees, and is East 420. miles, The city of Mentz. and the moon changeth later than at London .45. minutes, the longest day is 16. hours 25. minutes. etc. The city of Spiers, the longitude 31. degrees 30. minutes, Spiers. he latitude 49. degrees .15. minutes, and is East and by South 430. miles from London, and the moon changeth later than it doth at London .46. minutes, and the Longest day is .16. Hours 2. minutes. etc. The city of Strawsborow, the longitude 30. degrees 15. Strawsbrow. minutes, the latitude .48. degrees .45. minutes, and is East and by south, and to the south .432. Miles from London, the moon changeth later than at London .41. minutes, and the longest day is 16. hours .0. minutes. etc. Franckforde, the longitude .31. degrees .40. minutes, Francforde. the latitude .50. degrees, 10. minutes, and is east & to the south a little, .448. Miles from London, and the moon changeth later than at London 47. minutes, and the longest day is 16. hours 15. minutes. c&. The city of prague, the longitude .38. degrees 20. minutes, prague. the latitude .50. degrees, 6. minutes, & is East and a little to the south 700. miles from London, and the moon changeth later than at London 1. hour 14. minutes, and the longest day is .16. Hours .15. minutes. etc. The town of Hambrough, the longitude 34. degrees, Hambrough. the latitude is 54. degrees, 30. minutes, and is East north-east & to North .538. miles from London, and the moon shall change later than at London .56. minutes, and the longest day is .18. hours just, etc. Elson More in Denmark, the longitude .32. degrees .30. Elson in Denmark. minutes, the Latitude .58. degrees 20 minutes, and is North-east 577. miles from London, and the moon changeth later than at London .50. minutes, and the longest day is 18. hours 0. minutes. etc. The North Cape, which is the Northermost part of all Norway, hath longitude .39. degrees .30. minutes, and latitude .71. degrees 20. minutes, and is North north-east 1308. miles, and the moon changeth later than at London 1. hour 15. minutes, and the sun setteth not in the time of .78. Days and nights, that is 10. Weeks, when our days be at the longest: and in like manner the sun will not rise in the time of .78. Days and nights in Winter in like manner. etc. Iseland. Iselande under the King of Denmark, an island, the middle of it hath longitude 7. degrees, the latitude 65. degrees .30. minutes, and is North Northwest, 930. miles from LONDON, and the moon changeth rather then at London .52. minutes, and the longest day is 21. hours 44. minutes. etc. The city of Rome. The city of Rome in italy, the longitude is 36. degrees 40. minutes, the latitude 42. degrees, and is Southeast and by East, 887. miles, and the moon changeth later than at London .1. Hour .7. minutes, and the longest day is .15. Hours .4. minutes. Florance. The city of Florance, the longitude is 34. degrees 15. minutes, the latitude 24. degrees .45. minutes, and standeth from London Southeast a little unto the eastwards 802. miles, and the moon changeth later .57. minutes, and the longest day is .15. Hours 10. minutes. Pisa. Pisa, the longitude .33 degrees, the latitude is 42. degrees 15 minutes, and is Southeast 741. miles from London, and the moon changeth later than at London 53. minutes & the longest day is 15. hours 6. minutes. Venice. The city of Venice, the longitude is .35. degrees .30. minutes, the Latitude .44. degrees .45. minutes, and is East Southeast and too the southwards, 744. miles from LONDON, and the moon changeth later than at London 1. hour 3. minutes, and the longest day is 15. hours 20. minutes. milan. The city of milan, the longitude is .31. degrees .45. minutes, the latitude 44. degrees 15. minutes, and is Southeast and somewhat to the eastward 645. miles from London, and the moon changeth later than at London .48. minutes, and the longest day is 15. hours 22. minutes. The city of Naples, the longitude is 38. degrees, The city of Naples. 50. minutes, the latitude is 39 degrees .55. minutes, and is Southeast and by East 1051. miles from London, and the moon changeth later than at London 1. hour 16. minutes, and the longest day is .14. Hours 50. minutes. The city of Philippos in the kingdom of Macedonia, the longitude 50. degrees 45. minutes, the latitude is .41. degrees, Philippos' in the kingdom of Macedonia. 45 minutes, & is East Southeast 1395. miles from London, and the moon changeth later than at London 2. hours 3. minutes, and the longest day is .15. Hours .10. minutes. etc. Constantinople that is now the Turks, the longitude is 56. degrees, the latitude is .43. degrees .5. minutes, Constantinople that is the seat of the Turks. and is east Southeast 1547. miles from London, and the moon changeth later than at London 2. hours 24. minutes, and the longest day is 15. hours 15. minutes. etc. Athens, that hath been sometime a famous city, but now destroyed the longitude 52. degrees 43 minutes, the latitude .37. Athens. degrees, 15. minutes, and is Southeast and by East .1624. Miles from London, the moon changeth later than at London 2. hours 11. minutes, and the longest day is 14. hours .40. minutes. etc. Danswicke, lately under the King of Polonia, hath longitude .46. degrees, and latitude .54. degrees .55. minutes, Danswick. and is East north-east 961. miles from LONDON, and the moon changeth later than at London 1. hour .44. minutes, and the longest day is seventeen hours five minutes. etc. The kingdom of Swethen, The kingdom of Swethen. the middle thereof hath longitude 42. degrees, and Latitude .64. degrees, and is North-east from London 1040. miles, and the moon chanugeth later than at London. .1. Hour .28. minutes, and the longest day is .20. Hours .30. minutes etc. The city of muscovia in Rosey. The city of muscovia in Rosey, hath longitude 69. degrees, the latitude 57 degrees, and is East and by North 1747. miles from the city of London, and the moon changeth later than at London, 3. hours .16. minutes, and the longest day is 17. hours .40. minutes. etc. And thus I end the description of the Cities and towns of Europe. The sixth Chapter showeth the longitude and the latitude and the other things before rehearsed, of certain of the principallest places of Africa, and of certain islands nearer thereunto. AND now shall follow the longitude and the latitude, and the things before rehearsed, of some of the Cities and towns, and islands of Afryca. Morocco in Barbary. And first, the city of Morocco in Barbary, the longitude 5. degrees 5. minutes, the latitude 30. degrees 4. minutes, and is South south-west and somewhat in the westwards 1449. miles from London, and the moon changeth rather then at London .59. minutes, and the longest day is .14. Hours. S. Cruce road. S. Cruce Rode, the longitude 2. degrees, the latitude .30. degrees, and is South south-west and to the Westwards 1440 miles from London, and the moon changeth rather then at London .1. Hour, and the longest Summer day is .14. Hours. etc. Fez. The city of Fez, the longitude .10. degrees, the latitude 30. degrees, and is South south-west 1365. miles from London, & the moon changeth rather then at London 39 minutes, and the longest day is 14. hours. Tangie is a hold that the King of Portugal keepeth in Barbary, and hath longitude 6. degrees 30. minutes, Tangie. and latitude .35. degrees 40. minutes, and is South south-west .1113. Miles from London, and the moon changeth rather then at London .53. minutes, and the longest summer day is .14. Hours .25. minutes. Abilles', a Hill commonly called cap Hill, Abilles'. right against juberaltare, and is one of Hercules' pillars, the longitude .7. degrees, the latitude .35. degrees 40. minutes, and is South south-west .1116. Miles from London, and the moon changeth rather then at London 52. minutes, and the longest day is .14. Hours .25. minutes. Argeyll, the longitude .18. degrees, the latitude .37. degrees, Argeyll. and is South .872. miles from London, and the moon changeth later than at London, and the longest day is hours minutes. etc. Alexandria in Egypt, the longitude .60. degrees, 30. minutes, Alexandria in Egypt. the latitude .31. degrees, and is Southeast and by East .2169. miles from London, and the moon changeth later than at London .2. Hours 42. minutes, and the longest day is .14. Hours. etc. The mouth of Nilus that emptieth himself in Mari Mediterraneo, the longitude .62. degrees, The mouth of Nilus. the latitude .31. degrees 30.. minutes, Southeast and by East .2200. Miles from London, the moon changeth later than at London 2. hours 48. minutes, and the longest day is, 14. hours 8. minutes. etc. The North end of the Red Sea next unto the middle earth Sea, the longitude 64. degrees, the latitude 30. degrees, The North end of the Red Sea. and is Southeast and by East .2345. Miles from London, & the moon changeth later .2. Hours .56. minutes, and the longest day is .14. Hours .0. minutes. etc. Cape Devaca in Guinea, the longitude 2. degrees .20. Cape Deuard in Guinea. minutes, the latitude .14 degrees .50. minutes, and is South south-west .2426. Miles from London, and the moon changeth rather then at London 1. hour 10. minutes, and the longest day is but 12. hours 50. minutes. The Castle Demine. The Castle Demine, a hold that the King of Portugal doth keep in Guinea, the longitude 24. degrees, the latitude .2. degrees 30. minutes, and is South, a little to the eastwards 2940. miles from London, and the moon changeth later than at London, 16. minutes, and the longest day is .12. Hours 20. minutes. The mouth of the river of Bynney. The mouth of the river of Bynney, the longitude .32. degrees, the latitude .5. degrees, and is South and by East, and to the eastwards 2885. miles from London, and the moon changeth later than at London 48. minutes, and the longest day is .12. Hours .20. minutes. Cap boon Sperance. cap boon Sperance, the Southermost part of all Ethiopia, hath longitude .52. degrees, & latitude .35. degrees, 10. minutes, & is of the South pole called the pole Antarctic beyond the equinoctial, and is South and by East, and to the eastwards 5382. miles from London, and the moon changeth later than at London .2. Hours 8. minutes, and their longest summer day is in our winter, and is 14. hours long 20. minutes. etc. Goia. Goia, a city in Ethiopia, the longitude is .60. degrees, 50. minutes, the latitude hath the South Pole elevated 19 degrees 50. minutes, and is South Southeast .4685. miles from London, and the moon changeth later than at London .2. Hours 3. minutes, and the longest days are in our winter, and that is 13. hours 15. minutes. Garma. Garma, another city in Ethiopia, and hath longitude .57. degrees, and the South Pole is 24. degrees above the Horizon, and is South Southeast .4528. Miles from London, the moon changeth later than at London by 2. hours 28. minutes, and their longest day is as before is said, contrary unto ours, being 13. hours 30. minutes long. etc. The great island of S, Laurence. The great island of saint Laurence, on the East side of Ethiopia beyond Cape boon Sperance, hath longitude 85. degrees 30. minutes, and the South Pole is elevated 20. degrees in the middle of the island, and is Southeast and by South 5249. miles from London, and the moon changeth later than at London 4. hours .20. minutes, and the longest day is .13. Hours .15. minutes in our winter. etc. The island of saint Thomas, hath longitude 30. The island of S. Thomas. degrees .30. minutes, and no latitude: for that the middle thereof is right under the equinoctial, and is south and somewhat to the East wards .3696. Miles from London, and the moon changeth later than at London .42. minutes, and the day is continually always .12. Hours long, neither more nor less, what declination soever that the sun hath. etc. The islands of Cape devarde, hath Longitude 356. The islands of cap devade. degrees, the latitude .16. degrees among the middle of them, and is South south-west .2465. Miles from London, and the moon changeth rather then at London 1. hour .36. minutes, and the longest summer day is but 13. hours 0. minutes. etc. The islands called the Canaries, The Canary islands. and the bigest island called the Grand canary, hath no longitude, for that it is the assigned place to begin the Longitude: the latitude 28. degrees 30. minutes, and is south south-west .1914. Miles from London, and the moon changeth rather then at London 1. hour 20. minutes, and the longest day is .13. Hours 24. minutes, and is derectlye under the tropic of Cancer. etc. The bigest island of the Madera, hath longitude 358. The Madera islands. degrees 40. minutes, for that it is more Westerly than the Grand canary, where that the Longitude beginneth by one degree and 20. minutes, the Latitude is .29. degrees and .30. minutes, and is south-west and by South .1625. Miles from London, and the moon changeth rather then at London 1. hour 25. minutes, and the longest day is .13. Hours .54. minutes. etc. And thus I do end the description of the Cities, towns, and islands of Africa. ¶ The seventh Chapter showeth the Longitude, and the Latitude, and the other things before rehearsed of certain of the principallest places of Asia and in the East India. etc. ANd now shall follow the longitude and the latitude, and all the other things before rehearsed, of certain of the Cities and towns and other places of Asia as followeth. Claudiopoles. And first of Claudiopolis in the country of Pontus and Bethania, where S. Luke wrote the Gospel, and the acts of the Apostles, the longitude .59. degrees .30. minutes, the latitude .42. degrees 45. minutes, and is East Southeast 1697. miles from London, and the moon changeth later than at London 2. hours 38. minutes, and the longest day is 15. hours 8. minutes. etc. Nicaea. Nicaea where Nicaea counsel was, the longitude 58. degrees, the latitude 42. degrees 15. minutes, and is East Southeast 1668. miles from London, and the moon changeth later than at London 2. hours 32. minutes, and the longest day is 15. hours 6. minutes. etc. Troy. Troy that was destroyed, the longitude 55. degrees 50. minutes, the latitude 41. degrees, and is East Southeast .1605. Miles from London, and the moon changeth later than at London 2. hours 24. minutes, and the longest day is .15. Hours .0. minutes. etc., Ephesus. Ephesus where Saint John wrote the gospel, the longitude 57 degrees 40. minutes, the latitude 37. degrees 40. minutes, and is East Southeast, and to the South parts 1808. miles from London, and the moon changeth later than at London 2. hours 30. minutes, and the longest day is 14. hours 40. minutes. etc. Tralus. Tralus, the longitude is 58. degrees 40. minutes, the latitude 38. degrees .50. minutes, and is East Southeast, and to the South parts 1797. miles from London, and the moon changeth later than at London 2. hours 34. mnutes, and the longest day is 14. hours 44. minutes. etc. Philadelphia. Philadelphia in Bothlydias, the longitude 59 degrees, the latitude 38. degrees 50. minutes, and is East Southeast, and to the southwards 1816. miles from London, and the moon changeth later than at London 2. hours 36. minutes, & the longest day is 14. hours 44. minutes. etc. olympus a city in Lycia, the longitude 61. degrees 30. Olympus. minutes, the latitude 36. degrees 10. minutes, and is East Southeast a little to the South 1993. miles from London, and the moon changeth later than at London 2. hours 46. minutes, and the longest day is 14 hours 30. minutes. etc. Pompeiopolis a city of Galatia, and builded by Pompey, Pompeiopolis. the longitude .62. degrees, the latitude 42. degrees, and is East, Southeast 1814. miles from London, and the moon changeth later 2. hours 48. minutes, and the longest day is 15. hours 10. minutes. etc. Olbia in Pamphllia, the longitude .62 degrees, Olbia. the latitude 36. degrees .55. minutes, and is East Southeast .1989. Miles from London, and the moon changeth later than at London 2. hours 48. minutes, and the longest day is .14. Hours .36. minutes. etc. Pargamus in the country of Doris, the longitude .57. Pargamus degrees .35. minutes, the Latitude .39. degrees .45. minutes, and is East Southeast .1709.. miles from London and the moon changeth later .2. Hours .30. minutes, and the longest day is .14. Hours 54. minutes. etc. Cesaria in Capadocia, the longitude .66. degrees .30. Cesaria. minutes, the latitude .39. degrees .30. minutes: and is east Southeast .2064. Miles from London, and the moon changeth later than at London .3. Hours .6. minutes, and the longest day is .14. Hours .50. minutes. etc. Nicopolis in Armenia the less, the longitude .69. Nicopolis. degrees 20. minutes, the latitude .41. degrees .40. minutes, and is East Southeast .2129. miles from London, and the moon changeth later .3. Hours .18. minutes, and the longest day is .15. Hours .3. minutes. etc. Antiochia in Cilicia, the longitude .64. degrees 40. minutes, Antiochia. the latitude .36. degrees 50. minutes. & is East Southeast .2078. miles from London, and the moon changeth later than at London 2. hours 58. minutes, and the longest day is 14 hours 33. minutes. etc. Geldia. Geldia in Albania part of great Tartary, the longitude 83. degrees, the latitude .46. degrees 30. minutes, and is East and to the southwards 2458. miles from London, and the moon changeth later 4. hours 12. minutes, and the longest day is .15. Hours 40. minutes. etc. Bola. Bola in Armenia the greater, the longitude 76. degrees 10. minutes, the latitude 44.. degrees, and is East and by South 2294. miles from London, and the moon changeth later than at London 3. hours 45. minutes, and the longest day is 15. hours 20. minutes. etc. Alexandria in Syria. Alexandria in Syria, the longitude 69. degrees 30. minutes, the latitude 36. degrees 10. minutes, & is East Southeast 2277. miles from London, and the moon changeth later than at London 3. hours 18. minutes, and the longest day is 14. hours 30. minutes. etc. Tripoli in Phenicia. Tripoli in Phenicia, the longitude 67. degrees 30. minutes, the latitude 34. degrees 20. minutes, and is East Southeast, and to the southwards 2314. miles from London, and the moon changeth later 3. hours 10. minutes, and the longest day is 14. hours, 20. minutes. etc. Barut. Barut, and is the port of Damascus, the longitude 76. degrees, the latitude 33. degrees 20. minutes, and is East Southeast, and to the southwards 2321. miles from London, and the moon changeth later 3. hours 8. minutes, and the longest day is 14. hours 15. minutes. etc. Antiochia. Antiochia the Mount Taurus, the country of S. Luke, the longitude 69. degrees, the latitude 35. degrees 30. minutes, and is East Southeast 2319. miles from London, and the moon changeth later than at London 3. hours 16. minutes, and the longest day is 14. hours 26. minutes. etc. Damascus. Damascus, where Cain sleine his brother Abel, the longitude 69. degrees, the latitude 33. degrees, & is East Southeast and to the southwards 2404. miles from London, and the moon changeth later 3. hours 16. minutes, and the longest day is 14. hours 15. minutes. etc. port Jassa or Joppa, the longitude 65. degrees 45. minutes, Port Jassa. the latitude .31. degrees 55. minutes, and is Southeast, and by East and to the eastwards 2338. miles from London, and the moon changeth later than at London 3. hours .2. minutes, and the longest day is 14. hours .6. minutes. etc. The dead Seas or lake of Sodom, the longitude 66. The Lake of Sodom. degrees 50. minutes, the latitude 31. degrees 10. minutes, and is Southeast and by East and to the eastwards .2404. Miles from London, and the moon changeth later 3. hours 8. minutes, and the longest day is .14. Hours 4. minutes. etc. Bethsaida in Galilea, the longitude 57 degrees 5. Bethsaida. minutes, the latitude 31. degrees 15. minutes, and is Southeast and by East .2039. Miles from London, and the moon changeth later 2. hours 29. minutes, and the longest day is 14. hours 6. minutes. etc. Nicopolis in Samaria, the longitude 66. degrees 50. Nicopolis. minutes, the latitude 31. degrees .50. mi. and is Southeast, and by East and to the eastwards .2382. Miles from London, and the moon changeth later 3. hours 8. minutes, and the longest day is 14. hours 10. minutes. etc. Jerusalem in Judea, Jerusalem sometime the famous city on the earth, but now destroyed by Titus, in the time of Vaspatian the Emperor of Rome, the longitude 65. degrees 45. minutes, the latitude 31. degrees 22. minutes, and is Southeast, and by East, and to the eastwards 2352. miles from London, and the moon changeth later by 3. hours 3. minutes, and the longest day is 14. hours 8. minutes. etc. Charan in Mesopotamia, where as Abraham dwelled, Charan in Mesopotamia the longitude 73. degrees 45. minutes, the latitude 36. degrees, 10. minutes, and is East Southeast .2466. Miles from London, and the moon changeth later by 3. hours 36. minutes, and the longest day .14. Hours 30. minutes. Babylon. Babylon where the town of Babel was, the longitude is 79. degrees, the latitude .35. degrees, and is East Southeast, 2724. miles from London, and the moon changeth later by 3. hours .56. minutes, and the longest day is 14. hours .25. minutes. etc. Erupa in Arabia. Erupa in Arabia, the longitude .72. degrees 30. minutes, the latitude 30. degrees 15. minutes, and is East Southeast and to the southwards .2641. Miles from London, and the moon changeth later by 3. hours 30. minutes, and the longest day is 13. hours 56, minutes. etc. The Red Sea. The Red Sea, the place which Moses and the Children of Israel went through, the longitude 63. degrees 30. minutes. the latitude 29, degrees 50. minutes, and is Southeast and by East 2336. miles from London, and the moon changeth later 2. hours 54. minutes, and the longest day is 13. hours 56. minutes. etc. Mount Sinai or Mount Oreb. Mount Sinai or mount Oreb, where that Moses' received the ten commandments, the longitude 64. degrees, the latitude 30. degrees, and is Southeast, and by East 2344. miles from London, and the moon changeth later than at London, by 2. hours 58. minutes, and the longest day is 13. hours 58. minutes. etc. Michia. Michia in Arabia, where is the Sepulchre of the false Prophet Mahomet, the longitude 72. degrees 15. minutes, the latitude 23. degrees, and is Southeast, and by East, and to the East wards 2954. miles from London, and the moon changeth later by 3. hours 29. minutes, and the longest day is 13. hours 25. minutes. etc. The city of Niniveh. The city of Niniveh in Assiria where as Jonas the Prophet was sent, the longitude 78. degrees, the latitude 36. de-degrees, and is East Southeast .2635. Miles from London, and the moon changeth later by 3. hours 52. minutes and the longest day .14. hours 30. minutes. Asia. Asia a city in Susana, the longitude .80. degrees 10. minutes, the latitude 31. degrees 40. minutes, and is East Southest 2923. miles from London, & the moon changeth later by 4. hours 1. minute, and the longest day is 14. hours 8. minutes. Arima in Persia, the longitude 87. degrees, 45. minutes, Arima. the latitude 33. degrees 50. minutes, and is East Southeast .3108. miles from London, and the moon changeth later by .4. Hours .31. minutes, and the longest day is 4. hours .15. minutes. etc. Alca in Media, the longitude is 86. degrees 15. minutes, the Latitude .41. degrees, and is East and South 2791. miles from London, & the moon changeth later by 4 hours 25. minutes, and the longest day is 15. hours. The Caspian Sea, the longitude of the middle thereof is .90. The Caspian Sea. degrees, the latitude of the middle thereof is .45. degrees, 30. minutes, and is East and to the Southwards .2788. Miles from the city of London, and the moon changeth later than at London by 4. hours 40. minutes, and their longest day is .15. Hours 30. minutes. Argos in Carmania, the longitude .96. degrees .30. minutes, Argos. the latitude .23. degrees .30. minutes, and is East Southeast 3917. miles from London, and the moon changeth later by .5. Hours 6. minutes, and the longest day is .13. Hours .25. minutes, etc. The city of Hecatompilon in Parthia, which hath .100. Hecatompilon. gates, the longitude 93. degrees .20. minutes, the latitude 37. degrees, 50. minutes, and is East and by South 3714. miles from London, and the moon changeth later than at London .5. Hours .6. minutes, and the longest day is .14. Hours .38. minutes. etc. Harcan in Hyrcania, the longitude .7. degrees 30 minutes, Harcan. the latitude .40. degrees .30. minutes, and is East and by South 3332. miles from London, and the moon changeth later than at London by 5. hours .14. minutes, and the longest day is 14. hours .50. minutes. Sena in Margiana, the longitude .102. degrees .30. Minutes, Sena. the latitude .42. degrees .20. minutes, and is near East and by South .3430. Miles from London, & the moon changeth later by 5. hours 30. minutes, and the Longest day is .15. Hours 8. minutes. Chomara. Chomara in Bactriana, the longitude .106. degrees, the latitude 40. degrees, and is East and by South 3635. miles from London, & the moon changeth later by 5. hours, 45. minutes, and the longest day is 14. hours .50. minutes. Prepsa. Prepsa in Sogdiana, the longitude 130. degrees, the latitude .45. degrees, and is East and to the southwards, 4389. miles from London, and the moon changeth later by 7. hours 20. minutes, and the longest day is .15. Hours 30. minutes etc. Aspabora. Aspabora in Scythia within the mount Emaus, the longitude 102. degrees, the latitude 44. degrees, and is East and by south, 3311 miles from London, and the moon changeth later by 5. hours 28. minutes, and the longest day is 15. hours 20. minutes. Issedon. Issedon in Seythia, without the mount Emaus in Chatay, and under the Great Chane Emperor of Tartary, the longitude 150. degrees, the latitude 48. degrees .30. minutes, and is East and a little to the southwards 5008. miles from London, and the moon changeth later by 8. hours 40 minutes, and the longest day is .15. Hours 56. minutes. Isadon. Isadon in Serica, the longitude 162. degrees, the latitude 45 degrees, and is East and too the southwards 5622. miles from the city of London, and in this country of Serica, breed the silk worms, and the moon changeth later than at London .9. Hours 28. minutes, and the longest day is .15. Hours 30. minutes etc. Alexandria maria· Alexandria Maria, the longitude 110. degrees, the latitude .36. degrees, and is East and by South 3937. miles from London, and the moon changeth later by 6. hours just, and the longest day is 14 hours 30. minutes. Asta in Drangiana, the longitude .107. degrees .30. minutes, Asta. the latitude 30. degrees, 40. minutes, and is East Southeast, 4087. miles from London, and the moon changeth later by .5. Hours .50. minutes, the longest day is .14. hours just etc. Cuni in Gegrosia, the longitude .110. degrees, Cuni. the latitude 23 degrees 50. minutes, and is East Southeast .4461. Miles from London, and the moon changeth later by 6. hours, the longest day is 13. hours 30. minutes. Bardaxima in India within the river of Ganges, Bardaxima. the longitude .113. degrees, 40. minutes, he latitude .20. degrees 40. minutes, and is East Southeast 4735 miles from London, and the moon changeth later by 6. hours 15. minutes, and the longest day is 13. hours 15. minutes. Calicute the most famous city of merchandise in all India, Calicute. the longitude .112. degrees, the latitude .5. degrees, and is Southeast and by East and to the Eastwards .5224. miles from London, and the moon changeth later by .6. Hours .8. minutes, and the longest day is but .12. Hours .20. minutes. etc. Polibotra in Persia, the longitude 143. degrees, Polibotra. the latitude 27. degrees, and is East and by South and too the southwards 5710, miles from London, and the moon changeth later by .8. Hours 12. minutes, and the longest day is 13. hours .45. minutes. Pentapolis in India without Ganges, the longitude .150. Pentapolis. degrees, the latitude .18. degrees, and is East Southeast 6337. miles from London, and the moon changeth later by 8. hours .40. minutes, the longest day is .13. Hours .10. minutes. etc. Thagora. Thagora in India without Ganges, the longitude 168.. degrees, the latitude 6. degrees, and is East South East 7680. miles from London, and the moon changeth later by 9 hours 52. minutes, and the longest day is 12. hours .20. minutes, Ciamfa. West Ciamfa in Chatay, the longitude .188. degrees, the latitude .37. degrees .15. minutes, and is East and by South 7205. miles from London, and the moon changeth later than at London .11. Hours .43. minutes, and the longest day is .14. Hours 36. minutes. Quinsay. Quinsay, the greatest city in the whole World, in Chatay, and underneath the Great chain Lord of the East and South Indians, the longitude .192. degrees, the latitude .37. degrees 40. minutes, and is East and by South .7272. Miles from London, and the moon changeth later by 11. hours .28. minutes, and the longest day is .14. Hours .38. minutes etc. Geiten. Geiten in the East India, in the province of China, the longitude .183. degrees, and is near unto the South Sea, the latitude 25. degrees 15. minutes, and is East and by South 7312. miles from London, & the moon changeth 〈◊〉 then at London by 11. hours 12. minutes, and the longest day is 13. hours 35. minutes. Ciamfa. East Ciamfa, the longitude .97. degrees, the latitude .32. degrees 5. minutes, and is East and by South, 7787. miles from London, and the moon changeth later than at London by .11. Hours 48. minutes, and the longest day is 14. hours 10. minutes. Tangury. Tangury in Mugi, the longitude .178. degrees, 15. minutes, the latitude 31. degrees, & is East & to the Southwards, 6980. miles from London, and the moon changeth later by .10. Hours .28. minutes, & the longest day is 14. hours 5. minutes. Thebet. The province of Thebet, in which the great chain Lord of the East and South Indians hath his court, and all the Kings of India are under him, the longitude is 168. degrees, the latitude .3. degrees .20. minutes, and is east Southeast 7670. miles from London, and the moon changeth later by 9 hours 44. minutes, and the longest day is but 12. hours 10. minutes. Cyamba, in this place they use Coral in the steed of money, Ciamba and have great plenty of most sorts of Spices, the longitude 199. degrees 10 minutes, the latitude .25. degrees .30. minutes, and is East and by South 7980. miles from London, and the moon changeth later by .11. Hours .48. minutes, and the longest day is 13. hours .36. minutes. Barnia in the South India, the longitude .202. degrees .40. Barnia. minutes, the latitude .11. degrees .40. minutes, and is West and by South 8824. miles from London, and the moon changeth rather by .11. Hours 52. minutes, and the longest day is 12. hours. Nar in Moaber, the Inhabitants do worship Oxen, Nar. the longitude 196. degrees, the latitude hath the south pole 20. degrees, 10. minutes, and is Southeast and a little to the eastwards 8512. miles from London, and the moon changeth later by 11. hours .44. minutes, and the longest day is in our Winter, and is 13. hours .15. minutes. etc. Malaqua, the longitude is 189. degrees, Malaqua. the Latitude of the South pole is 15. degrees .30. minutes, & is Southeast and by East 8781. miles from London, & the moon changeth rather by 11. hours 16. minutes, and the longest day is 12. hours 56. minutes. In the kingdom of Lace there is a city called Lace, Lace. the longitude is .166. degrees 30. minutes, the latitude is 21. degrees, 40. minutes, and is East and by South .7047. Miles from the city of London, and the moon changeth later than at London by 9 hours 44. minutes, and the longest day is .13. Hours 24. minutes. ¶ The eight Chapter showeth the Longitude, and the Latitude, and the other things before rehearsed, of certain of the principallest places of America or the west Indies, that hath been found within these 100 years, and not known unto the old writers. ANd now shall follow the longitude, & the latitude, & all the other things before rehearsed of certain Cities, The straight of Magellenos the southermost part of all America. & other notable places of America. And first the straits of Magellenos the Southermost part of all America, the Longitude .305. degrees, the Latitude is the Pole Antarctic, or South Pole .25. degrees .30. minutes, and is South south-west, and too the westwards, and beyond the equinoctial 7224. miles from London, and the moon changeth rather then at London by .5. Hours .0. minutes, and the longest Summer day with them is our shortest Winter day, for that the pole Antarctic or south pole is above the Horizon, and is .16. Hours .36. minutes. etc. The great river of Platte. The great river of Plate, the longitude 327. degrees, the latitude is the South pole 35. degrees, and is South south-west 5685. miles from London, and the moon changeth rather then at London by .3. Hours 32. minutes, and their longest summer day is in our winter. & is 14. hours .30. mynuts long. Cap Crusos the Eastermost part of America. cap Crusos the Eastermost part of all America, & is commonly called the cost of Brasell, the longitude 345. degrees, the latitude 5. degrees of the south pole, and is South south-west 3792 miles from London, & the moon changeth rather then at London 2. hours 20. mi. the longest day is about .12. Hours .30. Minutes. cap de Planco. cap de planco, the longitude .306. degrees, the latitude 5. degrees, & is south-west and by West 4547. miles from London, and the moon changeth rather 4. hours .56. minutes, and the longest day is about 12. hours 20. minutes etc. Cap saint Marthae. cap S. Marthae, the longitude .284. degrees, the latitude 12. degrees, and is west south-west & to the southwards 5103. miles from London, and the moon changeth rather by 60. hours 24. minutes, and the longest day is 12 hours 45. minutes. Carthagena, the longitude .282. degrees, the latitude 10. Carthagena degrees .15. minutes, and is West south-west and to the South 5316. miles from London, & the moon changeth rather by .6. Hours, 32. minutes, and the longest day is 12. hours .38. minutes. Number de Deus, the longitude 276. degrees, the latitude 7. degrees, and is West south-west 5685. miles from London, Number de Deus. and the moon changeth rather by 6. hours 56. minutes, and the longest day is .12. Hours 25. minutes etc. The great & famous city of Mexico, the principallest place in all America, the longitude .238. degrees, the latitude .21. The city of Mexico. degrees 30. minutes, and is West and by south, 6844. miles from London, and the moon changeth rather then at London by 9 hours 28. minutes, and the longest day is 13. hours 20. minutes. The river of palm in Floryda, the longitude 260. degrees, The river of palm in Floryda. the latitude 39 degrees .20. minutes, and is West and to the southwards 5034. miles from London, and the moon changeth rather then at London by 8. hours .0. minutes, and the longest day is 14. hours 45. minutes. The Cape of Cerra Floryda, the longitude .272. degrees, The Cape of terra Florida. the latitude 31. degrees, and is West and by south .4935. Miles from London, and the moon changeth rather by 7. hours .12. minutes, & the longest day is .14. Hours .6 minutes. etc. Perru in America, the longitude .290 degrees, Perru. the latitude hath the South pole 5. degrees, and is south-west and by West .5528. Miles from London, and the moon changeth rather then at London 6. hours 0. minutes, and their longest day is but .12. Hours .20. minutes. Pannama, a town or city upon the Sea coast of Mare de Sur or South sea, the longitude .276. degrees, The port of Pannama. the latitude .20. degrees 40. minutes, and is south-west and by West, and to the westwards 5794 miles from London, and the moon changeth rather by 6. hours 56. minutes, and the longest day is 12. hours 15. minutes. tombs. tombs, a Port in the province of Peru, upon the cost of the South Sea, the longitude 276. degrees, the latitud 12. degrees of the Antarctic pole, and is south-west and by West 6045. miles from London, and the moon changeth rather by 6 hours 56 minutes, and the longest day is but .12. Hours 15. minutes in our Winter. Baculaius. or new found landlord. Baculaius is on the North-east end of America, commonly called the new found land, the longitude of the middle of them is 320. degrees, the latitude of the middle thereof is .54. degrees, and is West and to the North parts .2200. Miles from London, & the moon changeth rather by 3. hours .59. minutes, and the longest day is 16. hours 58. minutes. The land of Labrador. The land of Labrador, the longitude of the Eastermost Cape is 320 degrees, the latitude thereof 63. degrees, and the moon changeth rather by 3. hours 95. minutes, and is West Northwest and to the northwards .2768. Miles from London, and the longest day is 20. hours 0. minutes long. And thus I do end the description of the main, or firm land of America. etc. The ninth Chapter showeth the Longitude and the Latitude, and the other things before hearsed of certain of the most principal islands of Europe, within the middle earth Sea, and also of the most principal islands of Asia and America. ANd now shall follow the longitude and the latitude, and the other things before rehearsed, of certain of the most notablest islands of all Asia and America, and also of Europe: and first of certain of the most principal islands in the middle earth Sea. The island of Cicilia. And first, the island of Cicilia, being the principallest island in all that Seas, the middle thereof hath longitude 37. degrees, the latitude 36. degrees, and is Southeast and by South 1178. miles from London, and the moon changeth later by 1. hour .8. minutes, and their longest day is 14. hours .30. minutes. etc. The island of Corsica, the middle thereof hath longitude 31. The island of Corsica. degrees, the latitude 40. degrees, & is Southeast and by South. 829. miles from London, and the moon changeth later by .44. Minutes, and their longest day is 14. hours 50. minutes. etc. The island of Sardinia, the middle hath longitude 31. The island of Sardinia. degrees, the latitude 38. degrees, and is South Southeast, and to the eastwards .932. Miles from London, and the moon changeth later by 44. minutes, and their longest day is .14. Hours 40. minutes long. etc. The island of Maiorica, the middle hath longitude .17. The island of Maiorica. degrees, the latitude 38. degrees 30. minutes, and is South and a little to the westwards .792. Miles from London, and the moon changeth rather by 12. minutes, and the longest day is 14. hours 43. minutes. etc. The island of Minorica, the longitude .20 degrees,, The island of Minorica. the latitude 39 degrees, and is due South .752. Miles from London, & the moon changeth at that time that it doth at London, and the longest day is .14. Hours .45. minutes. etc. The island of Candie, the longitude .55. degrees, The island of Candy. the latitude 35. degrees .20. minutes, and is Southeast and by East, and to the eastwards 1791.. Miles from London, and the moon changeth later than at London by 2. hours .20. minutes, and the longest day is .14. Hours .25. minutes. etc. The islands of Nigropant, the longitude .54. degrees, The islands of Nigropant. the latitude 38. degrees, and is East South and to the southwards 1643. miles from London, and the moon changeth later by 2. hours .16. minutes, and the longest day is .14. Hours .40. minutes. etc. The islands called Ciclades, The islands called Cyclades. the middle of them hath longitude .56. degrees 10. minutes, the latitude .37. degrees .20. minutes, and is East Southeast, and to the southwards 1545. miles from London, and the longest day is 14. hours .35. minutes, and the moon changeth later 2. hours 24. minutes.. etc. The island of Cyprus, the longitude .65. degrees 30. The island of Cyprus. minutes, the latitude .35. degrees 10. minutes, and is East Southeast. 2190 miles from London, and the moon changeth later by 3. hours 2. minutes, and the longest day is .14. Hours 20. minutes. etc. The island of Scoyra. The island of Scoyra, the longitude 86. degrees, the latitude 12. degrees, and is Southeast and by East .3958. Miles from London, and the moon changeth later by 4. hours 24. minutes, and the longest day is 12. hours 45. minutes. etc. The island of Ormosa. Ormosa is an island in the narrow Persicke Seas, and hath longitude 99 degrees, the latitude .19. degrees, and is East Southeast 4070. miles from London, and the moon changeth later by 5. hours 4. minutes, and the longest day is .13. Hours 12. minutes. etc. The great island of Tabrobannu. The great island called Tabrobannu lying in the East Ocean, the longitude 151. degrees, the middle thereof hath no latitude for that it is directly under the equinoctial, and is East Southeast 7065. miles from London, and the moon changeth later than at London 8. hours 44. minutes, and the day is continual 12. hours in length. etc. The island of great Java. The island of the greater Java, the longitude 179. degrees, the latitude hath the South pole Antarctic 7. degrees 30. minutes, and is East Southeast, & a little to the South .8486. Miles from London, and the moon changeth later by 10. hours 36. minutes, and the longest day is but 12. hours 20. minutes. etc. The island of the lesser Java. The island of the lesser Java, hath longitude 188. degrees, and no lattitude for that it is under the equinoctial, and is East Southeast 8715. miles from London, and the moon changeth later by 11. hours 12. minutes, and the day is always 12. hours long. etc. The island of Berno. The island of Berno, hath Longitude 178. degrees, the latitude is of the South pole, and is .2. degrees .30. minutes, and is East Southeast .8320. miles from London, & the moon changeth later by 10. hours 32. minutes, and the longest day is 12. hours 8. minutes. etc. The islands of Molucke. The islands of Molucke that lie in the south Sea called Mare de Sur, the longitude 193. degrees, the latitude 9 degrees, and is East Southeast and a little to the Eastwards 8688. miles from London, and the moon changeth later than at London by 11. hours 32. minutes, and the longest day is but 12. hours 35. minutes. etc. The island of Gelilo the greatest island of all the Maiucke, The island of Gelilo. and hath longitude 204. degrees, the middle thereof hath no latitude for that it is directly under the equinoctial, and is West, south-west 9078. miles from London, and the moon changeth rather then at London, for that it is unto the westwards, and is because that it is more to the eastwards of London, than 180 degrees which is more than half the Circumference of the two parallels, that is to say, the parallel of London, & the parallel of the island being the equinoctial, Gelilo is near Antipodes unto London. and if that it had the south Pole elevated 51. degrees and a half, than it had been near Antipodes unto the city of London, and the moon changeth rather 11. hours .44. minutes, and the longest day is but 12. hours long. etc. The island of Japan near the coast of China, The island of Japan. the longitude 198. degrees, the latitude 32. degrees, and is East and by South 7919. miles from London, and the moon changeth later than at London by 11. hours 52. minutes, and the longest summer day is .14. Hours 10. minutes. etc. The island of Stipango, the longitude 200. degrees 30. The island of Stipango. minutes, the latitude 50. degrees, and is West from the city of London, for that it is more than .180. degrees unto the eastwards, therefore the shortest way is unto the westwards, and is 6668. miles from London, and the moon changeth rather then at London by 11. hours 58. minutes, and the longest day is 16. hours 4. minutes. etc. Cuba, The island of Cuba. one of the bigest islands in the West Indies in the great Bay of America, and the middle thereof hath Longitude .275. degrees, the latitude .23. degree .30. minutes, the very middle of the island that is directly under the tropic of Cancer, and is West south-west .5114. Miles from London, and the moon changeth rather 5. hours 0. minutes, and the longest day is .13. Hours 26. minutes. etc. The island called Hispaniola. The great island called Hispanyola near Cuba, the middle thereof hath longitude 285. degrees, and the latitude is 20. degrees in the middle thereof, and is West south-west, and somewhat to the south .4805. Miles from London, and the moon changeth rather by .6. Hours .20. minutes, and the longest day is 13. hours 15. minutes. Saint john's island. Saint john's island, the Longitude of the middle thereof is 293. degrees .30. minutes, the latitude of the middle is 18. degrees, and is West south-west .4536. Miles from London, and the moon changeth rather 5. hours .46. minutes, and the longest day is 13. hours 8. minutes. etc. The island of Jamica. The island of Jamica, the Longitude is 276. degrees, the Latitude .16. degrees, and is West south-west .5332. Miles from London, and the moon changeth rather 6. hours 56. minutes, and the longest day is .13. Hours .0. minutes etc. The islands of the Surres. The islands called the Surres in our West ocean Sea, the middle amongst them, hath longitude 344. degrees, and the Latitude amongst the middle of them is .39. degrees, and is south-west and by West 1674. miles from London, and the moon changeth rather 3. hours 24. minutes, and the longest day is .14. Hours .45. minutes. etc. And thus I do end the description of the principallest islands of Asia, Europa, and America. etc. ¶ The tenth Chapter is as touching certain things in the knowing of the distance unto any place assigned by Longitude and by Latitude. etc. AND furthermore, insomuch as the shortest distance unto any place assigned, cannot be by any one point of the compass, as is before declared in the first Chapter of this second book, wherefore if that you do desire for to know the distance over the Sea and land, the next way, and the shortest distance, If that you do desire to know the shortest distance unto any place, than you must do it with a Globe. than you must prepare a Globe terrestrial, and that the longitude, and the latitude of the towns and Cities, and other notable places, to be truly placed on the Globe: and then take a pair of Compasses, and then look those two places in the Globe, that you do desire for to know the true distance unto, and then open your Compasses, and set the one foot on the one place, and the other on the other place assigned, justly: and that done, than your Compasses standing stiff and not removed, set them unto the equinoctial circle on the Globe, and that done, then look how many degrees that it is justly between the two feet of the Compasses, How to know the true distance unto any place by the Globe. and that being known, then multiply the number of degrees by 60. and that shall show unto you the true number of miles, between any two places assigned, and this being done precisely, taking the true number of degrees, & the parts thereof, you shall not fail of the truth, so that the Longitude and Latitude of the places be truly set upon the Globe: and then 60. miles doth answer unto one degree both under the equinoctial, and the Meridian's. The whole compass of the earth is 28600 miles, no place can be no further distance from you then 10800. miles. And in every great Circle on the Globe of the Earth, whose whole circumference or compass is 21600. miles, so that no two places assigned, cannot be further distance asunder then 10800. miles, and then the one must be opposite, or right against the other, being Antipodes, going feet unto the feet of the other, and then as before is declared, it is neither East nor West, nor no point of the compass else, for which way soever that you do go by any right line, the distance is all one, but if that any two places be not directly Antipodes the one unto the other, then that is nearer one way, then that it is another way: and yet it shall not be by any one point of the compass, but by divers points of the compass, as before is rehearsed, except that the two places be both under one Meridian, or else under the equinoctial. etc. ❧ A Table of the contents of the chapters of the second part of this book called a treasure for travailers. FIrst to the Reader of this second part. The first Chapter of the second part showeth you how for to know the distance unto any town upon the face of the earth, and what is to be considered in the doing thereof. The second Chapter showeth unto you, how you may know the distance unto any town situate upon the face of the whole earth, so that you do know the true longitude and the true latitude of them. The third Chapter showeth how too know unto what quarter of the world that any place doth stand from you, that is to say, by what point of the compass, you knowing the true longitude and the true latitude. The Fourth Chapter showeth the longitude and the latitude, and by what point of the compass that sundry places within England and Scotland and Ireland, and also of certain islands near, unto them doth bear from the city of London, and what distance of miles they are from London, by the point of the compass over the water and the land: and also there is showed how much the moon shall change rather or later than it doth at London, and also it doth show the length of the longest Summer day, for as many places as are named. The fifth Chapter showeth the longitude and the latitude and the other things before rehearsed, of certain of the principallest places in Europe, as in Spain and Portugal, and France, and Italy, and Germany. The sixth Chapter showeth the longitude and the latitude and the other things before rehearsed, of certain of the principallest places in Africa, and of certain islands near thereunto. The seventh Chapter showeth the longitude and the latitude and the other things before rehearsed of certain of the principallest places of Asia, and in the East India. The Eight Chapter showeth the longitude and the latitude and the other things before specified, of certain of the princpallest places of America or the West Indies, that hath been found within these hundred years, and not known unto the old Writers. The ninth Chapter showeth the longitude and the latitude and the other things before rehearsed, of certain of of the most principal islands of Europe, within the middle earth Sea, and also the most principal islands of Asia and America. The tenth Chapter is as touching certain things in the knowing of the distance unto any place assigned by longitude and by latitude. Finis. The Argument of the third book, of the treasure for travailers. ¶ The third book of the Treasure for travailers, containing some matters for the measuring of superfycialles, as land, board, pavement, or glass, and also some matters as touching Solled bodies, as timber, Stone, or such otherlike: and also how to alter the Tonnage, burden, or bigness of ships, and to keep that mould and proportion with other necessary things belonging thereunto. etc. Being very necessary for all sorts of people that travail either by Sea or Land, written by William Bourne. To the Reader of this third book. GEntle Reader, although Master Leonard Dygges in his book called Tictonicon, and also Master Thomas Dygges his son in another book, called Pantometry, hath showed how for to measure all Superfycialles, as Land, Borde, glass, pavement or any such other like, & also how to measure all manner of Solled bodies, as Timber, Stone, & such other like, yet notwithstanding I have written in this third book, a little brief note as touching those causes, and also how to build ships for to make them of what tonnage or burden that you list, and to keep any form in the mould or proportion that you list, whereby that any mechanical workmen by following the order in the book prescribed, may make any ship the one like the other, and to make them of what bigness or smallness he list, and to keep that form and fashion in an points, both in the mould that is under the water, and also in the fashion aloft, above the water. And also there is contained in this third part, how for to know the bigness of Ropes, whether that it be as big again, or three times so big more or less, at your discretion, which in my opinion is very necessary to be known, both unto Naupegers or ship Carpenters, and also unto all sorts of Sea men: and also there is other necessary matters contained in this third book. ¶ The third book of the treasure for travailers. The first Chapter of the third book, showeth you how for to cast the contents of land by arithmetic, and also by the husband's rule which is by the account of money. etc. Now beginneth the third book, for that it is necessary for to know how to measure all manner of plat forms and bodies, both their superficial contents, and also there masey contents. Therefore as briefly as I may I will show unto you: yet there hath famous and wise men written thereof in our English tongue as M. Leonard Dygges, and M. Thomas Dygges, his son, & other notable men seen in the mathematical Sciences. Therefore I do intend to treat the less thereof, and especially of those things that those have written of, I will not meddle withal at this time, for that they have sufficiently declared it, as this: for to know the contents of land, to be measured in Triangles, being sure for to make a square angle and so forth, as M. Dygges doth declare in his Tictonicon, and for to cast the contents thereof, you shall do this: To know the contents of account of any piece of ground by arithmetic. When you have found a length and a breadth of any piece of ground, whose contents in Acres you do desire for to know, you shall do it by arithmetic, as thus. You shall multiply the length with the breadth, than that number that cometh of that multiplication, you shall divide by .160. and that shall show unto you the true numbers of Acres, then if there be any half rods or quarters of roods, if that they be in breadth, you shall add then to the length, and if that they be in length, you shall account them in the breadth, and so forth. Now I do know that every man hath not arithmetic, therefore you shall make your account by this means, for to know the true contents of the measure of any piece of land, when you do know the length and the breadth thereof, as thus: by the account of money, every mark for to contain one Acre, To know how many acres there is in any piece of ground by the account of money. as thus, by the account of money, every noble of money to contain half an Acre, and every 3. shillings and 4. pence, to contain a rood or a quarter of an Acre, and every groat or 4. pence to contain a days work, and every penny to contain a perch, or as some term it a rood, and for to cast the contents of Land, do this, as by ensample of a piece of Land that is 30. perches long, and 24. perches broad, the 24. pence is 2. shillings, then being .30. roods long, that is 2. times .30. Shillings, that maketh in money 3. pound, and 3. pound is .4. Mark, and a noble, so that the piece of land that is .30. roods long, and 24. broad, doth contain 4. Acres and a half. Yet furthermore for your better understanding, where there is half perches and quarter of perches, both in the length and in the breadth, than you shall do thus, by a piece of land that is 53. roods long, and a half, and of breadth 42. and a quarter, than 42. pence maketh 3. shillings and 6. pence: lay down 3. times 53. shillings, and that will be .7. Pound and .19. Shillings, and then there is 6. pence more, in the breadth: and 53. half shillings maketh 26. shillings and 6. pence, than lay that to the other sum, and then it maketh 9 pound 5. shillings and 6. pence, than there is in the length half a rood more, therefore you must account it in the breadth, and 42. half pence maketh 21. pence. Then lay that to the sum, than there is in the same breadth a quarter of a rood more, and that you must reckon in the length: and 53. farthings maketh 13. pence farthing, than lay the same to the rest, and it will make in money 9 pound 8. shillings and 4. pence ob. and that answers to, in measure .14. Acres and 5. dares work, and about half a perch, for that you may know that .9. Pound is 13. marks and a noble, and there is 8. shillings, & that is more than a noble by 4. groats. Then put that noble to the other noble, then that maketh 14. marks, than the 4. groats, put to the other 4. pence, maketh 5. groats, and so that piece of land which is 53. roods long and a half, and 42. roods broad and a quarter, shall be in measure 14. Acres 5. days work, near half a perch. And by this account of money, you may know the contents of any piece of land, better than you may know by any manner of table or tables, and this serveth both for the learned, and the unlearned, and is generally called the husbandman's rule, for that he may as soon learn this or sooner, than he shall understand the tables of measures, and that serveth but for a quantity of measure, and this serveth generally for all manner of measures, be it never so big or small, being sure for to cast the money right. The second Chapter showeth how to measure board and glass, and to cast the contents thereof, with other necesary things belonging thereunto. NOw furthermore in like manner, for the measuring of board or glass or any such other like, for that it is sufficiently declared in tables, in Master Digges his Tictonicon: yet notwithstanding thus you may know the contents without any tables, as thus. Look at what length your board is, multiply the number of feet into inches 12. inches to the foot, then that being done, multiply the breadth with the length, that is to say, the number of inches of the length, with the number of inches of the breadth, divide that number by 144. and that shall show unto you the number of feet: then if that there remain any thing, every 72. inches maketh half a foot, and then every 36. shall make ¼. Part of a foot, and for that every man hath not Arethmetick for to cast it by, yet this is a ready way that many Carpenters do use, and is exact ynouth, as thus. If that the board be more than a foot broad, than they do look how many foot long the board is: then they account that that there is so many foot of board as the length of the board is, and then for the odd inches and parts, they meet in the breadth how much it is, and then with the rule, as often times as there is foot long in the board they do measure or set it down, and then they do measure how many foot long it cometh unto, and then they do say that it is so many foot of board more than the length of the board is: and that is true without any fail, as for ensample thus, by a board of 10. foot long, and 14. inches and a half broad. Now for that the board is 10. foot long, then at twelve inches broad, there is 10. foot of board, and then there is two inches and an half more in the breadth, and for that with the inch rule that is laid down 10. times, for that the board is 10. foot long, and that being measured how long it reacheth, it will be 25. inches long, that is .2. Foot and 1. inch, then that 2. foot put unto the 10. foot, it maketh .12. foot, so that you may conclude that a board of 10. foot long, and .14. inches and ½. Broad, that there is 12. foot and 1.12. Part of a foot of a board, without any fail, and thus you may do, how broad or narrow so ever that any board or plank is. A note of measure. And furthermore, at one inch broad, then 12. foot long maketh a foot of board, at 2. inches broad, 6. foot long to a foot: at 3. inches broad 4. foot long to a foot, at 4. inches broad 3. foot long to a foot, then at 5. inches broad 2. foot and 5. inches long to a foot of board: at 6. inches broad 2. foot long to a foot of board, at 7. inches broad 1. foot and 8. inches and a half to 1. foot of board, at 8. inches broad, one foot and 6. inches long to one foot of board: at 9 inches broad 16. inches long to one foot of board: at 10. inches broad 14. inches long and ½. to one foot of board, at 11. inches broad 13. inches long and 1.11. Part of an inch to 1. foot of board: at 12. inches broad 12. inches long to one foot of board, at 13. inches broad 11. inches long and 1.13 part to one foot of board, at 14. inches broad 10. inches and 2/7. parts of an inch long to one foot of board: at 15. inches broad 9 inches and 9.15. Parts of an inch long to one foot of board: at 16. inches broad 9 inches long to one foot of board, at .17. inches broad 8. inches and 1.2. long, to one foot of board, at .18. inches broad 8. inches long to one foot of board, and for that there is no common boards sawn above 18. inches broad, therefore I leave of to proceed any further, & if it chance for to be brother than any of the measure afore named: than you shall take one of these measures afore, that is half the breadth, and then you shall take half the length for the true contents of the measure, and so forth at your discretion. Now furthermore, the square root of .17. Lacking one 33. part, will be corner to corner 24. foot, and it is a square root just as big again, as that of sixteen foot and a 23. part of 33. And now furthermore for Circles or long squares, all is one matter, as for an ensample thus by a Circle of 12. foot broad, and the compass shall be 37. foot and 8. inches and better, for this is general for ever look how many times 7. is in the Diameter, so many times 22. shall be the circumference. Or now contrariwise: look how many times 22. you have in the Circumference so many times 7. shall be the Diameter. Now to the purpose: An ensample in Circles. a Circle as much more in breadth or in compass, shall make a Circle four times so big in measure as the other, and for to measure a Circle truly, do thus. first, knowing the Circumference and the Diameter, multiply the one by the other, that is to say, the compass with the breadth, and then take the fourth part of the measure, for the true contents of the Circle, or else take half the compass, and half the breadth: then multiply the one by the other, that being done, it showeth the just contents of the Circle, as for ensample thus. By the Circle of 12. foot broad, and the compass 37. and 9 inches, and half 12. is 6. and half 37. foot and eight inches is 18. foot and 10. inches, and it being multiplied together, maketh 113. foot, the true contents of that Circle afore named. And now there is an other Circle that is 24. foot broad, and that cometh unto in compass 75. foot and 4. inches. And then take half the compass which is 37. foot and 8. inches and half the breadth, and that is .12. Foot, and then multiply the half compass with the half breadth, and that maketh .452. as by the ensample of these 2. Circles it doth appear. Now the square of 12. foot long and 6. foot broad, An ensample of long square● containeth but 72. foot, and the other of 24. foot long & 12 foot broad, containeth in feet .288. Which is four times so big as the long square 12. foot long and 6. foot broad. The third Chapter doth show how for to measure timber, and to bring it to a square, aswell without arithmetic as otherwise, and also how for to know the true contents of any piece of timber. NOw furthermore, for the measuring of all manner of bodies, as timber or stone, or any such other like, Master Dygges in his book named Tectonicon, hath made Tables of the squares of it: yet notwithstanding I will show unto you, how that you shall know how many inches long will make a foot of any portion of measure, as thus: first knowing the breadth and the thickness, and you would know how many inches long will make a foot, then look how many inches that the breadth of the timber is the brother way, and then in like manner look how many inches that it is in thickness the narrowest way, then multiply the broader side, with the narrow side, than that number that cometh of that multiplication, How to know how many inches long in timber will make a foot what square soever that it hath by arithmetic. you must divide that sum out of .1728. Than that sum that standeth before the quantity line, shall be the number of inches in length of one foot of timber or stone: and then if there remaineth any thing, then if that number which was the divider if that it be half the number, than it is half an inch more: if a quarter of the number, than one quarter of an inch: and if .3. quarters of the sum, than 3.4. Parts, and so forth to any part or parts of the remainder. And then according to that, the proportion shall be so many parts of an inch, as the remainder doth show, and thus you may know how many inches long will make one foot of timber or Stone, without any squaring of the timber. And as Master Dygges in his book called Tectonicon, hath made Tables of the squares, that you may do by extractions of the root, as afore is declared in this work. And now for because that every person that destreth for to know how for to measure timber, or any other thing, have not all manner of Arithmetyke, therefore you shall have a Table of the squares of timber, The length of a foot of Timber according unto the square. how many feet and inches will make one foot long of timber from one inch square, and so from inch to inch, till that you come to .36 inches square, as by this ensample it doth appear, and the uppermost row of this table is the number of inches of the squareness. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 1 4 36 16 9 5 4 2 1 1 1 1 1 0 0 0 0 0 0 0 0 0 9 0 11 3 9 5 2 0 10 8 7 6 5 5 1 8 3 4 7 16 1 4 1 4 3 8 13 16 11 16 3 4 15 16 1 4 The second, how many foot long will make one foot of timber, the third is inch, the 4. is parts of an inch, to be added 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 4 4 3 3 3 3 2 2 2 2 2 1 1 1 1 1 1 1 3 4 5 16 7 8 9 16 5 16 0 3 4 1 2 3 8 3 16 1 16 7 8 3 4 11 16 9 16 1 2 7 16 5 16 unto the number of feet, or inches, as by these 2. Tables it doth appear. And now for the measuring of timber or Stone, look what that it cometh unto in square number, than these tables afore made do show unto you, how many inches and parts of inches will make a foot long of that squares: and for because that every piece of timber that is to be measured, is not equally square, I will show unto you how that you may square it without extracting of the root, for that I know every person hath not that kind of arithmetic. And furthermore, for to make Tables thereof, it were but superfluous, for that Master Dygges in his Tectonicon, hath made Tables exact enough for that purpose. The fourth Chapter showeth how for too measure all manner of bodies, as timber, or stone, cubes, or globes: and to know what proportion of measure or weight the one hath unto the other. Now furthermore, for the measuring of all manner of bodies, that lacketh part of their form, and other that be more than their form, and other that be mixed bodies, being in one place more than their form, and in an other place lacketh part of their form, in the measuring of them, you shall do thus. And as it is declared afore, in the measuring of timber or Stone, or any such other like, if so be that it be equally square or partilye square, all is one matter, or round, or many squares, Master Dygges hath sufficiently declared thereof, as touching the measuring of it, How to measure any thing that lacketh part of his form. for that it is a body properly of itself. Then furthermore, there be bodies that lack part of their form, as thus, there is is a piece of timber either round or square, that may be hollow in the core or middle, or else it may be hollow like a Trough or with hollow notches into it, as by these ensamples it doth appear, and the black doth signify the hollow: and for to measure them truly, do thus. By a piece of timber or of Stone, being a foot square every way like unto a die. And there is an other cube of timber or Stone of two foot square every way like a die in form. Now that cube of one foot square, is but one foot of timber or Stone: and the other cube of two foot square every way like unto a die, is eight foot of timber or Stone, as these two figures do represent. Now you do see this to be true: and if that the measure of any thing being as much more in length, bredthe and thickness, that it is 8. times so big, whether that it be cubes or Globes, long timber or Raske, or what soever it be. And furthermore, as it is afore rehearsed, if that you have a piece of timber, Ensample of large timber. if that it be in squareness as long more and as thick or broad more, that it is 8. times as big, whether that it be round or square all is one matter, as for ensample thus. By a piece of timber of 10. foot long, and .12. inches square, that piece of timber shall be 10. foot of timber: & if that you have an other piece of timber, that is 24. inches square and .20. Foot long, that piece of timber shallbe 80. foot of timber, as by these 2. figures it is showed. And furthermore, if that you would have an other piece of timber just as big again, as that of 10. foot long, and one foot square, being just 10. foot of timber, and to be of that proportion in length and in squareness, that is declared hereafter in the 7. chapter. And furthermore whether that it be in Cubes or Globes, and if that you do know the contents of the one, and would know how much the one is bigger than the other: then shall you do it thus. You must triple the proportion of the sides of the cubes or Globes, and then multiply them together, To know the proportion of Cubes or Globes, the one by the other. as you do in fractions: then look what that number cometh unto. Then if that you do know the contents of the lesser, and would know the contents of the bigger, then multiply the contents of the lesser cube or Globe, with the number of the bigger: and look what that number cometh unto: then divide that sum with the number of the lesser cube or Globe, and that number that standeth in the quantity line, shall be the contents of the bigger cube or Globe, as for Ensample thus _____, by a Bullet of Iron of .5. inches in height, or Diameter, and suppose it to weigh 16. pound. And you have an other Globe or Bullet of that stuff of 9 inches in Diameter, how many pound shall that way? you shall know it thus. triple the proportion of them both, & set them down thus .555.999: Then multiply thus .5. times 5. is .25. and then .5. times .25. maketh 125. An ensample of Globes. And now to the bigger Globe, 9 times 9 is 81. and then .9. times 81. maketh 729, and now the lesser Bullet weighing .16. Pound therefore multiply .729. by .16. and that will make .11664. and now divide this number by 125. and then there will stand in the quantity line 93. then there remaineth over 39 so as you may conclude, that the bigger Bullet doth way 93. pound, and .39.125. Which is near 5. ounces, the true weight of the bigger Globe. And now contrariwise, you knowing the contents or weight of the bigger cube or Globe: than you must multiply the contents by the number of the lesser, and then divide it again by the number of the bigger. And for more plainness, by the Bullet before rehearsed of .5. inches high, The second ensample. to way 16. pound. Now I have a lesser that is but 4. inches in his Diameter, what shall it way: you shall know it thus 444.555. first multiply 4. times 4. and that is 16. and then 4. times 16. is 64. Then multiply 64. by the weight of the bigger Bullet, and that is 16. times 64. and that maketh 1024. and then divide the number by 125. and then there will stand in the quantity line 8. & 24. will remain over. So that ye may conclude, that the lesser Globe or Bullet doth weigh 8 pound & 3. ounces. And so by this order you may know the proportion of all manner of other bodies, what form so ever that it hath: by multiplying the length, breadth and thickness, and then doing as before is rehearsed, the contents shall appear. The fifth Chapter showeth how for to measure Globes, and to know the contents in inches or feet. ANd furthermore, for the measuring of Globes by proportion, how much that the one is bigger than the other, it is no otherwise then the proportion of any other body, as by ensample of the measuring of cubes, as afore it is declared. For this is general for ever in the measuring of all solled bodies, as timber and Stone, or Raske, or any other thing what so ever that it be, if that the proportion of measure be as 1. unto 2. the body contents as 8. unto one, that is to say, that if a shot or Globe of Iron of .2. inches height do weigh one pound, then shall a shot or Globe of Iron of 4. inches height, weigh 8. pound, and so forth as afore is rehearsed. And also this is a very good way to know the contents of a Bullet or Globe, a cube of .4. inches, will go very near to make a Globe of .5. inches in Diameter: and for Ensample of this matter before rehearsed, they do use for to measure Globes or Bullets in this sort, to know their contents. first thus. The measuring of Globes. The Circumference bring known, as 7. unto 22. the Diameter is found. Then multiply the half Circumference with the half Diameter, and that being done, look what number that cometh unto. Then multiply that by the Diameter again, and look what that number riseth unto: then take ⅔. Parts of that number, and that shall be the contents of the Globe or Bullet, Ensample thus. By a Globe of 12. inches high in the Diameter. Now to know the Circumference: then multiply 12. by 22. and that cometh unto 264. and then divide 264. by 7. and that shall show unto you the Circumference: so that cometh unto .37. and .5.7. the true compass of the Circle. Then take the half of both the Circumference, and the half Diameter, that is to say, half 37. and .5.7. and that maketh 18. and 6.7. partes and half 12. and that is .6. Then multiply 18.6.7. times .6. and that cometh unto .113. and then multiply that number by the whole Diameter again, and that cometh unto 1356. & that is like unto the end of a pillar: Then for that take ⅔. Parts of the number, and that will be .905. the true contents of the number of inches in that Globe, and by this order you may measure the contents of all Globes how big or small soever they be. But now if you would know the contents of the superficial, that is to say, what number of inches would cover the Globe or Bullet: than you must do thus: multiply the Circumference with the Diameter, and that number shallbe the contents of the outsyde of the Globe or Bullet. etc. And furthermore, to know the true contents of a Globe, how many inches it doth contain, this is the easiest may that may be devised. Take the true Diameter of the Globe, and multiply it cubitly, and then multiply thathy 11. and then divide that by .21. and that shall show unto you the true contents of the number of inches in that Globe, as for ensample thus: by the Globe before rehearsed of 12. inches in Diameter or height, and 12. times 12 is .144. and then 12. times 144, maketh 1728. and then that multiplied by 11. 19008 and then it maketh 19991. and then that being divided by .21. and then there will stand in the quantity line 905. and 3. will remain over: So that you may conclude that the Globe of 12. inches in height or Diameter, doth contain 905. inches and 1. of .7. Part of an inch. To measure the plain of a Circle. And furthermore, to know the contents of a plain Circle how many inches or feet that it doth contain: then multiply it by the Diameter squarely, and then multiply it again by .11. & then divide that number by 14. & that shall show unto you the true: contents of the platform of that Circle. Ensample by a plain Circle of 12. foot broad or over, and to know how many feet that it doth contain: Then multiply 12. times 12. and that maketh 144. and then multiply 144. by 11. and that maketh .1584. and then divide 1584. by 14. and then there will stand in the quantity line 113. and 2. will remain over: so that you may conclude, that the contents of that Circle that is 12. foot broad, that the platform of that Circle doth contain 113. foot, and 1/7. part of a foot. The sixth Chapter showeth how for to build ships by proportion, that is to say, if that you have one Ship for an ensample, if you would have an other as big again, more or less: this Chapter doth show unto you how you may do it, keeping that mould and proportion in all points, that is to say, by extracting of the cubike root. AND furthermore, I do think it convenient, for that I do know that many that are Naupegers or Ship carpenters, have not the exact knowledge in these causes, that is to say, that when they have builded any ship or Boat, and the tonnage then known unto them, Of the building of Ships. if that you would have an other Ship or boat of that mould and of that proportion in all points, to be double that tonnage or burden that the other is: I do know that there is but few Naupegers or Ship carpenters that can do it: for that they do lack for the most part of them the extractions of cubic roots for otherwise it is not possible for it to be done: for no man may keep just proportion in all points without the extracting of Cubes, they may well keep the tonnage or but then, but not the proportion and mould in all points. For according as it is afore declared, by the measuring of Cubes or Globes or any massy bodies, if that they should double the measure, than it were 8. times so big. Therefore whensoever that you have builded any ship or Boat, or any other craft, whatsoever it be, How to alter the bigness of a ship and yet to keep the proportion mould, and fashion. then if that you would have an other of that self some mould in all points, and would have the other as big again, or twice or thrice so big again, or half so big again, or any other quantity more or less, then shall you do thus. First for the length of the keel, you shall multiply it cubitely, and then in like manner every beam: the mydshippe beam and all the rest of the beams, to multiply them cubitelye, and also the racking of the ship both the Stem and the stern post, to multiply them cubitely, and also the principal timbers that doth mould the ship, to multiply them cubitely, and also the depth that the ship is in hold, to multiply it cubitely, and so consequently every place or places with the Ship that doth lead any work, to multiply it cubitely. Then that being done, if that you would have the other ship or Boat as big again, then double that number that you have before multiplied: Then extracting the cubit root thereof, then according unto the number make your reel, your timbers, your beams, and so consequently all the rest of your things, according unto the cubit root so extracted, and that being done, you shall make her of that mould and proportion, and of double burden, without any fail, otherwise it is not to be done. And furthermore, if that you would have one thrice so big, then 3. fold your number, and so forth: then if that you would have her but half so great, then take half the number so multiplied, and the cubit root so extracted, shall make a ship or Boat, but half the burden: and thus you may make a ship or boat of what proportion so ever you list, and also to be of that self same mould that the other was. Provided also, for the squareness of your beams, and your timbers, and also the thickness of the plank, that you do observe this order before mentioned, or else in otherwise doing, you may put more timber or less timber, than the proportion of the burden doth come unto, and so by that means you may commit error. As for Ensample thus briefly. By a ship that was .44. Foot long by the reel, and .20. Foot broad upon the mydshippe beam, and did rack it with the stem forwards 13. foot, and the stern post did rack 7. An ensample of the altering of the burden of a ship, and to keep the mould and proportion. foot offwardes, and the ship was 9 foot deep in hold. Now this ship was .100. Tons, my desire is to have a ship of that self same mould, in all points, to be of just double burden, that is .200. tons. Then first multiply the length of the keel cubitely, and that is 44. foot: therefore multiply .44 times .44. and that maketh 1936. and then again by 44. that maketh .85184. so it is multiplied cubietly. Now double the number, and that maketh 170368. and now extract the cubit root, and that will be 55. foot and .3993.9075. Part, which maketh in inches .5. and. ⅗. Parts of an inch, so that you may conclude, that the ship must be .55. Foot, and .5. inches, and near .32. quarters in length by the keel. And now for the breadth of the beam, and that is 20. foot, and .20. Times .20. is .400. and that multiplied by .20. maketh .8000. and this double is .16000. then extract the cubit root, and that is .25. and .375.1875. and that maketh in inches 2. and. ⅗. Parts of an inch, so that you may conclude that the ship must be .25. Foot and .2. inches, and near a half inch upon the beam, for the breadth of the ship. And now for the racking of the Stem, that is .13. times .13. and that cometh to .169. and now cubitely, and that maketh 2197. Now this number double, maketh .4394. Now extracting the cubit root it will be .16. and .298.768. and that cometh unto .4 inches and 4/7. parts: so that you may conclude, that the ship must rack forwards with the Stem .16. Foot, & .4. inches & near. ¾ parts. And now for the stern post, and that is .7. Foot, therefore .7. Times .7. is .49. and that multiplied again by 7. and that maketh .343. Than it being double .686. then extract the cubit root, and that is .8. and 174.1.92. and that cometh unto .10. inches, and .7.8. Part, so that you may conclude that the ship must rack with the stern post 8. foot and .10. inches, and .7.8. Parts of an inch. And now for the depth in the whole, that being 9 foot, 9 times .9. is .81. and that multiplied cubitely, maketh 729. and that being doubled, than it is .1458. and then the cubit root being extracted, is .11. foot & 127. of 363. part, & that cometh unto in inches .4. & 4. of 5. parts, so that you may conclude that the ship must be in deepness in hold, 11. foot and 4. inches, and 4. of 5. parts of an inch just. And now the ship of 100 tons, did draw 12. foot, when that she was Laden. Wherefore you must keep a proportion, in all the parts of the work, as is afore declared unto you: then shall the ship of 200. tons, draw or go into the water by this aforesaid means, 15. foot, and one inch and a half: and by this means which is the extracting of the cubic root, you may make a ship or boat or any other craft, of what burden soever you list: and to keep that mould and proportion that the other was made of, in all points. And by this means and order, you may know the quantity of any manner of cask, and to make it by proportion how big or little soever you will have it. The seventh Chapter doth show in like manner the making of ships by proportion, saving that the cubike root is extracted already with an easy way how to make them, of what tonnage or burden, you list, and of that mould and proportion in all points. ANd now for that I do know the most part of men cannot extract the cubike root, for that kind of arithmetic is very hard, and not easy too be learned, therefore I mean to make a little easy note, for that they shall not altogether lose their time, in reading of this, but that they shall have some help for the doubling of cubes, although it be nothing in the respect of them that have the use of the second part of Arithmeticks, as the extracting of roots and cubes, and cubike numbers. etc. first thus: if so be that you have a cube or globe, and would have an other as big again, or but one quarter more, Of Cubes. than put the side of the cube, that you have for ensample, into 4. equal parts, and if that you would have that one quarter bigger, then make the bigger cube of 4. of those parts and 1. of 3. To make a cube a quarter bigger. part, and then have you your desire. And if that you would have it half so big more, still putting the side of that Cube that you have for ensample, into 4. equal parts, then make the side of the other cube of 4. of those parts, and 2. 3. parts more, and that shall make an other cube as big, and half so big again, as the other. And furthermore, To double a Cube or globe. if that you would have a Cube to be two times the bigness of the Cube that you have for ensample, that is double measure, than put your Cube into 4. equal parts, and make the other Cube of 5. of those parts, and 1 of 25. parts more, and that shall make a Cubbes big again: To make a Cube 3. times so big. and to have a Cube three times so big, then make the Cube of 5. of those parts, and 8. of 9 parts more, and that shall make a Cube .3. Times so big. And furthermore, for to have a Cube 4. times so big, then make the Cube of 6. of those parts and 5. of 14. parts. And furthermore, to make a Cube 5. times so big, then make the Cube of 6. of those parts and 6. of 7. parts more: If a Cube or Globe be double measure, them that is 8. times to big. then to make a cube 6. times so big, then make the cube of 7. of those parts and 1. of 6. part more, & if you would have a cube 7. times so big, them make that cube of 7. of those parts, 13. of 18. parts more: than if you would have a cube .8. times so big, then double the measure, and that is just 8. times so big without any fail, as afore it is declared, the one being 4. and the other being .8. Than your measure is doubled. Now this short note or remembrance, you may according unto the Chapter going before, you having a ship or boat that you would have an other of that mould and proportion in all points, and would have her as big again, more or less, you may do it by this note afore written: as thus: if you would have her as big again, Then put the length of the keel of the ship that you would have an other made by, and to keep that mould and proportion in all points, into .4. Equal parts, and then make the bigger of 5. of those parts, and .1.25. How large or short soever that it be, and do this also by every beam and every principal timber: and every other thing that leadeth any work, and you shall not fail of the truth, for so much as this doth show, which is nothing in the comparison of them that can extract the cubit root, it maketh not matter how big or small soever the proportion is. And this note is but till the root is increased to .8. times his bigness, and so much as this doth show, you shall find it reasonable exact enough. And yet furthermore, this is an easier way to build any ship or boat by proportion. An easy way to make ships by proportion. And first this: if you do mean to be one quarter bigger, that is to say, if that you would have a ship of 4. score tons, and would have an other .100. Tons: then for every 12. foot or inches, that the ship that you have for an ensample, is, in length, breadth, and deepness, and so consequently every part that leadeth any work, make the bigger of 13. foot or inches, and you shall have your desire. And further, if that you would have her half so big more, that is to say, your ship that you have for ensample, being .80. Tons, and to have the other 120. tons, then for every 6. foot or inches, make the other of 7. foot or inches. And furthermore if that you would have her full as big again: then shall that be for every 50. inches, make the bigger 63. inches, and then that ship shallbe of .160. Tons, that is, double burden. And then to be three times so big, then for every .36. inches, make the bigger of .53. inches. And then if that the lesser ship be .80. Tons, the bigger shallbe 240. tons: and if that you would be 4. times so big: then for every 56. inches, make the bigger of 89. inches, and then have you your desire, the one being 80. tons, the other shallbe 320. tons. And further, if that you would have be 5. times so big, then for every 7. foot or inches make the bigger of 12. foot or inches, and then the one being 80. tons, the other shall be 400. tons, and if that you would have the bigger to be .6. Times so big, then for every .24. inches make the bigger of .43. inches, and then the one being .80. Tons, the other shallbe 480. tons, and then to be .7. times so big, for every .72. inches, make the bigger .139. inches: and then the bigger ship shallbe, 7. times so big: the lesser being .80. Tons, the bigger shallbe .560. Tons: and then as afore is declared, if that the measure be double, than the bigger is .8. Times so big: that is .640. Tons. The eight Chapter showeth how much that one rope is bigger than an other: and if that you have a rope of any size, than you may know how to have another of what size you list: and also if that you do know the weight of one rope: you may know the weight of any rope by proportion. YEt furthermore, I do think it convenient for diverse considerations, for that I do do know that there is but very few Sea men, that hath the use of the extracting of the square root: and without that they cannot know how for to fit a ship with ropes, but that they must of force, many times put too big or too small a rope in diverse places, not meet for that room, How to altar the bigness of ropes & how to double the size until they do see it by common experience, and afterwards amend it. Wherefore I will make a little brief note, for the doubling of ropes by proportion. And first by a rope of .3. inches compass: and to have another as big again, some will hold an opinion, that it must be .6. inches compass, but than it is 4. times so big: therefore to have it as big again, it must be in compass .4. inches, and 1. of 4. parts, and then to have a rope of .3. times so big as the rope of .3. inches compass, than that rope must be of 5. inches, & .1. of 5. part, in compass: then to be 4. times so big, then that must be double measure: that is 6. inches compass. Then too have a rope .5. Times so big: then that must be in compass .6. inches and .3. of .4. Part of an inch: then to be 6. times so big, than it must be in compass .7. inches and .5. of 14. part: and then .7. times so big to be in compass .8. inches, lacking 1. of .16. part: then to be 8. times so big, to be in compass .8. inches .1. of 2. part: then .9. times so big, to be in compass, just 9 inches: then being 10. times so big: than it must be in compass .9. inches, and 9 of 20. part: then 11. times so big, to be in copmasse .9. inches, and 9 of 11. parts: and then to be 12. times so big, to be in compass 10. inches 2. of 5. parts: then .13. times so big, to be in compass .10. inches: and 17. of 20. part: then to be 14. times so big, as the rope of .3. inches compass: therefore that must be 11. inches, and 5. of 22. parts in compass: then to be 15. times so big, then to be in compass 11. inches, and 7. of 11. parts: then 16. times so big, in compass just 12. inches. And then to be 17. times so big, them to be in compass .12. inches, & 3. of 8. parts: them to be 18. times so big, than it will be in compass 12. inches, 9 of 12. part: & 19 times so big, than it will be in compass 13. inches, & 1. of 13. Then being .20. times so big, them it willbe in compass 13. inches 11. of 26. part: and then to be .21. times so big, it must be in compass .13. inches 10. of 13. parts. Then to be 22. times so big: than it willbe in compass 14. inches and .1. of .14. Parts: then to be .23. Times so big, it willbe in compass 14. inches, and 11. of 28. part: then too be .24. Times so big, it willbe in compass 14. inches, and .10. of 14. parts: then 25. times so big, too be in compass just 15. inches: and then too be 26. times so big: than it will be in compass 15. inches, & 3. of 10. parts & then to be 27. times so big, it will be in compass 15. inches, 3. of 5. parts: and then too be 28. times so big, that willbe in compass 15. inches, and 9 of 10. parts: then 29. times so big too be in compass 16. inches, and 5. of 32. parts. Then too be 30. times so big to be in compass 16. inches, and 7. of 16. part: and then to be 31. times so big, to be in compass 16. inches, and 23. of 32. part: then to be 32. times so big, must be in compass 17 inches, lacking 1. of 34. part: and then to be 33. times so big, that willbe in compass 17. inches, and 4. of 17. part: and then to be 34. times so big, it willbe in compass 17. inches, and 1. of 2. part: and then to be 35 times so big, that willbe in compass 17. inches, and 13. of .17. part: and then to be 36. times so big, it willbe in compass just. 18. inches. And then to be 37. times so big, then too be in compass 18. inches, and 1. of 4 part: then 38. times so big, to be in compass 18. inches, and 1. of 2. part, and then to be 39 times so big, it willbe in compass 18. inches, and 3. of 4. part: then to be 40. times so big, it willbe in compass 19 inches, lacking 1. of 38. part. And now by this little note, you may know how big or small that one rope is by another, so that the ropes be all of one kind of stuff, and also of like hardness in the woorekmanshippe, or laying. And yet furthermore, I do think it convenient, for to compare one rope by another, of the bigger sort: Of doubling of the bigness of of ropes. for that which goeth before, they be all compared but unto one rope of 3. inches compass. And first by a rope of 6. inches compass: and to have another as big again, that must be in compass 8. inches, and 1. of 2. part: and to have a rope 3. times so big as that of .6. inches compass, that must be in compass 10. inches, & 2. of 5 parts: and then to be 4. times so big, as afore is declared, that must be double measure 12. inches compass. And you have another, of 7. inches compass, and would have another as big again, it must be in compass, 9 inches, and 17. of 18 parts: and to have another 3. times so big, must be in compass .12. inches, and 1. of 8. part: and 4 times so big, is 14. inches compass: than you having a rope or cable of 8. inches compass, & would have another, as big again, then that must be in compass .11. inches, and 7. of 22. parts: and to be 3. times so big, that must be in compass 13. inches, and 23. of 26. parts: and 4. times so big, double measure, that is 16. inches. And then you having a rope or cable of 9 inches compass, and too have an other cable as big again, must be in compass 12. inches, 3. of 4. parts: and then to be 3. times so big, must be in compass .15. inches, and 3. of 5. parts: and then to be .4. Times so big, that is double measure .18. inches. Now you having a cable of .10. inches, and would have another, as big again, that must be in compass .14. inches, and .1. of 7. part: and to be .3. Times so big, must be in compass .17. inches, and .11. of .34. Parts: and to be .4. Times so big, to be .20. inches. Now you having a cable of .11. inches, and to have another as big again, that must be .15. inches, and .17. of 30. parts: and to be 3. times so big, must be in compass .19. inches, and 1. of .19. part. Then to be 4. times so big, to be double measure, that is, 22. inches. Then you having a cable of .12. inches compass. And to have another as big again, that must be in compass 17. inches, lacking .1. of 33. parts: and to be .3. Times so big, must be .20. inches, and .4. of 5. parts: and to be .4. Times so big double measure, that is, 24 inches in compass, and then furthermore, if that you have a cable of .13. inches, and would have another as big again, then that must be in compass .18. inches, and 7. of 18. parts, and to be .3. Times so big, must be in compass 22. inches, 23. of .44. Parts: and then you having a cable of .14. inches, and would have another as big again, then shall that be in compass .19. inches, & 31. of .38. Parts. Then you having a cable of .15. inches compass, and to have an other, as big again, then shall that cable be in compass .21. inches, and 3. of 14. parts. Now I do think this sufficient enough, for to know the proportion of ropes, the one by the other, and also by this little note they may fit any ship with a mast, doing, even as you do by the proportion of ropes, in all points: for if that you should double the measure of any mast, that Mast shallbe .4. Times the bigness of the other, so that by the order of the proportion of ropes or cables, they may know the proportion of the masts without any fail. And furthermore, I do think it convenient to show unto you, how to double any rope or Mast: and that you shall do thus: How to double any rope or mast, by extraction of the square root. Take the compass of that rope that you have for ensample, and that being known: then multiply that number in itself: then that being done, look what quantity you would have the other bigger: then increase that number unto that bigness, then extract the square root thereof, and that rope shallbe in compass your desired purpose. As for ensample thus, by a rope of 5 inches compass, & I would have an other rope as big again, & you must do that in this manner. first multiply that rope in itself number, that is to say, 5. times 5. and that maketh 25: then double that number, and then that is double 50. and then the square root of .50. is 7. & 1. of 14. so that you may conclude that the rope of 7. inches compass, and 1. of 14. part, is as big again as that rope of .5. inches compass: and by this order you may double any rope as often as you list. And now furthermore, in like manner, Ensample if that you do know the weight of the fathom of one rope, you may easily know the weight of a fathom of an other rope, how big or small soever that it be, as thus: double the proportion of the 2. ropes, and multiply them as you do in fractions: suppose it as thus. I have a cable of 13. inches compass, and that weigheth 16. pound every fathom: now what shall a fathom of that cable, weigh both of one kind of that stuff, that is 16. inches compass? first multiply .10. Times 10. and that is 100 and then multiply .16. times 16. and that maketh 256. and then multiply the number of the bigger rope by the weight of the lesser, that is to say .256. times 16. and that maketh 4096. and now divide this number by the number of the lesser rope, and that is 100 and then there will stand in the quantity line 40. and 96. will remain over: so that you may see the cable of 16. inches compass, that a fadone thereof doth weigh near 41. pound, & by this order you may know the weight of any rope or cable, and if that you would know the weight of a lesser rope; you knowing the weight of his bigger, then multiply as afore is said, and then shall you multiply the weight of the bigger with the number of the lesser, and then divide that sum by the number of the bigger, and so shall you know how many pound that a fathom of the lesser rope weigheth. As for Ensample thus, by the cable afore mentioned, of 10. inches compass, and a fathom did weigh .16. Pound, what shall a fathom of a rope of 8. inches in compass weigh: now as before is declared .10. Times .10. is .100. and .8. times .8. is 64. therefore multiply 64. by 16. and that maketh 1024. and then divide that by 100 and then there will stand in the quantity line 10. and 24. will remain over: so that you may conclude that the rope of 8, inches, that every fathom doth way 10. pound and near a quarter, and this is true without any fail, and by this order you may know the weight of all manner of ropes. etc. The ninth Chapter is as touching the mould of ships, to have good qualities. ANd furthermore, in as much as I have showed how for to double or alter the tonnage or the burden of ships too what bigness you list at your discretion, and also to keep that mould and proportion in all points: therefore I do think it necessary and convenient to say somewhat in this point, that is to say, what manner of form or fashion that the mould of a Ship should be, that should go or fail well, and to have good qualities in the Sea. And although that it is possible that some will think that I do meddle with those matters that I have no skill in for that I am neither Naupager or ship carpenter, neither usual Sea man: therefore it is possible that I may be dislyked, for that I do meddle in this matter or causes. Yet not with standing you that do read this, use not to condemn any thing before that you have perused it well: and so weighing it in a pair of indifferent balances, that affection doth not lead you, it is possible that it is not altogether untrue, but that there is some matter in it that is good to be considered of in the building or the making of ships: and those matters that you do know by experience to be untrue, them you need not make any account thereof. etc. And first thus, Of Ships that sail well with the wiend. as concerning the making of the mould of any ships, this is to be noted, that those ships that are of easy draft, that is to say, not to go to deep in the Sea or water, and will bear a good sail, and doth steer well, that is to say, that it will feel the Ruther as soon as the helm or Tyller is put to or fro, and those ships do go or sail well beeringe or afore the wind, that is to say, the wind to be large or to come right after them, all those ships do sail well and close by the wind, that is to say, the Bowline to be haled hard or close, and the ship to stand or come as near the wind as may be: those ships must draw a reasonable draft of water: and also to be a reasonable good length, and these ships will go well a head the sea, Of Ships that sail well by the Bowlyne to be hard pulled or also to sail well a head the Sea. that is to say, the Ship to stand close by the wind in such places as the grating of the tide doth cause the sea to come against the head or bows of the Ship. Then those ships that have a reasonable length and well breasted or bowed, and not the buttocks or stern of the ship to be to big or to full quartered behind, but to be reasonable lank at the stern, those ships do go or sail well a head the Sea, so that they will bear a good sail, Of ships that ride well or ill at anchor. and not over held, that is to say, not to go to much on the one side, but if that any ship be too fat buttocked or broad behind at the stern, & the bows or breast of the ship before be to slender or narrow, those Ships will never go or sail well a head the sea, but will fall or beat into the sea, that it will let or hinder the way or going of the ship. And also those ships will ride very ill at road or anchor in the Sea, for that the broadness of the buttocks of the ship doth so thrust down the head of the ship into the Sea, and especially if that the bows of the Ship he to narrow or slender, that the Sea shall fly into the ship or quite over her, as well at an anchor or sailing, or going a head the sea: which is a very ill property in a ship in a number of causes. And all those ships that doth draw or go a good deepness into the water; as before is said, do sail well by the wind, & also will lie a hold well in the sea, that is to say, the ship having no sail abroad, will not seel in roll so much, neither in like manner it will not go so much unto lewards, that is to say, that the wind nor the sea shall not drive it so fast back again, as it will do a ship that doth draw or go but a little way into the Water: and also those ships that do draw but a little water, be very ill in two causes, if that they do lie a hold in the sea, that is to say, to have no sail abroad, for they will seel or roll in such sort that it will put all in danger, besides the driving to lewardes with the sea & wind. Therefore these Ships must have always sails abroad, if they be lose at the sea, and also those kind of ships will ride ill at an anchor, at such time as the tide doth go unto the wyndewardes, for lying thwart, it will seel or roll so much. But the wind and tide to be all one, that the Ships head to be right upon the Sea, and as before is said, the Ship well bowed, and the stern not to full quartered, than it will ride very well at an anchor at that time. etc. Of Ships that steer well and do bear a good sail. And now furthermore, as touching the building or making of ships for to steer well, and also to bear a good sail, which is two of the best qualities that is or may be in a Ship: and except that it be a very chance those Ships do always sail very well, if that the mould of them be any thing well ordered in the form thereof. etc. And although that the mould of a ship be never so finely made, and if it do not steer well, than it can never sail well. And also if the mould of the Ship be never so well made, and if it will bear no sail but over heeled, that is to say, to lay down the side in the water, than it can never go well, how fine so ever the mould is, for it is ill shapen to go, when all the one side is down in the water, and the other side all out of the water, and then it cannot abide the force of the wind to drive it: whereas the Ship that is able to bear a good sail, must needs go well, for that the force of the wind must needs draw it, for that it is able to bear sail, and then the wind must needs force it to go. etc. And first thus, as touching the cause that any Ship doth steer well, is this: that the quick water of the way of the ship doth come unto the Ruther being put either the one way or the other way, that must needs, cause the Ship to cast or turn accordingly and the faster that the ship goeth, the nimbler or quicker the ship steereth or turns. Therefore when soever that they do build or make any ships, than it is good for to let them make the mould of a ship to have a sufficient tuck or run, which tuck or run must be in length the third part of the length of the reel, and in height, by the stern post, three quarters of that depth that the ship goeth into the Water, A thing to be noted. and so to grow narrower and narrower forwards: for it is the sufficientnesse of the tuck or run that maketh a ship to steer well. For if that be not well made, than it requireth to have the brother Ruther, and that is evil in two respects: the one is this: the helm being put over, and if that the ship will not feel the Ruther quickly, than the Ruther lieth cross the stern of the ship: and the Ruther being broad, than it must needs hinder or let the going or way of the ship very much: Whereas a ship that hath but a narrow Ruther, and yet is yare or quick of sterrage, than the Ruther cannot hinder the going or way of the Ship: etc. And also it is evil in an other respect to have a broad Ruther, and that is this: for a ship being at Sea in foul weather, a broad Ruther the Sea doth beat it one way and an other way, by the means of the labouring of the ship to and fro, that it is apt to break the tiller or the head of the Ruther & Ruther Irons: and besides that, it is uneasy for the ship in like manner. etc. And thus I do omit the rest of the proportion of the mould of the ship unto the discretion of the Naupeger or ship Carpenter, as touching the fore way and the flowringe of the ship, and the leading of all the rest of the work etc. The cause that a Ship doth bear a good sail. And furthermore, as touching this point to cause a ship to have a stiff side to bear a good sail, than this must be considered in the building or making thereof: and first thus: that commonly those ships that have a sufficient breadth according unto their bigness and length, will bear a reasonable good sail, for that the breadth doth bear it up. But commonly those be not the best, and finest sailors, neither are they of the best qualities, in divers respects. Yet notwithstanding, in my opinion, this is the principallest point to observe in the building of ships, to have them to bear a good sail, and that is this, for to lay the breadth of the ship above the water, a foot, or a foot and a half, more or less, according unto the bigness of the ship, and to hang well of, that is to say, to be 4. or 6. inches on a side brother than it is just at the edge of the water, and to be more or less, according unto the bigness of the ship: and then upwards the work may be housed inwards, that is too say, narrower and narrower upwards, which will do well, both for the ease of the ship in the Sea, and less charge of timber bathe in weight, and otherwise: and in so doing, the ship will bear a good sail, what length so ever it have, how fine so ever the mould is, so that it have quarters proportionally unto it. etc. And the cause thereof is this: the breadth of the ship being above the water in such sort, as if the ship come unto heelding, that the same brother place doth come into the water: then the Nadry or reel of the ship, doth grow the further of, by the means of the hanging ofwardes of the side or work of the ship. And for that the ballast or the lading of the ship, the weightiest part lieth downwards towards the reel, therefore it maketh the ship the loather to held a tosyde, for that the side hangeth outwards, and then the water doth support it up, for that the bigger or brother part is out of the water, as the reason thereof more plainly shall appear in the fourth book of the property of Water in weight, called Statick, wherein you shall see the reason thereof more manifestly etc. Whereas those ships that have an upright side, must needs held much the sooner, for that the Water doth not support the side, not until it do held very much. Wherefore thus much I have said as touching the mould of ships, as concerning their qualities, as thus: Note a ship that hath Tuck or run enough, will steer well: a ship that doth hang well of on the nail above the water, will bear a good sail: a ship that doth draw a reasonable good draft of Water, and well weighed forwards, will sail well by the wind: and being well bowed and not to fat buttocked, will go well a head the sea, and also ride well at road, and also will hold well at the Sea lose. and floty ships that steer well and will bear a good sail, will sail well, the mind being large. etc. And thus I do end this third book. etc. FINIS. ❧ A Table of the contents of the Chapters of the third book, called a rteasure for travailers. The first Chapter of the third book, showeth you how to cast the contents of land by arithmetic, and also by the husband man's rule, which is by the account of money. etc. The second Chapter showeth how to measure board and glass, and too cast the contents thereof, with other necessary things belonging thereunto. The third Chapter doth show how for too measure timber, and to bring it too a square, aswell without Artihmetike as otherwise, and also how for too know the true contents of any piece of timber. The fourth Chapter showeth how for to measure all manner of bodies, as timber, or stone, Cubes, or Globes: and too know what proportion of measure or weight the one hath unto the other. The fifth Chapter showeth how for to measure Globes, and to know their contents in inches or feet. The sixth Chapter showeth how for too build ships by proportion, that is to say, if that you have one ship for an ensample, if you would have an other as big again, more or less this Chapter doth show unto you how you may do it, keeping that mould and proportion in all points, that is too say, by extracting of the cubic root. The seventh Chapter doth show in like manner the making of ships by proportion, saving that the Cubike root is extracted already: with an easy way how to make them of what tonnage or burden you list. and of that mould and proportion in all points. The eight Chapter showeth how much that one rope is bigger than another: and if that you have a rope of any size, that you may know how for to have another, of what size that you list, and also if that you do know the weight of one rope, you may know the weight of any rope by proportion. etc. The ninth Chapter is, as touching the mould of ships, to have good qualities. FINIS. ❧ The fourth book of the treasure for travailers. Wherein is touched the art of Staticke or weight, showing unto you how you may know the weight of any ship that swimmeth upon the water, with all her lading, and all the rest of her furniture. And also how you may know the weight of any metal that is sunk in the water, to know what it weigheth in the water, and also how you may measure any strange form, such as geometry cannot give you any order for the measuring thereof, and also how for too lift or way any thing sunk into the water, with other necessary matters belonging thereunto, very necessary for all land men, and seamen. etc. Written by William Bourne. To the Reader of this fourth book. GEntle Readers, it is possible that you will marvel, that I should take upon me too deal in these causes, that is to say, to teach any new Art, and Science, that hath not been as hytheretoo, written in any language or tongue, the which Art or Science, called Staticke, doth show the heaviness or lightness of any thing. Wherefore there is contained in this fourth book, how too know the weight of any thing swimming in the water, as the weight of any ship, with all her loading, and all her furniture: as ordinance, Ankers, Cabels, masts, sails, with all other implements in them, and also it doth show the weight of any thing sunk into the water, what it weigheth, to be lifted from the bottom, till the appearing of it above the superficies of the water: with divers other necessary matters that are contained in this fourth book, and not before this time mentioned by any other, but only by that famous and learned man Master John Dee, who hath made mention thereof in his mathematical preface, wherein I have had my principal instructions, as touching that art or Science. Wherefore Gentle Reader, bear with my rudeness, that I being utterly unlearned, should enterprise too take upon me too be so bold, too give the first attempt, to employ that Art or Science unto any purpose: for I do know the nature of most people, is to dislike all things that are not done by themselves, whether it be good or evil: and as I have known many times by experience, that those persons that have learned any thing at any man's hand, when he doth understand it, than he will not be known where he learned it, but that he knew that before or ever he showed it unto him, which is a manifest robbery of any man, to learn any thing at any man's hand, & then afterwards to deny it, & to say, that he knew it before he told it him: as I do know a number of persons, that when they are ignorant in matters, than they will use diligence till they have attained it, and then when they have a little instructions to serve their turns, than they will seem too be very cunning, and that they never learned any thing at any man's hand, which is a great point of ingratitude, too offer that person that he hath learned of, such a great injury: but yet notwithstanding the earth is greatly infected, with such manner of persons. The fourth book, of the treasure for travailers. The first Chapter of the fourth book, showeth you by the proportion of a ship swimming in the water, for to know the true weight of any ship, with all her tackle, ordinance, and lading. etc. FOR that I have said somewhat heretofore as touching the making of Ships by proportion and otherwise: Therefore I do think it necessary and convenient to treat partly of this, as touching the nature and quality of water, for the sinking or swimming of things in it, and according unto the simple opinion of the common people, Of things that do swim. who think that things in the water do swim or sink, for that it is wood, Iron, or Stone: but the only cause of things that do swim, is this, that it is lighter than the proportion in quantity, than the water is. For this is general for ever: look how much of any timber or any other thing that is hid, or in lownes even with the water, as just of weight as of so much water, as the true quantity of that part that is from the edge of the water downwards into the water neither heavier nor lighter, and then that part that is above the water doth show justly what diversity of weight is between the water and the wood, or any other stuff that is put into the water. For any thing swimming in the water, the half being above the water, and the other half underneath the water, that thing that swimmeth in that form, is just half the weight of so much water: and if in the swimming .3. quarters be buried in the water, that thing is just 3. quarters of the weight of so much water, and so forth, to any other proportion, and then adding so much in wait, to make it of the just weight of the water: then that thing being in the water, shall swim even with the edge of the water neither higher nor lower. But if it be any thing heavier than the proportion of so much water, than it sinketh unto the bottom: and then look how much in weight it is hevier than the proportion of so much water: so much it weigheth in the water the lighter, Of things that sink. as the weight of the water cometh unto. For if any thing in the water, be double the weight of the water, proportion for proportion, then shall that thing weigh just half the quantity of that weight, till it be lifted from the bottom unto the very edge of the water, and then if that the thing do weigh but half the weight more than the quantity of so much water: then shall that thing in the water to be weighed, weigh but one third part of his weight that it would weigh, if that it were out of the water, and so forth to any other weight or weights, having proportion in bigness, according to the quantity of the water, whether it be brass, Stone, or Iron, or any other stuff what soever it be. And also things that do swim, as wood, or any other stuff. Wherefore this is to be noted by the way, the perfect weight of any ship with all her lading, ordinance, masts, sails, and Tackle, with all other implements in her, may be easily known by her only swimming, as thus: Look what quantity of the Ship is buried in the water, that is to say, from the edge of the water downwards: then if there were a vessel or great thing made of the proportion of the mould of a ship, as much as is buried in the water, if that were filled with that water that the ship were in, the water should be of just equal weight, that the Ship were of, with all her tackle and implements in her. And now this being true, as it is most certain, than the weight of the water being known, any vessel or body is to be measured by geometrical means. etc. And furthermore, here is one special thing to be noted, and that is this, All water is not of like weight. all waters are not of like weight, for the finest water is lightest: therefore if that any Ship be in the lightest water, then doth she swim the deeper, according unto the weight of the ship, and the weight of the water, quantity for quantity, and in like manner any ship being in the heavier water, then shall not the ship swim so deep, for that the water of his own force, will life the Ship out of the water, until there be that just quantity and proportion, according unto the just weight of the water and weight of the ship: for this is seen daily by common experience, amongst Sea men and mariners, that if you do lad any ship in a fresh water or river very deep, Salt water is the heaviest water. then when she is in the Sea, and specially in the Occient Sea, that the ship shall be lifted up higher by .3. or .4. inches out of the water wards: And then when the ship is come again into a fresh water river, than she shall be as low laden as she was before. Wherefore in the building of Ships, the one of the principal points is this, the flowering and quartering of them: for there may .2. ships be made both of one length, and of one breadth, and of one deepness in the water, and yet the one may be near as big again as the other, for if that the one be full quartered, and a broad flat flower, (as the Hulks be commonly) it must needs be of a greater burden, than a sharp ship that hath neither flower nor quarters, as commonly the Spanish building is: for the water cannot bear it before it be deep enough into the water: therefore these kinds of ships draw very much water & be but of small burden, for a sharp ship must have very much ballast, or else she will bear no sail: and especially if they be very high builded or larged above the water. etc. The second Chapter showeth how for to measure the proportion of the mould of any ship, whereby is known the weight of any ship with all her lading and furniture. FOR to know how to measure the proportion of the mould of a ship whereby may be known her weight, with all her lading, it is somewhat tedious, and asketh long work, and must be precisely handled, for that it keepeth no form long together: therefore it must be measured in many parts. How to measure the mould of a ship. And for to measure the mould of a ship, the ship must be brought a ground, and then begin at the broadest place of the ship in this manner: first measure the breadth of the ship from outside unto outside, at that very place of the upper edge that the ship doth swim in deepness into the water: then that being known, measure the true deepness that the ship doth swim into the water, at that place of the broadest part of the ship: then that being known, take the true contents of half the breadth of the ship, and then with a rod or pole lay the end of the rod or pole that is just the length of half the breadth of the ship, unto just the half keel in breadth at that place before spoken of, and then with an other rod or pole of the just length that the Shppe doth swim in deepness into the water, lay the end of that rod or pole at that place that the upper edge of the water doth touch: and then let both the other ends of the two rods or poles touch just together, and so will they make a square Angle: and then measuring or trying between the Ship and the 2. rods or poles as you do in the measuring of superficial or plat forms, so shall you know the contents of that part that is within the inside of the ship, by subtracting or taking away of that measure between the two rods or poles with the outside of the ship, for that you must consider that it is a square enclosed from the middle of the inside of the ship, unto the deepness that the ship doth swim in the water, and unto the two rods or poles, and hath four square or right Angles or corners: and then if that you do multiply it according unto the breadth of the ship and the deepness that the ship doth go into the water, as you would do if that it were a plat form: then pulling away the contents of that same being doubled that the measure is between the ship side, and the two rods or poles, then that which doth remain shall be the true contents of that part which is within the inside of the ship as though it were a plat form: and then look how many foot long it runneth in that form and proportion in breadth and roundness of the side: then according unto the length multytiply the one by the other, that is to say, the contents of the measure before taken of the inside of the ship, and the length that the mould doth keep in one proportion, and then cast the contents thereof. And that being done, do as before is rehearsed, according unto the breadth of the Ship in an other place: then according unto the deepness that the Ship doth swim in the water, and then doing with the two rods or poles as before is rehearsed, and so trying between the ships side, and the two rods or poles, and casting the contents in all points as before is rehearsed: and thus you must do in as many places and as often times as the proportion of the mould doth alter: and then adding them altogether, you must see how many foot that the ship doth contain, if it were all one whole piece of Timber, and not hollow within. And now this being done exactly as it may be done with precise diligence, you knowing the true contents how many foot the soled body of the mould of the ship doth contain as much as is buried into the water, you may know justly the whole weight of that ship that you have so measured, with all her lading, ordinance, tackle, anchor, and cables, with all other implements in her, as thus: Take of that water that the ship swimmeth in, and make a cube of metal or wood of just .12. inches square, and deep: for that 12. inches square every way, maketh a foot, and then weigh the water justly how many pounds and part of a pound the water doth contain in weight, and that shall show you justly how many pound and parts of a pound every foot square of the mould of the Ship doth weigh justly, and then if that you do multiply the contents of the number of feet, that the mould is, and the weight that one foot of the water doth weigh in pounds and parts, then according unto that number, the ship with all her lading, doth weigh justly without any fail: so that you have measured the mould of the ship truly, and also weighed justly the contents of one foot of the water: and then by that number you may say justly, it containeth so many tons in weight, as thus: by dividing the number of the weight of the ship by .2240. for that a tun containeth 20. hundredth weight, and every .100. Weight, to contain 112. pounds. And furthermore, you may measure the mould of a ship in this manner, with such a thing as the ship Carpenters do take the mould of a Ship, and that they do call a mould, or lynck gin, and that is made of many pieces, of a foot long, or there about, and it is clenched together with roof and clench, that the joining will be put to and fro at your pleasure, and will stand stiff as you do leave it. And now with this instrument, you may work more easily than before is rehearsed: for to know the contents or quantity of the mould of any ship in this manner: Take at every place the half of the true breadth of the ship, and then in like manner the true deepness that the ship doth go into the water, at every place that you do measure the ship at, for that all ships do draw more water at the stern, than they do at the head: and then you may put three pings of wood into the ground, the one pin to be at the middle of the ship, and the other to be for the outside of the ship, and the third to be for the middle of the keel of the ship, and to set them truly in distance, according unto the half breadth of the ship, and the other unto the true deepness that that ship doth go into the water, and so shall that pin for the middle of the ship, make a square Angle unto the pin, for the side and the keel of the ship, and then with the instrument lay that unto the side of the ship, and put it in and out as the ship doth round from the place of the upper edge of the water unto the keel, and then laying that mould of the ship unto the two pings, that is to say, to that pin for the side, and the pin for the keel of the ship: and then measuring that in closer, as you do a platform, the truth of the contents shall appear, and then doubling that number, it will show you the contents of the whole breadth of the ship, and then to multiply so much in length, as doth keep one proportion: And thus doing as often times as the proportion of the mould doth alter, and then adding all your numbers together, and casting the contents in all points, as before is rehearsed, the truth of the solid body of the mould of the Ship shall appear, and so taking the true weight of one foot of that water, as before is expressed in all points. And thus I do make an end of the measuring of the mould of ships, for that there wanteth or lacketh nothing, but to show how to measure plat forms, and as for those matters, there are divers books extant, sufficient enough for that purpose, as Master Leonarde Digges in his book called Tectonicon, and Master Thomas Digges his book called Pantometria, with other. The third Chapter showeth you an easier way than before rehearsed, by the art Saticall, to know the true weight of any ship, with all her lading, and all the rest of her furniture. AND furthermore, for that it is somewhat tedious and asketh long work, beesydes divers other encumbrances that must be used to measure the true proportion of the mould of a ship, I will show unto you a more pleasant and easier way (by the art Scaticall) both very true and exact, for to know the true weight of any ship, with all her lading, masts, sails, anchor's, Cables, and ordinance, with all other implements in her. And any Noble man, or Gentleman may do it at home in his Chamber, that hath any knowledge in the mathematical Sciences, as thus: An easier way to know the weight of a ship. first cause the Carpenter that doth build the ship, or otherwise, if that you desire to know it by any other ship that is builded already, if that ship have any occasion for to come a ground: then get some cunning Carpenter to take the true mould of that ship, as though that he should build an other of that mould and proportion in all points, as much as is buried into the water, when the ship is load unto her load mark, & that being exactly done, then cause him for to make the true mould and proportion, than cause the Carpenter for to cut out of a piece of timber the true proportion of the mould of the ship in all points, as thus. For every foot long, make the mould in timber in length, an inch: and for the breadth in like manner, for every foot make the other an inch, and also for every foot in deepness, that the ship swimmeth into the water, make the mould in timber one inch, and so consequently every part and place both of the roune, and way, and floor, with the quarters of the ship, to cut the mould for every foot, and part of a foot, an inch, with those parts, even as the work or mould of the ship doth run, in all points: and that being exactly done, then let there be made in some kind of metal, as lead or tin, the true proportion of the mould, hollow, and sight, that it may hold water, as the mould in wood will show or lead them how to do it very truly: and then that being done, then cause an other square vessel too be made of metal in cubic wise, such a one as you may measure the hollow thereof as easily as you may measure a square piece of timber, and if that there were lines or pricks at every inch in deepness, it were all the better. And then this being done, then fill that vessel, that is made for the mould of the ship, with that water that the ship doth swim in, and that being exactly filled, then put that water into the other vessel, and look that there be none of the water shed, than you may know justly how many inches square that the water is, by measuring the water with an inch rule: and that being known, than you do know how many foot that the solled body of the mould of the ship doth contain. And then weighing instlye one foot square every way of that water, and then you knowing how many pounds, and parts of a pound, that one foot square of water doth way, then multiply the number of feet of the Ship, with that you have found before, by pouring the water into the square vessel: and then for every inch, the ship is a foot, and so by that number multiplied by the number of the weight of the pounds, and parts of pounds, the true weight of the ship shall appear: and if you do commit any error, the fault shallbe in not weighing, and measuring of it truly. The ensample of the knowing the weight of a ship. And for your better understanding hereof, you shall have an ensample of that matter before rehearsed, by a ship of .100. Tons, and the length of the mould of the ship, to be 50. foot long, and the broadest place of the mould to be .20. Foot broad, and the deepness that the ship goeth into the water, to be .12. Foot: and I first caused the Carpenter to take the true mould of the ship, and also to cat the mould in wood, according unto the length, breadth, and deepness, that is to say, for the .50. Foot long, to be 50. inches, and for the 20. foot broad, to be 20. inches: and for the 12. foot deep, to be 12. inches, with all the other proportion of the mould of the ship, to be one inch for a foot: And that done, there was caused too be made a mould in Lead, agreeable in all points, to the mould of the shp, as led, will mark easily enough: and then there was made the other vessel in lead of 12. inches square, and .48. inches deep, and then the mould for the ship was filled with water, and that being justly, and equally filled, the water was put into the square vessel, and then the deepness of the water was exactly measured, & was found to be 42. inches in deepness, & then for that the vessel was 12. inches square, 12. times 12. is 144. & so many inches there is at 1. inch deep: and then for that it is .42. inches in deepness, multiply .144. by .42. & that maketh .6048. so that you may conclude, that the mould of the ship, as much as is under the water, if that it were not hollow within, that it would contain .6048. Foot of timber. And now suppose that the water was of our water, here at Grauesende, and that is not of the lightest sort, neither of the heaviest sort, and a foot square of that water weigheth .55. Pound, most commonly, although that it may weigh sometime less, and sometimes more, it weigheth less, after much rain, and neape tides: it weigheth more in spring tides at a full Sea, upon some cause of winds, but it altereth no great matter within a pound under or over. Wherefore multiply 6048. by .55. and that maketh .332640. so than you may conclude, that the ship weigheth .332640. Pound: And then as is declared in the Chapter going before, for to know how many tons that the ship doth weigh, divide that by .2240. and then there will stand in the quantity line .148. and there will remain over .11209. so that you may conclude, that the whole ship with all her lading, and all other furniture, and implements in her, doth weigh .148. Tons, and a half of a ton. And by this order, you may know the true weight of any ship, how graat or small soever that it be, or boat, or any other thing that swimmeth. And furthermore, you may know by this art Statical, Another way to know the weight of a ship, with all her furniture. the true weight of any ship, without putting of water into the square vessel, although that you do not know the contents, how many foot square that there is in the ship, as thus: the mould of the ship being taken, as before is declared, and the proportion of the mould, made in metal hollow, as before is rehearsed. And furthermore, you may make the mould lesser than before is rehearsed, that is to say, you may make the proportion of the mould, for every foot that the ship is in length, breadth, and deepness, you may make it but half an inch, or but a quarter of an inch, at your discretion: and then filling that with water, and then weighing the water truly, look how many times the length of that mould that is filled with water, is in the length of the ship, multiply the weight of the water with that number Cubickely, and that shall show unto you the true weight of the ship, with all her lading. As for ensample by that ship, before rehearsed, that was .50. Foot long, and, 20. foot broad, and .12. Foot in deepness. And now I caused the mould too be made for every foot, A ensample. but a quarter of an inch, so that for the .50. Foot long, the mould was made .12. inches, and a half: and for .20. Foot broad, but 5. inches: and for .12. Foot deep, but .3. inches: & that being filled with water, the water being weighed, did contain in weight 3. pound, & 2. of .73. Parts of a pound, and that is scant half an ounce, and the true contents of the weight of the water: and then for that you do see that the proportion of the length of the mould, is but twelve inches, and one of 2. part: that is, but the .48. Part of the length of the ship: therefore multiply it in this manner 48. times 48. and that maketh 2304. and then to multiply it by 48. again, and then it maketh 110592. wherefore now multiply .110592. by the weight of the water, that is too say 110592. times 3. and 2. of 73. parts: and that maketh 334620. so that you may conclude, that the ship weigheth 334640. pounds. And now to know how many tons that the ship doth way, as before is declared by dividing that number by 2240. and so further, as before is rehearsed. And furthermore, you may cause in the proportion of the mould of lead or tin, to be certain Parallel lines, to be made but a quarter of an inch asunder, as many as you list, and then you may know by those lines what weight that the ship is of, when that she is not laden. And also if that you list, you may know how many tons more in weight, will load the ship, as often times as you do know how many foot or inches the ship doth lack of her load mark. And yet furthermore, you may know, how for too know the weight of any ship with all her loading, although that you have not made the hollow mould of the ship, as thus: by that mould that the ship Carpenter hath made, Another ensample how to know the weight of any ship. the wood being not so heavy as the water, then make certain holes in the mould metal, then at those holes, put in lead, until such time as the mould is heavier than the water, and then stop the holes again, that no water may go into them, and cut of that part that there is more than the mould of the ship: and that done, then in some small thing or vessel put in water unto some certain mark, and then put into that water, the mould for that ship which you do desire for too know the weight of, and be sure that the water doth cover all the mould: and then take out all that water very precyselye, that is fed by that means of the mould for the ship, until such time that the water be just in that height that it was before, that the mould was put in: and then weighing that water truly, you doing as before is rehearsed, to multiply the length of the mould of the ship according as before is declared, Cubickely, and then the weight of that water that is highed more than it was before that the mould was put into the water, and the weight of that water being perfectly known too be multiplied by that cubic number, shall show justly the true weight of the ship, as afore is declared in all points. And by all these rules or order, you may know the just weight of any thing that sooymmeth in the water, saving that you must have consideration, that any mould made of wood, when it is dry, doth receive or drink up water, and when it is wet, it swelled the bigger with the water. The fourth Chapter showeth by the art Statical, the weight of any metal or stone, how much, or what weight that it doth wayghe in the water, to be lifted or weighed from the bottom, unto the brim of the water. Now for that I have said somewhat for too know the weight of things sooymming on the water, I think it convenient too treat partly by the art Statical, to know the weight of any thing that sinketh into the water: and to know truclye how much that it weigheth more than the weight of the water, proportion for proportion, whereby you may know what it weigheth justly, being sunk into the water: and also you may know by this means, how for to measure such things, whose form, whether that it be metal or stone, that for the strangeness of the for me is not to be measured, as branches of metal, or pillars that be inbowed or hollow in one place, and boileth out in another, or any such other strange form, which is to be done by that means, that Archimedes found the deceit of the kings crown of gold. And first for to know the true weight of any metal that is sunk in the water, whether that it be brass, iron, or stone, you knowing the weight thereof before that it was sunk: then make a cube, or any other square, of that kind of metal that you would know what it weigheth in the water, and weigh that metal truly, and that being known how many pounds, and parts that it weigheth, then take of that water, that the metal is sunken into: and then if you do make a Cube, or any other square hollow, in form like unto the massy Cube or square, neither bigger nor lesser, then that you have made in metal, and weighed. And then fill that hollow cube with the water, and then weigh the water truly, and that done, look what that water weigheth, pull that sum truly away from the weight of the massy Cube or square, and that which doth remain, shallbe the true weight that the massy Cube doth weigh in the water: and so by that Cube you may know the weight of the greater portion that is sunk, as thus: The weight of the sunken metal being known, look how many times the weight of the small Cube is in the greater quantity, that is sunk, so many times multiply the weight of the water in the hollow Cube, and that done, subtract or take away so much in weight from the sunken metal, and that which doth remain, shallbe the true weight of the sunken metal in the water to be weighed, till that it doth begin to appear above the water: Or otherwise, you may do it in this manner, by the small Cube, before rehearsed, being iusty weighed, and the weight known unto you, take of that sort of water that the metal is sunk into, and put it into some vessel, fit for your purpose: and that done, then mark the edge of the water justly upon both the sides, than put your massy Cube into the water, that it be covered with water, and then take out, as much of the water as is risen above the marked places, and then weigh that water truly. And now the true weight of the water being known unto you, then as before is rehearsed, subtract or take away the weight of the water from the weight of the cube in metal, & then that which doth remain, shallbe the true weight of the Cube in metal, when it is sunk to the bottom of the water, and then by the small is known, the weight of the greater portion, as before is declared, by knowing how many times, that the greater quantity is more than the lesser, and then multiplying the weight of the water so many times as the quantity doth show, and then subtracting or pulling away that weight, then that which doth remain, shall be the true weight of the metal in the water, as for ensample thus: By a piece of ordinance of brass, that is sunk, that is to be wayged out of the water, and the weight is known to be .7000. Weight, for that it is a double Cannon, that is sunk, and I do desire for to know the true weight, what it doth weigh in the water. Wherefore I do take another piece of that sort of metal, that weigheth .100. Weight, it maketh no matter, what form that it hath, so that it be of that sort, or of that kind of metal, for whereas I spoke of a Cube before, that was to no other end, but to make the thing the more plainer, as hereafter it shall more plainly appear: and then take of that water, that the piece of ordinance was sunk into, for that all waters are not of one weight, and then put that water into some convenient vessel, meet for your purpose, and then mark the water very precisely, round about, even at the very edge of the the water, & then put the piece of metal into the water, & then having some convenient vessel already weighed, and then take out, without any shedding of the water, all that water that is above the place marked before, neither more, nor less, nor higher, nor lower, and that being done truly, then take the weight of the water, and by supposition, it is found to be .14. Pound just, and the brass, that is put into the water, being one hundredth weight, that is .112. Pound. Therefore I do conclude, that the weight of the water, is but the .8. Part of the weight of the brass or metal, so that I do conclude, that the piece of brass or metal doth weigh in the water .7. of .8. Parts of his own proper weight, that is, but .98. Pound. And now for to know the weight of the sunken Rannon, do thus: look how many hundred weight that you have in .7000 weight, and that is .70. hundred weight. Wherefore multiply .14. by .70. and that cometh unto .980. Pounds, which maketh 800 weight, and 3. of .4. part: And this sum being pulled away from 7000. weight, which is .7840. Pounds, than there remaineth .6860. Pounds, and that is .6100. and .28. pounds in weight: and every .100. Weight, to contain .112. Pound. All thing in the water, is lighter than his own proper weight by the quantity of the water in weight that it occupieth, and out of the water, it weigheth his own proper weight. And now by this order you may know the true weight of any sunken metal, what it weigheth in the water, to be weighed from the ground, unto the appearing of any part thereof above the superficial of the water: and then too be weighed above, out of the water, than it hath his own natural weight, what kind of metal soever it be, as silver, and Gold, Copper, lead tin, Iron, Steele, or Stone, or whatsoever it be that sinketh into the water, you may know the true weight of it, in the water, by the order before rehearsed, by putting into that kind of water, any piece or lump, what form soever it hath, it maketh no matter, so that it be of that sort of metal or stone, being truly and exactly weighed, and then to take out so much of that water, as by the means of that metal or stone is highed more than it was before the putting in of the metal or stone: And that water truly weighed, and the weight thereof known unto you, then rebate that weight from the weight of the metal or stone truly, and then that which doth remain, shallbe the true weight of the metal or stone, being sank into the water. And by that means you may know the true weight of any great quantity that is sunk into the water, by knowing how many times the great quantity is more than the lesser, and then to multiply the weight of the water, so many times as the weight of the greater is more than the lesser, & then that which doth remain, shall be the true weight of the greater quantity of metal, or stone, that is sunk into the water. The fifth Chapter showeth how to know the true measure in the inches or feet, of any strange form, such as geometry can give no ordering for the measuring thereof, as to measure a branch in metal, or a pillar that is enbowed and full of hollowness in divers places, and boils out in divers places: and also how to know the diversity of the weight of metal, or the diversity between the weight of Stone and metal. AND furthermore, by this means you know the true measure in inches or feet, of any strange form, what shape soever it hath, such shapes that no art by any capacity are not to be measured, whether it be in metal, stone, wood, or in wax, or gums, or what soever it be, or a crown, or crowns, or a branch, or branches, or a pillar, or pillars, or things that be inbowed in one place, and boils out in an other, or a cup, or bowl, or a pot or pots that keep not in thickness one quantity, but it is thicker in one place then in an other, as there be divers other forms not beer spoken of, that no man by art is able to measure them, for that they keep in no place one proportion. Wherefore I do think it convenient, to treat partly hereof, and to know the true contents of any form what soever it be, in inches or feet, then do thus: 'cause to be made some hollow Cube or Square, in such form that you may measure it with an inch rule with ease, and to know the true contents thereof, or any part thereof at your pleasure, within the hollow part, and then you having of diverse sorts of these hollow cubes or squares, some that do contain more, and some that do contain less, as near as shall require: and then take some convenient vessel meet for your purpose, and put water into it, and that done, then take that thing which you do require too know the true contents of the number of inches or feet, & then before you do put that into the water, mark the side of that thing or vessel round about by the very edge of the water very precisely, that you do not commit error by that means: and that being truly done, them put that metal or thing into the water, that it be covered: and that done, take out as much of the water as is risen by the means of the thing of metal put into the water, until the water do stand just at the mark that it was before: & then put that water into the hollow cube or square, without any of the water shed or spilled by, for that may cause some error: & then with an inch rule measure the true deepness of the water in the cube or square, and so shall you know justly, how many inches or feet of metal there is, by the multiplying of the length, breadth, and deepness of the water: As for ensample thus: by a branch, or candlestick (to hang in a house) of Latin or brass, my desire is to know, how many inches of metal there is contained in it: and then I did first put in water into a tub or vessel, that I had appointed for that purpose, and then I marked the water in the tub or vessel round about at the very edge of the water: and then I put the bravach or candlestick into the water, and that sunk unto the bottom, and then I took out all that water that was did by the means of the branch or candlestick of Latin, & then I did put that water into a little cube of 6. inches square every way, like unto a dee, & did it precisely & shed none of the water, neither took I out any more or less of the water, but in I unto the mark upon the tub or vessel side, & then I measured the true deepness of the water in the little cube, & found it to be 5. inches, & ⅝. Parts of an inch, that is to say, that it was 5. inches & a half & half a quarter & then I did multiply it in this manner, for that cube was 6. inches square .6. Times .6. and that was .36. and then that being multiplied again, by .5. & ⅝. Parts: & that maketh .202. and. ½. part so that I did conclude, that the branch or candlestick in Latin or brass, was .202. inches and a half in metal, and so by this means you may know the true contents of any form, whatsoever it be: It is also very good, to try the parts of a globe, or globes, or you may double any cube what soever it be, you may do it very exactly, by this order, having this consideration, that you do mark the water truly, and shed or spill none of the water, and that you do measure the water truly, the deepness, and that must be done with some fine stiff wire, for if that you do put in any big rule, then that will swell, or high the water somewhat, according unto the bigness of the rule or thing. Wherefore it is very good for to have the cube or square to be marked with inches, and parts of inches, within the inside round about with parallel liens at every inch end, and also it is not good to have your square vessel too broad, for the narrower that it is, the more certain: and also you may not shift your water into to many things, and especially if it be wood, for that same water will hang upon it, and also wood will receive, or drink water. And all these may be causes that may hinder the exact truth: and also this order of measuring is very good, to know if any thing be made in gold, for that it is a very heavy metal, and no other metal so heavy as it is, if there were made any vessel in gold, and any deceit in it, then putting that vessel into water, then mark how high the water doth rise, than take out of that water the vessel again, then take that weight of gold, and put it into the water, and if the vessel did raise the water higher than the gold, than there is deceit in the vessel, but if the water be at both the times of one like height, than there is no deceit in it, as this was the very way, that Archimedes found the deceit of the crown of gold, & also this art or order of mesuring doth not altogether show the contents of inches or feet, but also you may know the diversity of weight of every several sorts of metal, how much the one sort is heavier than the other, as thus: you having of 2 sorts of metal, the water being first marked, & then weighing the metal before you do put it into the water, them mark the water how hie it riseth, and then mark it there again, & then take that metal out of the water, and then put in of the other metal so much in quantity, till that it raise the water, unto that just height that it was before: and it maketh no matter, although it be of many pieces, so that it be all of one sort of metal, and then take out the metal, and weigh it justly, and so shall you see certainly how much in weight it doth differ quantity for quantity, or otherwise: you may know the diversity of the weight of metals, by weighing two sorts of metal, and let them be both of one weight just, and then the water being marked, put in the one sort of metal first, and then take out that water, as much as is risen by the means of the metal unto the first marked place, and put that into the hollow Cube, as before is rehearsed, and then cast the contents how many inches it containeth justly: and that done, then take that metal out of the water, and put in the water that is in the hollow Cube or square, again, into the vessel, that the water may stand at the first appointed mark justly again: and then put in the other sort of metal, that is of the just weight the other was before, and then take all that water out, and put it into the Cube, and if that the water in the Cube be fewer number of inches than it was before, than that metal is heavier than the first metal, as the proportion of the number of inches will show you justly: and if there be more water at the later time than there was at the first time, than that metal is lighter than the first metal, and the number of inches will show you the true quantity, by multiplying them, as before is rehearsed. And if the water at both the times be of one height, or measure in the little cube, then both the metals are of one weight. And by this means, or Art Statical, you may know the diversity between the weight of Stone and metal, or the diversity of weight of one kind of Stone and an other, for that all sorts of Stone, is not of one kind of weight, as all sorts of metals are not of one weight. And also by this art statical, you may know the diversity of the weight of wood and stone, or any other kind of metal, although the one sort doth swim, and the other sort sinketh, and that you must do in this manner. All those kind of woods that do swim, and if their form be such, that you may measure them, than the matter is of no opportunity, to know the contents thereof, for that it requireth no other thing, but to measure the contents in inches, & to weigh them how many pound they do both contain: and if the form in wood be such, that you cannot easily measure it, by such order as afore is declared, you may know the contents of the wood, by putting it down into the water by some slight, although it would swim, to sink it, you weighing it before it cometh into the water, to know how many pound it containeth. And as touching all these matters before rehearsed, it is a very easy matter to know how many inches, and parts of an inch, will make a pound weight of any kind or sorts of metal, or water, or wood, as thus: You knowing how many inches, that any stuff doth contain, whether it be gold, silver, Copper, led, tin, Iron, stone, wood, or water: the weight being known, then divide the contents of the number of inches, by the number of pounds, and that will show you the true contents, how many inches and parts of an inch, will make a pound weight, The sixth Chapter showeth by art statical to know the weight of any ship, that is sunk into the Sea, or any other river, too know how many tun will weigh her up again. AND furthermore, insomuch as I have declared heretofore, how to know the true weight of any kind of metal, that is sunk into the Water, now I think it convenient, too show unto you, how too give a near guess, or an estimation, if any ship by any misfortune should be sunk, either in the Sea, or in a haven, or river, to know how many tons would weigh her up again, that is to say, to know how many tun in weight she doth weigh in the water, being sunk, which is to be done in this manner: first they must know what kind of goods the Ship is laden withal, that is sunk, and to set down a remembrance or note of every sort, & how much of every sort of the said goods, & also to set down a remembrance or note of the contents of the weight of her ordinance, & anchors: also if it be such goods as do require knitlege or ballast, you must know how many tuns there may be thereof, & also what kind of ballast it is, whether it be sand, or stones, or earth: & all these being known, then according as the kind of goods is, then try how many tons every sort of that goods may weigh in the water, as thus: if it be Copper, led, tin, Iron, Steele, or stone, or such other like, that do not penetrate, or do not drink, or suck in any liquor, or water: and the weight thereof known, then for all those matters, by the rules before rehearsed, do show unto you the truth of the matter. Then if the lading, or part of the lading, be wax, pitch, or tar, or honey, or such like, gums, or what soever it be that is heavier than the water, the consideration of the rule statical before rehearsed, will show unto you the truth of the matter, accordingly as is before rehearsed in all points, and if the lading or any part thereof be such things as do penetrate, or do receive or drink in liquor or water, upon that matter there may grow some error. But to take away some part of that error, you shall have this remedy or help, and that is this. If it be Wool, or Woollen cloth, or Cotten, silk, flax, hemp, or linen cloth, or any such other like, then shall you make your proof in this manner, as before is rehearsed in the Chapters going before, and that is thus: fill some vessel with that kind of water, that the Ship is sunk into, & then mark the edge of the water, and that being done, if there be any great quantity of that kind of goods or merchandise, then take of that sort dry, as the goods were before it was laden, whether it be wool, or woollen Cloth, or Cotten. etc. And then that being dry, weigh it, and then open it loosely, that the water may drink into it, and that being soaked, by imagination as the goods is or may be, then take out so much of the water as is risen by that means of the wool or woollen cloth, or what soever it be, and then the weight of the water being known, pull the weight of the water from the weight of such things as you have made proof thereof, and that weight which doth remain, shall be the weight that the said goods doth weigh in the Water. And furthermore, if the lading of the ship be such, Some kind of goods is of that nature that it weigheth no weight in the water. as doth requrie kintlege or ballast, if it be wines, or oils, and such other like, for that kind of goods is of no weight in the water, for it is rather lighter than the water: than you must make account of the Kintledge or Ballast, and if it be stones, than the order or Art statical doth show you what it may contain in weight very well, by making your proof as before is rehearsed. Some sort of goods must have kintledge or ballast. But if the Ballast be earth or sand, than put the sand or earth into the water, & then let the earth or sand settle unto the bottom: & that being done, you shall see the water will be clear aloft: and then take out of the water, until the water be of that height that it was before, & then weigh the water, & then pulling the true weight of the water from the weight of the earth or sand, than that weight which doth remain, shall be that weight that so much earth or sand shall weigh in the water. And then doing as before is rehearsed, by the weight of a little, by the proportion of the weight of a greater, is known what it doth weigh in the water. And furthermore, there is some kind of goods, although it be heavier than the water, yet in remaining long in the water, it will consume, & that is sugar or salt. etc. But most kind of goods, the longer it remaineth in the water, the heavier it is, for that the water soaketh into it thoroughly. And also any ship being long sunk, there groweth divers, accidents to make it the heavier, that is, by the means there will settle both sand & owes into her, & also the dry timber that is a fit in a ship, will become heavier by the soaking of the water: for this is to be noted, that a ship would not sink unto the bottom, but by the means of the ballast or such other like heavy goods: & therefore for the very hold of the ship, as much as is timber, a very small allowance will serve for the weight of it in the water. For although it besoked, yet it is but little more than the weight of the water, for the Tackle or ropes will weigh more in the water, than the hold of the ship will, for they be much the heavier, for the pitch and tar that is upon them. Wherefore, you must take a note, what number of Cables, and other ropes may be in her, and their weight being known, then make your proof, as before is rehearsed, by the art statical. But if that any part of the loading be oil, or Wine, or Tallow, or such other like, it is not heavier than the water: all such kind of goods is of no weight in the water, but will rather help then hinder. And also if any part of the lading be of Timber, as masts, or Sparres, deals. or wainscot, or such other like, all such kind of goods will rather help it to swim, than hinder any thing. And now this being done, and you knowing what kind of goods there is in the ship, and how much of every sort, and your proof being made by this art statical, and you knowing the weight of every particular thing, what it doth contain in the water, as well the weight of the ordinance, Cables, Ankers, Ropes, and the Ballast. etc. And then adding all your numbers together, then shall you see very near what all the whole weight of the ship with her lading doth weigh in the water, and that being known, than you do know what number of tons will weigh the ship up again, and that being known, than the matter is the more easier to know how to make provision for to weigh her up again. The seventh Chapter showeth how to weigh a ship that is sunk, where it doth ebb and flow. etc. Now you knowing the weight of any ship that is sunk, if you would weigh her up again, then when you do make your provision for to weigh her, take as many ships, hoys, or lighters, as will bear that number of tons, that the sunk ship doth weigh in the water, and in every .40. or 50. tons, take .10. Tons more, for that it is better to have too much, than any thing too little: And look that you have good Ropes that are able to bear so much in weight, as the sunken ship doth weigh in the water, and then when you have made your Cables, hawseres, & ropes fast upon the sunken ship, you must take such order in the making fast of your Cables, or Ropes, that every ship Hoye, or Lyter may weigh or life up the weight of her proper burden, for else you may be deceived, for that I have seen by experience, that the ship which hath been sunk in the water, hath not weighed .40. Tons, and the hoys or Lyters would carry more than .60. Tons, and yet they were not able to weigh the said ship, but were driven to let go their fasts or Cables, and ropes again, or else they should have been sunk, and that was but for lack of knowledge in that matter, for the ships, hoys, or Lyters will weigh or lift most from the bottom, when they have no lading, and yet notwithstanding they will weigh or lift the lesser, if they do use that matter as I have seen, for that they do make fast their Cables & ropes some unto the side of the ships, hoys, or Lyters, and some unto the head, and so forth. And now the ships, hoys, or Lyters, are not able to weigh or life, not one quarter of their proper burden, and they lift or weigh much the less, for that they have no lading within: for if they do make fast their Cables or Ropes unto the side, than it will not life the .10. part of their proper burden, for that the side will soon go down. And if they do make fast their Cables and Ropes unto the head, (for there it will weigh or life most) yet it will not weigh or life one third part of their burden, for having no loading, the head will soon go down into the water. Wherefore whensoever they do mean for to weigh any ship that is sunk: How to use the lighters to make them lift or weigh their own proper burden. then they must prepare long, strong, and great Timber, or strong masts, and let them be laid cross the ships, hoys, or Lyters, over both the sides, and to match .2. and .2. Together of equal burden, as near as you can, and let the long timber or masts lie cross both the ships, hoys, or lighters, and over both the sides, and then bring your Cables or ropes that are fast unto the sunk Ship, over the long Timber or masts, and then make the ropes fast within the ships, or lighters: and this done, than the ships, hoys, or lighters will weigh or life, their own proper burden, otherwise they will not. And then it standeth you in hand to get such Timber that will not break for that burden, for if the timber doth break, it will put all in hazard of synking again. Also it is very good to weigh a ship with kaske, and every hogshead, pipe, or butt, will weigh or lift as much in weight, as it would weigh, if it were full of that water, excepting the proper weight of the vessel or kaske, so that the Kaske be made sight, that no water may come into it. And then when you do mean for to weigh or lift up any ship, that is sunk, your Ropes, or Cables being fast unto the sunken ship, than you having all your things in a readiness, your ships, hoys, or lighters, and the great timber or masts laid cross over both the sides of them, and two and two of them, and also your kaske, then make fast your ropes and Cables unto the ships or Lighters, at a low water, the flood being in hand. Provided always, that you bring the ropes or cables over the timber, you must make your ropes fast at a low water, the flood being in hand. that lieth cross the hoys or lighters, and also then to make fast the Kaske unto your ropes or Cables. And then as the flood riseth, so shall the sunken ship rise from the bottom: and then as the water doth rise or high, so go towards the land, or shore, till it be a full Sea, and then the sunken ship will rest upon the ground again. And then at the next low water: they shortening or making fast their cables or ropes again, than the next full Sea, they may bring the sunken ship, nearer unto the land or shore. And thus they may bring the sunken ship unto the land or shore, until such time as the sunken ship shallbe laid upon dry ground at a low water. For you may know in how many tides that you may weigh her, and lay her upon dry ground, at a low water, as thus: sound, How to know in how many Tides you may weigh a ship. or look how many fathom, the sunken ship lieth in at a low water, and then look how many fathom the water hygheth, or floweth till it be a full Sea, and then consider how deep that your ships, hoys, or lighters, will go into the water, before they are able to lift the sunken ship from the bottom: and then consider how much, or how many fathom or feet, the water will rise afterwards: and so shall you see in how many tides that you shall bring her to be dry at a low water. As for ensample thus: Suppose that any ship or Hoye is sunk at eight fathom at a low water, and the water doth rise or high two fathom and a half from the low water unto a full sea: An ensample of the weight of a ship. and then the hoys or Lyters will not be able to lift or weigh the sunken ship from the bottom, not until they be laden down two foot, and better. So that you may conclude, that the water will not rise or high little more than two fathom, after that the sunken ship is lifted or weighed from the bottom: and then going unto the land or shore, till that it was a full Sea. And then the sunken ship did rest upon the ground again at .6. Fathom, at a low water, and then at the next low water the Cables and Ropes were made fast again, and when it was flowed two foot and better, the sunk ship was lifted from the ground again. And then going unto the land or shore, till it was a full Sea, than the sunken ship did rest at .4. Fathom at a low water: & then at the next low water, the Cables and ropes being made fast again, when it was flowed .2. Foot, and better, the sunk ship was lifted from the bottom, and so going in unto the land or shore till it was a full Sea: then the sunk ship did rest again, at .2. Fathom at a low water: and then the Cables or ropes, being shortened, and made fast again, then going unto the land or shore, until that it was a full Sea, and then resting, the sunk ship shallbe dry at a low water: so that you may conclude, that the ship that was sunk at .8. Fathom at a low water: and the water rise or did flow .2. Fathom and a half, from the low water unto the full Sea, and the hoys and Lyters would weigh or life the sunk ship from the bottom, by that time they were title more than .2. Foot buried or settled into the water, and then in four tides the sunk ship willbe laid upon dry ground, at a low water. And by this order you may know in how many tides that any Shyppemaye he weighed, and laid on dry ground at a low water, you knowing how deep that the ship lieth at a low water, and how much it doth flow in any place where it doth ebb or flow. The eight Chapter showeth how to weigh a ship, where it doth not ebb and flow. ANd furthermore, if that any ship or any other vessel be sunk in such places, where that it doth neither ebb, nor flow, that is too say, where the water doth not high and low, there is some matter, and asketh great charges, and labour for to weigh or lift any great weight from the bottom: yet this way it is to be done, the weight of the sunken ship or vessel being known, what that it doth weigh in the water, as before is rehearsed. Then the number of tons being known, As touching the weighing of ships, whereas it doth not ebb and flow. prepare so many ships, hoys, or lighters, as will carry six or eight times the weight, that it doth weigh in the water, and then let them be near half laden every one of them, with some handsome ballast that is weighty, and good to be removed too and fro. And then when you have made your Ropes, and Cables fast unto the sunken ship or vessel, then bring your hoys, and lighters unto the sunk vessel, and let all that Ballast be thrown into one end of all the hoys and lighters, and then make fast your Ropes and Cables unto that end that hath the lading or ballast: Then your ropes and Cables being made fast, throw or carry all the ballast or lading unto the other end, and then it will weigh or lift the sunken ship from the bottom. Wherefore you must have double so many as is able too lift or weigh it: Note this this point. for when that all the lading is thrown unto the other end: then whilst that the one hath lifted or weighed it, the other hoys or lighters must make fast their Ropes and Cables unto the laden ends again. And thus they must do as often times as the lading is thrown unto the further end, they must have as many lighters as are able too lift or weigh it, whyllest that the other lighters do hang or turn the laden end, and to be made fast unto the Ropes, and Cables again. And thus in time, they shall weigh or life the sunken thyp or vessel, unto the drymme of the water, and then they may carry the sunken vessel unto the land or shore. And by this order or means, they may weigh any ship or vessel up unto the brim of the water, in such places whereas it doth neither ebb nor flow. The nyenth Chapter showeth how to bring in any ship over a should or bar, and to make the ship bear sail, when all the ballast is out: and also if need require, how to life the ship higher out of the waterwardes, to the intent to bring her in. etc. ANd now, insomuch that I have showed how to weigh any ship that is sunk, as well in such places whereas it doth not ebb and flow, and also ebb and flow. In like manner, I do think it convenient too show unto you, how for to bring a ship in over a bar or should, whereas there is not sufficientnesse of depth of water to come into any haven or river, and if that all the ballast is out, and if there is not sufficientnesse of depth of water: Then how to life her higher out of the waterwards, until the ship is sufficiently out of the water, to bring her in over the should or bar. etc. And first thus, if that any ship be come into any haven or harborowe, and by the means of a should or bar, that she hath not depth of water enough, and yet the ship is but in her ballast: Then do thus: Prepare two great hoys or lighters, and also strong haulsers or Cables, and then bring the one of the hoys or lighters, on the one side, and the other, on the other side, and that done, then make fast the head, and the stern of both the hoys or lighters, with strong Ropes or Haulsers, and make them fast, as high in the ship, as you can conveniently, and then heave all the ballast out of the ship into the two hoys, or Lighters: And that done, the Ropes and Haulsers being fast unto the head and stern of the lighters or hoys, and unto the ship, the ship cannot overthrow, although all the Takle, and masts are standing: for look when the ship would shield, than it cannot do it, except that it should life the furthest lighter or Hoye out of the water, which is not possible for to do, as long as the Ropes, or Cables do hold: and then if that it do offer to hold the other way, than that lighter that is on the other side, will not suffer it, as long as the ropes or fasts do hold: wherefore the ship may bear sail, although all the ballast were out, etc. But if that there be not sufficientnesse of depth of water upon the should or bar, to bring the ship in over it, when all the ballast is out: yet notwithstanding you may make such provision, that you may lift her higher up out of the water, until such time as the ship may be able to come in, as thus: you having provided two such lighters, meet for the purpose, as before is declared, then prepare long and strong great Timber or masts, that may be of such sufficient length, that will reach the breadth of the ship, and the breadth of both the lighters all at once. And then the lighters being made fast, as before is rehearsed, and all the ballast heaved or thrown out of the ship into the two lighters, than the lighters being laden with the ballast, then make holles thorough both the sides of the ship in sundry places, and then put the long and strong great timber thorough both the sides of the ship, that it may be overthwart cross over both the sides of the lighters, and in such sort, that the ship may rest or hang upon the long and strong great timber or masts, and rest or lie upon the two sides of both the lighters. And then having out all the ballast out of both the lighters, the two lighters will heave up out of the waterwardes, as much in weight as their own proper Tonnage or burden cometh unto, etc. And by this means you may life any ship out of the water, unto what proportion you list: and also you knowing the weight of the ship, as you may know it, as it doth appear in the second and third Chapters going before: Then accordingly you may make your provision of the two lighters, to life such sufficient quantity of the ship that shallbe able to serve your turn, and also if that it should happen, so that the ship should be a ground upon the should or bar, and yet the place that the ship is a ground on, doth neither ebb nor flow, yet notwithstanding you have this remedy to help it, then lad both the lighters again, and let the ship rest upon the ground, and then you may bolster it up by some provision between the two lighters sides, and the long timber or masts, until that it be sufficient to serve your turn: and then discharging the lighters, they shall life up the ship higher again: And by this means you may bring in any ship, higher again over any should or bar, so that the water be sufficient deep, that the lighters being laden, may pass in over the bar or should. etc. The tenth Chapter doth show unto you, how for to come unto the Keel of any Ship, without the grounding of her, whereby you may collect any ship, and make her sight unto the Keel, which is called carrying of them. etc. AND for that our country of England, is environed round about with the Sea, so that no other Nation, or country can come unto us, neither we unto them, but only by sea, scotland only excepted: therefore it standeth us most principally in hand too be most skilful in shipping, for that it is our most principal force, and for that it is a very necessary matter for to know how to calk a ship, or to stop a leak, and to make her sight down unto the Keel of the ship, in such places whereas it doth not ebb and flow water in, for to ground any ship, than they must use such means as those do that are in the levamt sea, that is, the sea called Mare Mediterraneum, as the Genewayes & Vemsians & Rogosones, with a number of other, that have shipping in that Sea, that I do omit, & that have great ships, and yet never do ground them, but only do bring them over on the one side, which is called carrying of them, and many people that have heard thereof, have thought that they have wound them over by force: and some have judged one way, and some an other way, but few or none of them have judged the truth of the matter, although that divers Englishmen have been there, and have seen the thing done: yet as far as ever I could perceive at their hands, they could never understand the truth of the matter, and the cause thereof was, that they were never in the ship where she was a karrening, and yet for to karren a ship, it is a great deal more ease for the Ship, than it is to be grounded in divers respects, and also they shall have more time and leisure both to search the ship, and caulke her, and to mark her sight, than they shall have in the grounding of a ship, and also they shall the better perceive where any leak is in the karrening of them, then in the grounding of them. And as touching the karrening of a ship, this is too be done, first thus, Cauke the sides of the ship sight above the water, and especially that side that you do mean to bring her over on, and also caulke the deck and ports, and the sperkettes sight, and that done, then prepare labourers enough, and bring the ship reasonable light, that she may have little more ballast, than she may bear herself well. And that done, her ordinance, and every lose thing taken out of the ship, then let the labourers heave the ballast over, unto that side that you do mean to bring her over upon, and so heaving the ballast over, the ship will go over unto what proportion you list, and by that means you may come unto the Keel of any ship, and mark her sight at your pleasure, But divers people have made argument and said, that the ship will not rise upright again, and some have said, that lying at one side, it would overthrow, and other would think that the ballast would slip, but the truth is this: as soon as ever the ballast is thrown or heaved backwards again, the ship will begin to rise, and so in the end become to be upright again. Wherefore it is a strange matter, to see the strange opinion of some people in the world that seemeth to be wise, and for that generally the most part of men have thought that in the karrening of Ships, that they have been wound down with caxslienes, and gearres, & tackles by great force, and therefore they have made fast the ballast by some provision, & also have made raftes of masts, to the end that they might lay the side of the ship upon them, to help to bear up the ship. And see the simple opinion of them that should be wise, to think that the same should do any good, for masts being massy, and not hollow, are but little lighter than water, so that .20. tons weight of them, will not support up two tons, therefore that can do no great good at al. And what a vain folly is it for them to make fast the ballast, that it should not slip, for .20. Tons of ballast, being made fast at the bottom of the ship, must require the force of 20. tuns to wind it down over: and then the ballast, for that it is made fast, and the ship wound down by force, the ship is forced down with more than forty tons, for that the Ballast doth hang over one way towards the Keelwardes, and the ship is wound down the contrary way on the one side, which must of force be in such sort, as a thing that lieth in a colepresse, and doth charge the ship with a double weight or burden, to press it into the waterwardes: and then what can the quantity of the supporting of any thing that cannot lift a tun or two tun weight thereof, do them any pleasure, besides the great cumber that they shall have in those causes, to get such a number of masts, and also to make them fast, or to frappe them together: and also in deed the ballast would slip, the ship being wound down by force, for when that the ship hath her Ballast into the end, to make her to swim upright, and then to be wound down by force, than the ballast doth hang towards the keel, and the ship being wound down to the side, than it must needs slip, as before is said, except that it be made fast, for that the Ballast doth hang over one way, and the ship is wound down the other way, and then it is not possible to come unto the keel, so well as they shall do, when the Ballast is but thrown or heaved over unto the one side, for that it hath then no more than his own proper weight, where as otherwise the ship is charged with double weight, for if she should have but fort tons of Ballast, the ship is charged with more than eighty tons in weight, and also it is very hurtful and uneasy for the ship. etc. And furthermore, as before is declared in this fourth book, called Staticke, that no kind of thing doth enter no further into the water, than the quantity or body or any thing that weigheth so much in weight, as the proportion in bigness of so much water. Therefore any thing that is in the water, how light soever it is, can enter no further into the water, than the proportion of such a magnitude of water. For if the thing be not the twenty part of the weight of the water, than the one of twenty part of the body doth enter into the water: and 19 of .20. Parts shallbe above the superficies of the water, etc. And furthermore, for that the water is an Element ponderous or heavy, and yet thin: therefore it is the nature and quality of water, to support or bear up a thing that is lighter than itself: and yet it doth give any thing place or leave to turn itself in the water, so that it shall swim with the heaviest part downward, as by experience is seen of any thing that is put into the water, as thus: Take a Raske, as a pipe or Hogshead, or a Barrel, and put it into the water, the thing being thyght, the tenth part of the bigness or magnitude doth not go into the water, for that it is so light. And yet notwithstanding, if any one part of the kaske be heavier than the other, that same part will turn downwards. And if you do turn it upwards, as soon as ever you do let it go, it presently turneth of itself downwards again. So that experience doth show this to be true, that the heaviest part of any thing that is in the water, doth always turn, and seeketh downwards. Therefore we may perfectly conclude thus of any ship, if the ballast be cast or heaved over unto the side of any ship, that the ship doth turn over accordingly, always to have the heaviest part downwards. Wherefore, contrary unto the vain opinions of a number of persons that should be wise, that if the ballast be thrown over unto the side, that the ship shall swim upon the side, and yet the ballast shall never slip, for that always the ship doth turn of itself, to bring it unto the level, except it be let by some cause, which is, either by making it fast, or else by some other accidental matter, or else it will follow accordingly. etc. And some people have been of that opinion, that no ship doth swim upright, but that there is as much weight or more below in the water, as is above the water: but that is untrue, as before it doth appear, by the ensample of a cask or Barrel. For you do see that it will swim, and the heaviest part will turn downwards: & if that it be not one quarter of a pound heavier on the one side, than it is on the other, that part will turn downwards: and yet for all that, that part that is in the water, will not weigh the .10. part of that which is above the water. Therefore you may conclude, that if the ballast do lie all upon the one side of the ship, the Ship shall swim upon that side, and the Keel shall come out of the water. And if that the ship side be thight, there is no more danger in her swimming on the one side, than if she were upright in the water. And also the Ship doth not swim so deep into the water, lying on the one side, as she doth swim when she is upright, for that the ship is more lancker, or slenderer, or sharper: that is to say, not so full and round, by the means of her Tuck and run, and the Foreway, as the side is round and full. Therefore it cannot go so deep into the water, for as before is said, that nothing can go no further into the water then the proportion of so much water in weight. Wherefore the side being round and full, it is the more boyenter a great deal, etc. And also it is very good to bring a ship in over a bar or should, for lying upon the side, it doth draw much less water, then when it doth swim upright etc. But notwithstanding it is not so good for to Karrene the Queen's majesties ships, as it is the merchants ships, for two special caves, and the first is this: the Queen's highness ships have always as much ballast in them, as they do usually go to the Sea withal, to be fast to bear a sail, which is no small quantity in her bigger sort of ships: and than what a charge is it to take the greatest part of the ballast out of them, and too take it in again, for they must take more than .3. quarters of the Ballast out, when they do Karren them: whereas the merchants ships do deliver all the ballast out when they do lad their ships: therefore the merchants shall not occupy the 20. part of the charges that the Queen's ships must. And the second cause is this, that in the Queen's ships, the ballast is always firm and hard, by the means that it is seldom or never stirred, and also the cook room is made up with brick upon the ballast, and also there is set up in the cook room with Brycke work the furnases, to boil their beef, and other provision, that is made for the dressing of men's victuals, as Quens and hatches etc. which were no small charge to remove and make up again, whereas in the grounding of them all, these two great charges are saved, that merchants ships in their karrening shall not need to be at. etc. And thus I end the fourth book. ❧ A Table of the contents of the Chapters of the fourth book called a Treasure for travailers. The first Chapter of the fourth book, showeth you by the proportion of a ship swimming in the water, for to know the true weight of any ship, with all her tackle, ordinance, furniture, and lading, etc. The second Chapter showeth how for to measure the proportion of the mould of any ship, whereby is known the weight of any ship, with all her lading and furniture. The third Chapter showeth you an easier way, than before rehearsed, by the art Statical, to know the true weight of any ship, with all her lading, and all the rest of her furniture. The fourth Chapter showeth by the art Statical, the weight of any metal or stone, how much, or what weight that it doth weigh in the water, to be lifted or weighed from the bottom, unto the brim of the water. The fifth Chapter showeth how too know the true measure in inches or feet, of any strange form, such as geometry can give no order for the measuring thereof, as to measure a branch in metal, or a pillar that is enbowed and full of hollowness in divers places, and boils out in some places: and also how to know the diversity of the weight of metal, or the diversity between the weight of Stone, and metal. The sixth Chapter showeth by the Art Statical, to know the weight of any ship, that is sunk into the Sea, or any river, too know how many tun will weigh her up again. The seventh Chapter showeth how to weigh a ship that is sunk, where it doth ebb and flow, etc. The eight Chapter showeth how to weigh a ship, where it doth not ebb and flow, etc. The ninth Chapter showeth how to bring in any ship over a should or bar, and to make the ship bear sail, when all the ballast is out: and also if need should require, how to life the ship higher out of the waterwards to the intent to bring her in, etc. The tenth Chapter doth show unto you, how for to come unto the keel of any ship, without the grounding of her, whereby you may collect any ship, and make her sight unto the keel, which is called carenning of them. etc. FINIS. ❧ The fifth book of the treasure for travailers. Wherein is showed the cause of divers things that are to be seen on the Sea, and the Sea coasts, and the cause of rocks and sands in the Sea, and the cause of the ebbing and flowing of the water, and the cause of currants in the Sea, with such other like matters. etc. Being very necessary for all sorts of travailers, either by Sea, or by land, to know. etc. written by William Bourne. To the Reader. GEntle Reader, it is possible that some will think that I have taken upon me to meddle with those causes, that are past my capacity, for that this fifth and last book is as concerning the natural causes of Sands in the Sea and rivers, and the cause of marish ground, and cliffs by the sea Coasts, and rocks in the Sea, and also the cause that the sea doth ebb and flow, and the cause that the water in the Sea is salt, and the cause of Earth quakes, with other matters. And for that my opinion doth differ from some of the ancient writers in natural philosophy, it is possible that it may be utterly dislyked of and condemned to be no truth. But yet notwithstanding they may give such credit unto it, as the sequel of the reasons shall support unto them, for that they be but my simple opinions: wherefore they may believe them as they lift. Therefore gentle Readers, I desire you to bear with me, for that I am so bold to show my simple opinion unto the world, for it is possible, that some people may malice me, for that I am so bold to deal in these causes, considering what a great number of so excellent learned men there are in England, both in the vniversyties, and in divers other places in this land. The fifth book of the treasure for travailers. The first Chapter of the fifth book showeth the natural causes, how sands and banks are engendered or made, both in the Sea and Rivers. NOw beginneth the fifth book which is concerning the natural causes of sundry things that are to be seen in traveling upon the face of the earth. And although there be nothing that happeneth, but the providence of almighty God, doth bring it to pass: yet notwithstanding it hath a natural cause why it is so, although it seemeth supernatural or unpossible for that God doth work all things by a means, and yet doth come to pass by some natural cause. And first of the natural cause of sands and banks in the Sea and rivers, my opinion is this: that whereas a great number of sands and Banks are many times seen at the mouths and entrance of many great rivers both into the Sea, and also up into the river, that it happeneth by this means, by the shalownesse of those seas, and the great indraft of the river. And then by the means of the soil of the country in the rivers, being a good distance from the sea, and especially after any great rain, doth bring down the soil, for all the land water doth always run down towards the sea, where as it doth ebb and flow, and sometime the water overfloweth the banks, and then the swiftness of the running of the water doth fret away the banks, and sometime it happeneth in the winter after a great frost. And such other like causes, sometime from sandy ground, & sometime from clay ground, & sometime stony ground: & other good mould doth fall into the river, and so is mixed and tumbled too and fro with the water, and is always carried towards the sea by the violence of the stream, for that always, where it doth not ebb & flow, the stream runneth towards the sea: & whereas it doth ebb & flow, there the ebb doth run both swifter & longer than the floods do, & so by that means, it is always carried towards the sea, & also any thing is apt to roll, or run down the hill, rather than against the hill. And thus the soil of the country being tumbled too & fro in the water, is washed and soaked in such sort, that the water is made thick therewith, and the fat or clammy substance, become owes, but the greety or sandy, or gravelly substance doth always keep towards the bottom, for that it is more ponderous or heavier than the fatty or clammy substance, and then this gravelly or sandy substance, being driven down towards the sea, by the violence of the stream, going by the bottom, then where it doth find any place to stay at by the way, there it resteth, and so groweth more and more, and so becometh a sand, and then the tide, by the means of ebbing and flowing, doth make or scour out a channel, or pasadge between one sand or bank, and another. And always this happeneth, whereas the Sea is but shallow, and the river or haven hath a great indraught, that is to say, to run a great distance into the land, whereby there is much soil brought down by the means afore rehearsed. And then the Sea being but shallow, it hath no great descent to run down the hill. And then by the means of the floods, & the bellows of the Sea, doth cause it to be stayed, although that sometime it happeneth, that one sand or bank doth decrease, and wear away, and another doth increase and wax bigger, and many times the channels do alter, sometimes deeper, and sometimes shallower: and sometimes whereas a channel was, becometh a sand, & sometime whereas a sand was, is become a channel, as experience hath many times showed, which happeneth many times by some storms or great winds, sometimes from one quarter of the world, and sometime from another quarter. And by that means the greatness of the bellows of the Sea, doth beat, or wash away the sand from one place, and so doth rest upon another place: and then the tide or stream doth scour or fret a new channel, between one sand and another. etc. As we may see by experience in divers places, as the mould of the river of Thames, and Humber, and the river of Roan, and such other like places, which I do omit at this tyme. The second Chapter showeth the natural cause of Marish ground, and other plain meadows or ground by the sides of rivers. etc. AND furthermore, as touching the natural cause of marshes or Marish ground, and other plain and level ground, that is by the sides of great rivers. etc. and in such other like places: mine opinion is this, as in the Chapter before is expressed, by the bringing down of the soil of the country, which is ground or earth, of all kind of sorts, which is fallen into the water, and brought down by the stream. And as before is rehearsed, the gravelly or sandy substance doth drive with the stream, Of the soil of the country. by the bottom, but the fatty or clammy substance is mingled with the water: for although you should take any earth or substance, and wash it and tumble it in water never so much: yet notwithstanding it cannot be consumed all away, but if you do let it stand still, than it will settle itself unto the bottom, and you shall find the substance again. So although the earth is mingled with water, by the means of the fretting of the stream and the Tide, and also the soussyngs of the bellows in great winds, tossing it to & fro in stormy weather, yet notwithstanding in fair and calm weather, in such places, whersas there doth not run a great tide or stream, than that earthy substance doth settle itself again on such places as are defended by some Naase or point, and in some Bay or place, that the grating of the tide or stream doth not greatly trouble it, & is then called Owes, or as the common people that be not near dwellers unto such rivers, do call it dirt, mire, or Mud. And then in such places where it doth ebb or stowe, being settled, now a little and then a little, the wind and the sun do something harden it, until at the last, How Marish groude is engendered. through the settling now some and then some, and still dried with the wind and the sun, that it is as high as the common foul Seas: and then it will begin to bear some green thing, and so it will become marish ground in time, and so is overflowed in the spring tides, but in the Neape tides, it is bare at a full Sea. And then many times it happeneth, that those that are the dwellers there abouts, or else the Lords of those soils, do inn that same ground, and make the walls for the defence thereof. And in process of time, it becometh main land, and by this means cometh all your plain and leveled grounds near unto rivers sides: And this kind of ground must needs be very fertile and rich, so that it be not overflowed with salt water, for that all the stony and sandy substance is washed out thereof, and it must needs be plain and level, for that it is brought to be level with the water at a full Sea. etc. And furthermore, it happeneth divers times, Marish ground is fertile, if the salt water come not at it, as in the Chapter before is rehearsed, by great winds and storms in sundry ages of the world, that the Channels do alter by the washing or fretting away of some point or firm land or Naase, and then that which hath been many years before, main ground, may be fretted away, and be overflown again. And the substance of the ground may be landed in some other place, as by experience in many places hath been seen, so that, that place that hath been before meayne ground, hath become Sea and water, How land hath been sea, and sea hath been land. and that place that hath been before sea and water, hath become dry land. And these things have happened in pracesse of time, by the means of the changing of the channels, which do alter the setting of the tides in rivers and havens, whose principal cause hath happened, as before is rehearsed, by fretting away some Naase or point, and then some Naase or point hath turned the tide some other way, and so worn or fretted a new channel: so that whereas the tide or stream hath run most swiftest, hath become an eady, and so in process of time, ground in like manner. etc. The third Chapter showeth the natural causes of the high cliffs by the Sea coasts. etc. AND furthermore, as touching the natural causes of cliffs that are by the Sea coasts, as we may see some of hard stone, and some of chalk, and of a monstrous height, and some of clay, and other of earth. etc. My opinion is this, as the age of the world is of no small time, so in process of time the often sufferings of the bellows of the Seas have beaten away the feet of those hills, that are by the sea coasts. And so undermining it, although it were of hard stone, yet the weight of that which was undermined hanging over, in rainy wether, or after great frost, must needs fall down into the Sea. Of cliffs by Sea Coast. And then that sail or substance that fell down, in process of time was beaten or washed away again, by the often soussing of the bellows of the sea, in the time of great winds and storms. And then the stuff so fallen down, being washed and consumed away, the sea doth begin to undermine it again, by little and little, till at the length by the means before rehearsed, there falleth down an other portion of the said substance, or stuff from the hill, so that in the end, they become such monstruous cliffs, as we may see by experience, are on the sea coasts in a number of places: And thus they do were away by little and little, until that an other place is become aforelande, without that land, that is to say, an other Naase or head land to stand further out into the sea, then that doth, and then that cliff will stay without falling down any more, of the substance or stuff of long time, by the means of some beache, or shingle, or sand, or stones that shall be brought thither, by the cossing to and fro of the bellows of the sea, and that shall lie there, and defend the foot of the sand cliff, as by experience we may see in a number of places by the sea coasts, and then doth we are away an other cliff, in some other place of the sea coasts: for it happeneth many times, in sundry ages, that at one time, one place doth were away, and an other doth increase again: and in an other age again, that which did increase, shall wear away, and the other shall stay, or perhaps increase again, by the means there is some head land, or Naase without that, which doth break away the fretting or grating of the tide: For many times it happeneth upon the sea coasts, through some great and huge storm, that maketh a breach by the monstruousness of the great bellows, that teareth away some great quantity of ground, from some one place in short time, and the bellows of the sea shall drive or bring it, or land it in some other place, yea even in a short space, as experience hath many times showed it, and as it many times happeneth, that in one age of the world, that the great huge winds or stormed do happen sometime in one quarter of the world, and at an other time, in an other quarter. In four years the great storms are in one quarter of the world, and an other year in an other quarter. For as we may see, that in some years, the most great winds and storms do blow in the East quarter of the world, and in other years, in the West quarter of the world, and in other years, in the South quarter of the world, and in other years, in the North quarter of the world. etc. By which means it fretteth at one time away the substance or stuff from one place, and then the bellows of the sea do drive or force it to land in an other place: and so it continueth for a certain time, until such time that the great winds or storms do blow in a contrary quarter of the world: and then the stuff or subtaunce is beaten by the bellows of the Sea, and driven and forced from that place, and so is landed in an other place: And it is possible to be forced or landed at the place that it first came from, although it may be 20. or 40. miles distance asunder. And thus those that are near dwellers unto the sea coasts, do see the great and mighty works of God, wrought by his greatness and almighty power, the great or huge bellows or waves or knots of the sea, in great winds and storms or tempests, For even those things that show or seem unpossible, he bringeth to pass, as by experience hath been seen at sundry times. etc. The fourth Chapter showeth the natural cause, why that the beache, and the great bolder stones, on the sea coasts, are become round and smooth, without any edges or corners. NOw furthermore, as touching the natural causes, why that the Beache, and the great bolder stones in the sea, and the other small shingle are all smooth and round, without corners or sharp edges, and yet they be of all kinds and luites of stones, The shingle beach or the bolder stone is of the substance of the nature of the cliffs near unto them as Marble stone, and Flynt, and other hard stone. etc. For they be of those substance & natures, as the cliffs that are near unto those parts, as in the Chapter going before is declared, by undermining of the hills or banks, with the bellows of the Sea, the substance falleth down into the Sea, what soever manner of stuff it be, according unto the minerals of those grounds or hills that falleth into the Sea, whether it be hard stone, or Marble stone, or Flynt, or what stuff else soever it be, according unto the veins of the minerals in the ground, that so by that means before rehearsed, do fall into the sea. Then when it is forced or brought to land upon any place of the Sea coast, it is all smooth, without any corners or sharp edges. The cause thereof cometh to pass by this means, for when it doth first fall out of the cliff into the sea, than it hath the fashion and form as those have that are digged forth of the ground: The cause or reason that the beach and the great bolder stone is round without any sharp edges. but after it is fallen into the sea, & hath had any continuance there, & so tossed to & fro by the waves and bellows of the sea, a great number of them together, the one doth so fret and rub or grind against the other, that it must needs rub or fret away all the sharp edges of those stones, how hard soever the stone is, for the soussing of the bellows of the sea doth never forget itself to stand still, neither is ever weary, nor desireth rest, but is always labouring and tossing that is in it to and fro, according unto the bigness of the wind. etc. as by experience upon the sea coast may be seen, the great and mighty force of the bellows, in the soussings and forcing of the Beach a shore in the time of any great winds or storms, amongst the Beache & shingle: The force of the Sea. for you shall hear the soussing of the bellows of the sea amongst the Beache, as though it were the pouring down of a thousand cart load at once: So that you may hear it two or three miles from the place where as it is, yea and sometimes after a storm, you may see Stones that weigh a pound weight, thrown from the full sea mark, into the landewardes two or three rods, by the very means of the soussing of the bellows or waves of the sea, as those that do occupy the sea coasts, do see by experience. etc. The fifth Chapter showeth the natural cause of the rocks in the Sea. etc. AND yet furthermore, as concerning the natural causes of rocks and pinnacles that do stand in the sea very strangely unto such as do behold and see the same in sundry places in the sea, and some on the sea coasts, and some in havens, & harborows that are adjoining unto the sea. And this is general for ever, that look whereas there is any great store of rocks, it is a token of a deep sea, it is a token of a shallow Sea, that hath many sands. And the cause of rocks in the sea, in mine opinion is this, as it is known unto all persons, that the age of the world is of no small time: so that I am of that opinion, that the rocks that are now standing in the sea, have been parcel of the maynelande, or at the least, some islands standing in the sea of long time ago, although there be no mention made of any such islands standing in the seas, in those days. The cause thereof might be this: for that they that were of long time ago, made no account of any small islands, that were towards our West Occian. For these west parts, in those days were scant peopled, as Ireland, and England, and scotland, and britain, the west part of France. For it is no long time ago, that Ireland hath been thoroughly well peopled, although it be a long time ago, since the first entrance of Brute, yet it was long since the Incarnation of Christ, before that this country became thoroughly peopled, as it doth appear both by the Chronicles, and other ancient histories. And also in those days, Navigation not much used in the West Occian. navigation was not so much used in these our West Occian Seas, for the Sea was little used in these our parts, except it were by small Botes, to go a fishing, and to transport people from place to place, as we do see by experience. Yet in these days, those that do inhabit, and dwell upon the Coast of Afryca, to the West Occian, do occupy no shipping unto the Sea, except small Cannoses, to go on fishing, and such other like, as all Barbary and Ginny, which were countries well people before these Northwest parts were peopled as it doth appear by Histories. And furthermore, in the old time, those people that were the dwellers in these Northwest parts, were very simple and ignorant, as touching the drawing of plaits and cards, whether they were cards Geography, or Hidrographie. etc. Although that Pitholomias made Tables, as touching the description of the Countries, yet he did not manifestly or plainly show the islands in the sea, not to this west Occian, as they be now well known. And furthermore, it is but a very short time ago since that English men did much occupy the sea, to travail on long voyages, neither did few or none know or understand the use of their Sea plaits, called cards Hydrography, for within these three score or four score years, it hath been thought a great long voyage, for to go into Spayre, and then when they did go into Spain, Now Englishmen are as sufficient to travail a long voyage, as any other nation. they went all alongst by the coast of France, and so to the coast of Byskey. etc. But thanks be unto God, now in these days, Englishmen are as sufficient to travail in long voyages, as any other nations be. But now to return to our former matter, as concerning the causes of Rocks in the sea, and as I have said before, that the Rocks have been parcel of the main land, or else some island long agone, & by the often soussing of the bellows or waves of the Sea, that never standeth still, the other substance or stuff is beaten and consumed away, through the great deepness of the sea: the other substance or stuff is tumbled to the bottom, and is no more seen. And as the minerals in the ground be of divers kinds of substances, as some earth, and some sand, and some stones: to conclude, of a hundred several sorts, so that all those lose substances, that would be mollysted with the water, are beaten and washed away, so that there doth remain nothing but the hard mine of stone: and so he doth stand in the sea, as a pinnacle or Rock, The cause of Rocks in the Sea. as by experience is seen in a number of places to the west Occian, as the West part of England, and the West part of Britain on the Coast of France, and such other like places, whereas there be innumerable companies of Rocks, some being of a great height above the water, other some do show themselves just with the water, and other some are sunken rocks being rounded with the water, some deeper than other some, which would not be known, but only by the breaking of the sea over them. etc. And this is my opinion as concerning Rocks in the sea, that have been of long time agone parcel of the main land, though they be now rocks in the sea. Then it may be said, that the land is much lesser than it hath been before time, and so it is. And yet it is but a trifle in respect of any great quantity or bigness, as it may be compared unto the ragged edges of a piece of cloth, and yet the ragged edges thereof being pared away, the thing hath not much changed his fashion or form, neither in respect is become little the worse. etc. The sixth Chapter showeth the natural cause of the ebbing and flowing of the Sea, and the ebbing and the flowing of the havens and rivers. AND furthermore, as concerning the ebbing and flowing of the sea and other rivers, we do see by common experience, that the moon doth always govern the same. Wherefore it may be supposed, that the waters do seek and repair, The waters are drawn by the power of the moon. or most specially are drawn by the power of the moon, that when the moon is in the midst of the sky, that is to say, upon the Meridian, than the waters are deepest or thickest, and also in like manner, in the opposite part, or else it would ebb and flow but once in .24. Hours and 4/5. Parts, according unto the daily motion of the moon, which we do see by experience, that it doth ebb & flow but once in 12. hours & ⅖. part of an hour, and then by this reason it should flow or be a full sea in all places at a South moon, and a North moon: & so as the moon passeth unto the westwards to be a full sea in those parts, and so to go with the diurnal or daily motion of the heavens, which we see by experience is contrary, for we do see by daily experience, that upon the Coast of Spain, and all those parts that are upon the West Occian Seas, that the moon in the south-west doth make a full sea, which is 3. hours after the moon is upon the Meridian: and yet notwithstanding it would be a full sea always where as the moon is upon their Meridian, and so to follow the daily motion of the moon, as the moon is carried with primum Mobile: so that it were not let by this great accidence that this West Occian Sea, is shot in between the firm land of Ameryca, on the West part, and the main land of Afryca, and Europe, on the East side, by which means the waters cannot follow to be a full Sea, according unto the moons course, as she doth go in her daily motion, according unto the moons coming unto the Meridian. Wherefore it is to be supposed, that if there were no such accidence in the Sea, to be let by the land, that then it would follow orderly, that the waters in the Sea would go round, according unto the moons course in .24. Hours, and so the stream or currant, to go from the East into the West, and so round about. etc. But now we see that the waters, in the ebbing and flowing, are let by this great impediment: for Ameryca doth enclose the West part, The moon doth govern the ebbing and flowing of the water, in two great and notable causes. and Europe and Afryca the East part, and yet we do see by experience, that the moon doth govern the ebbing & the flowing of the waters of the Sea in two great and notable respects. The one is this, as it is daily seen in every place, whereas it doth ebb and flow, that the moon in one quarter of the sky doth make a full sea for ever, in that place, or haven, or harborough. And the other great effect of the moon is this: as it is always seen, that at the full of the moon, and also at the change of the moon, how that the waters are quickened, and do raise or life themselves much higher than they do at any other times, and also doth descend much lower, where by it maketh the tide or stream to run much the swifter, as it is seen by daily experience, in such places whereas it doth ebb & flow, at which times it is called in the time of the full moon, and the change of the moon, spring tides, or spring streams: & in the quarters of the moon, it is called Nepe tides, or Nepe streams, for that the waters do not life themselves, or flow so high as they do at any other time, neither do they descend, or ebb so low, as they do at any other times of the moon, and by that means the stream doth not run so swift as it doth at other times, for as in spring tides it doth flow or lift itself higher, and descend or ebb lower, then of custom. So in neape Tides it doth lift or flow less in height, & also ebb or descend less in deepness, than it doth of custom, as it is seen daily by common experience. etc. But yet furthermore, The variety of being a full sea in one river. as touching the ebbing and flowing of the water, both in the Sea, and also in havens and rivers, and although that it doth keep an order or method in any one assigned place, yet is there great variety in places hard by: yea in one river, it shallbe a full Sea in one part of the river, and in that river, and at that instant, a low water, as the proof thereof may be manifestly seen here in the river of Thames, as it is not unknown, that the moon in the South doth make a full Sea on the lands end, at the entrance of the river of Thames, and the moon in the south-west, doth make a full Sea at London, and then it is half ebbed on the lands end: But in Rychmonde above London, there the moon in the West, doth make a full Sea, and then on the lands end, there it is a low water, as it is manifestly to be seen. etc. And furthermore, as touching the ebbing and flowing upon the Coast of the Occient Sea, for that it floweth generally a south-west moon, so mine opinion is this, A full sea and a low water act at one instant in the river of Thames. by the means of the shutting or enclosing of the Sea between America, and Europe, and Africa, that it cometh to pass thus, for the water cannot follow the course of the moon, for after that the moon is passed the Meridian in the Bay of America, commonly called the Bay of Mexico, that then the waters can no longer follow the course of the moon, for that it is let by the main land. And then when the moon doth come round about, unto the Southeast, than the powers of the moon do tract or draw the waters unto the eastwards, by which means the waters having a great course or sway unto the eastwards, are drawn so vehemently by the powers of the moon, until such time, as the moon doth come unto the Meridian, that it cannot suddenly reverse, although the moon be passed the Meridian to the westward, as we may see many times by common experience, that any thing forced to move violently, is not presently stayed, but that it must have a time in the staying, as the force of the drift doth decay, which must be by little and little. etc. And so by that means the moon is in the south-west before the water's willbe descended: and for proof thereof, if that you do put water in any broad or long vessel, and stir the water in such sort, The cause of the ebbing & flowing in havens, and rivers. that it may sway from one end unto the other, and after that it hath begun to sway from end unto end, it will be a long time before it will stand still: for you cannot make it to stay upon the sudden, but it will sway too and fro, until that it doth stay itself by little and little. etc. And furthermore, as touching the ebbing and flowing in the other inferior Seas, and havens, and rivers, that happeneth by this means, as it is a full Sea in all the places upon the West part towards the Occian Sea, so that when it door find the water of our inferior Sea, lower than that which doth come out of the Occian Sea, than it runneth in until that it cometh to be level. For the property of water is always to run unto the lower parts, and so by that means, and also the sway that it hath, it runneth and floweth into all havens, and Harbours, and rivers, as long as it findeth any place lower or inferior in height unto itself. And then as soon as it findeth the water behind it, lower than it is before it, than it stayeth, and beginneth to run back again, for as is said before, the property of waters is always to run to the lower parts: and by this means it floweth into all rivers, havens, and Crickes upon the Sea coast, and in some place it doth higher flow more water upright, The cause that the water doth rise and flow higher in one place than it doth in another and doth ebb more water in like manner down right, then that it doth in some other places, and that happeneth by this means, and if any place have a wide entrance, and then afterwards is shut up into a narrow room, having some distance to reverse back again, than the water doth rise and flow very high, for that the water cometh in with a great sway, and will not upon the sudden reverse back again, as by ensample it may be seen in Severn, that cometh up to Bristol and as before is said by the river of Thames, that it is not a full Sea in all places at one instant. For when that it is entered in at the mouth, and hath taken his sway withal, than it runneth in by the means that the water is lower within, than it is with out at the Sea, for that it is a quarter flood, and more at the Sea, before that the flood entereth into the river, and so floweth upwards, for it must have a time, before that it can high so much water at the mouth or entrance to be higher than it is within up into the river: for it is three parts flood upon the lands end, before that it be any flood at London, for that the distance is a great way in, & the river very crooked and narrow, and many points, and Naases that do let and stay the tide, but afterwards, when it is in, and hath taken his sway, than it cannot so soon reverse back, until that the water is well descended or ebbed behind it too the seawards, as it doth manifestly appear by experience. And by this order it floweth into all havens and rivers, according unto the indraught. The seventh Chapter showeth the cause of currants or streams, that runneth in the Sea, in such places, where it doth not ebb, and flow, and of currants or streams in the Sea, there are three several sorts, as in the Chapter it doth appear. etc. AND furthermore, as touching the currants, or the stream in many places in the Sea, whereas it doth not ebb and flow, as that is perceived in many places, as by experience is seen and known in the Sea. And to let you understand what those currants or Strames be, that it is a continual running of the water in the Sea always one way, and not reversing or coming back wards to and fro, as it doth in such places where it doth ebb and flow, but that the water always in those Seas or parts doth run continually one way, 3. sorts of Currantes. or else at the least a long time, according unto the natural cause of that currant. And of these currants I do find three several sorts, that do come of three several causes, and the cause of every one of them is contrary unto the nature of the other. And first concerning the natural cause of the principallest currants, as by experience of them is seen in divers places, by those that have travailed into those parts by the Sea, as thus: The currant runneth forcibly, and continually from the East unto the West, The principal and chief Currant of the sea. at the cap bone speraunce, the Southermost cap of Africa, or Ethiopia, and so reboundeth upon the Coast of America, which is drawn by the powers of the moon by her daily motion, as in the Chapter next before is rehearsed, as it doth appear by the ensample of ebbing and flowing, and so rebounding upon the Coast of America, by that impediment, that it cannot get passage that way, according unto the daily motion, than it is forced to seek other passages, so that part thereof doth seek, and doth go thorough the straights of Euphrates into the South Sea, and there the currant doth go continually from the East, into the West. But that straight or passage being unsufficient, for that it is so narrow, the currant is forced to seek some other way. Wherefore partly it doth divide itself, and so doth run up unto the coast of brasil, towards the equinoctial by cap Crucis, and Saint Domyngs, The reversing back of the currant. and so into the great Bay of Amerrica or Bay of Mexico, and so reverseth back again, and so thorough the Cannel or channel of Bayhaina, between the cap of Terra Florriday, & the great island of Coba, going from the West into the East, which is the cause that those that do go into the West Indies, do first go to the Cannaries, and so to the westwards, to the intent to have the currant to the westwards, into the Bay of Mexico, and then when they do return home, than they do go by the North part of the Bay of Mexico through the channel of Baphamea, for that the currant doth reverse back from the West into the East, so that they have the currant or stream to help them back home again. etc. And then in like manner, partly the currant that cometh about Cape bone sperance, being beaten by the main land of America, as is said before, part runneth or goeth thorough the straight of Magalenus, and partly thorough the great golf or Bay of Mexico, as before is rehearsed, and part doth reverse or go back alongst the coast of the South land that lieth on the South side of the straights of Magalenus, where the South pole or pole Anterticke is raised more than .50. degrees, and so goeth back from the West into the East, alongst the South Coast, until it doth come into the East Occian sea again. etc. And this is the principallest currant, The second sort of currants or streams. as those that do occupy those parts by sea, do know, and these currants are well known to run continually always one way. etc. The second sort of currants or streams, is this, as it is seen in divers places, that they shall have a currant or stream, where it doth not ebb & flow, that always doth go unto the windewards. But that never happeneth but in the time of great wind, and the cause thereof is this, that the sea being wrought or troubled with great storms of wind, doth raise great bellows or waves, or great knots in the sea, and that runneth rolling with the wind, and doth cause the water too be unlevell or uneven, as it is the nature of water to seek to the lower parts till that it doth come unto his level: The cause that it doth not ebb and flow in some seas. so by that means as the wind beareth the water in the sea, with great waves or bellows, so the currant in the water doth go against the wind, to come unto his level again: as the experience thereof is seen in divers places, where it doth not ebb and flow, as in the middle earth sea, or Levant seas, and within the Sound, that is to say, within Elson Nore that hath narrow entrances, and yet is great seas within, which doth take away the effect of ebbing and flowing, for that the strait is not sufficient to let in water enough, for to cause it too ebb and flow. And this effect in like manner is many times seen, sometime on the coast of Barbary, and in such other like places, where it doth not ebb and flow. etc. The third sort of streams or currants. The third sort of currants or streams that runneth in the Sea, where it doth not ebb and flow, as by experience is seen in divers places, is caused by the sailing into the Sea of some great and mighty river, that the land water coming forcibly down the river, and so emptyeth or runneth into the Sea, doth cause a currant to go in the sea, against the mouth of the river, as it is seen in the middle earth Sea, against the mouth of Nilus, and also it is many times seen in the North parts, at the spring of the year, when the snow and the ice is melted or consumed into water. And then against the mouths of such rivers, as do empty them into those seas, doth cause a great currant to run a great distance from the land, in such places as this effect happeneth in those seas. etc. The eight Chapter showeth the cause that the waters of the Sea are salt, etc. AND furthermore, as touching the natural cause that the water of the Sea is salt, whereas the opinion of some Authors is, as Aristotle, & other, that it is made salt by the powers of the sun, by the drawing of the fine substance of the water, up into the air, the Sea is made salt by that means. Then if that were the whole cause, them the water of the Sea should be most saltest under, or near the equinoctial. For that the sun hath a greater force by the means of the direction of the shadow of the sun, whereby the sun should draw or distill it more faster, than it doth in any of the other climates. Yet notwithstanding, it is seen by experience, that the water of the Sea is as salt in the Latitude of .60. degrees, The sea is salt very far to the froth parts. in the Occian Sea, as it is under the equinoctial. And as some have said, it is as salt in Iselande, and at the North cap, which is within the Polle or circle, near five degrees. And there the sun cannot have any great power, for that the sun hath but a very glaunsing shadow in June. And in the winter part of the year, the sun will not appear or rise unto them, in the space of ten weeks. And furthermore, if the water of the sea were made salt only by the powers of the sun, than those seas must needs become fresh, by another great cause, and that is this: For in the Spring of the year, in the melting of the snow and the ice, there falleth such abundance of fresh water, that it would make it fresh, and yet the water is very salt, insomuch that in divers places in the North part, they do make salt of the sea water, although that it is not made by the heat or powers of the sun, as it is made in Spain and in France, for that they do make it in scotland with the heat of the fire, Salt is made of the sea water in Scotland & in Rosey. & so as some have said, it is made in Rosey, not far from saint Nicolas. And furthermore, as it may be proved, the water is not made salt by the power of the sun, for that the head of the great river Nilus that cometh from the mountains of the moon, & hath Latitude beyond the Equinoctial twelve degrees: And so in sundry places, standeth in sundry great pools, Fresh water in seas or pools under the equinoctial. not far from the Equinoctial, and so passeth from under the equinoctial, unto the Northwards, and doth empty itself in the middle earth sea: and yet that water is fresh, and not salt. So that it is manifest that the powers of the Sun, are not altogether the cause that the water of the sea is salt. Wherefore in mine opinion, the water of the sea is become salt by the Minerals or substance of the nature of the ground, which is salt properly of itself, and so mollified or soaked, that it turneth unto water, having any moisture or liquor to come unto it. As for an ensample, that in sundry places, it is known that there is Salt found and digged out of the ground, and is perfect Salt, and occupied for Salt, after they have made it clean, and beat it small. And as it hath been credybly reported unto me, there is a hill or mountain in Barbary in Africa, Salt mines. that Salt is digged out thereof, and is a great distance from the sea. And the like is reported to be in the kingdom of Hungary, here in Europe, that there is salt digged out thereof, and is sold and bought into divers places, as into Polonia, and into some places of Germanye. The sea made salt, by the substance of the ground. Then it is a plain case, that there be such wines or minerals in the ground, which maketh the thing to be most manifest, that the Sea is made Salt by the minerals or substance of salt in the ground. And yet for further proof thereof, here in England, at the Wyches in Chesseshyre, there is in sundry places, a water or brine that they do make Salt of, and is a good distance from any Sea. And some have made argument, that it may come from the Sea, thorough the veins or Coves in the ground, which is most contrary, by this means: for if that it come from the Sea, thorough the ground, than it could not be salter than the water of the Sea, for that at the Wyches, is much salter than the Sea water. For if that it come from the Sea, than it must be somewhat fresher than the Sea water, by the means of the scouring itself thorough the earth, and by meeting of some fresh waters, as the earth is not without fresh water. etc. And furthermore, as concerning the saying of the Philosopher Plato, in his Dialogues of Tymeus, and Crecia, and also is written by marcelius Ficius, that in the old time, there was an island in the Sea, over against Africa, bigger than Africa and Asia, which island was called Atlantyda, and that the Kings of this island did govern a great part of Africa and Europa, and as marcelius Ficius, and Plato say, by the means of a great earthqake, and a great rain, this island sunk, and the people thereof were drowned: and after the sinking of this great island, the Sea Atlanticus was so full of mud by the means of the sinckng thereof, that the sea Atlanticus could not be sailed with ships in a great time after. Now if this be true, Of the great island called Atlantica that sunk. that there was any such island, that did so sink, & that the Sea was so full of mud, then after that the mud is settled unto the bottom, as it will do in process of time, than the sea must needs be a very shallow sea, for such a great mass of earthy substance being sunk with water, must needs make a very shallow Sea: and yet it is seen and known almost generally unto all men, that it is a deep sea, yea no man can tell of what depth, for that they cannot find any ground: for that sea is greatly occupied with ships, and that island lay wast from Spain and Barbary, which is most occupied with Ships, of any sea: for all the great trade of shipping is now in these days used out of Europe. And then what place can be greater occupied, then into our west Occian sea, called in old time, the sea Atlanticus, as it is the whole trade from England, France, and the low country, and Denmark, and such like places of Europe, into Spain, and Portugal, and Barbary, and into the middle earth Sea, and into Ginny, and into the Carnarie islands, the Madera islands, and the islands called the Syrtes, and to the West Indies: so that it is the greatest occupied sea with shipping in the whole world: so that the same sea is not unknown, but that it is a great deep sea: therefore it is to be supposed, that the fundamental nature or stubstaunce, or ground thereof was of Salt, and so soaked or moyllfied with the water, that the superficies thereof might be sunk under the water, and so in process of time to soak the mineral of the Salt, that the stony and earthy substance is now settled down so low, that it seemeth unto the simple people, that it hath no bottom: for otherwise such a huge mass of earthy substance could not be so lost, as it doth appear by that great island called Atlantida, that Maccellius Ficius, Plato, and Proclus, with other Authors, doth make mention of. etc. The ninth Chapter is as touching the cause of Earthquakes. AND furthermore, as touching Earthquakes, and the synking both of the main land, and also of islands in the Sea, and also of the drying up of Waters, as great pools & rivers, and also of the casting up of ground both in the sea, as well as upon the main land, although it be the providence of almighty God, to bring it so to pass, for the punishment of the people, When god doth plague the earth, he doth punish both good & bad. that are upon the face of the earth: and as well the godly do perish, as the wicked, when these things happen, which are the scourge of the wrath of God, for that he will have his divine glory known: yet he doth nothing but that it is done by a mean, & hath a natural cause of the coming of it so to pass, although the thing itself be supernatural. And furthermore, although I am simple and utterly unlearned, neither to the judgement of the people to have any great experience in these causes, yet notwithstanding being as one more bold than wise, to show mine opinion unto the world, and also it is possible that in some points my opinion doth not agree with some of the ancient Writers, that have written of sundry things in their books of natural philosophy. Yet notwithstanding I am so bold to show my opinion, although it be possible that it may differ from the truth. Wherefore they may use such credit unto the matter, as the reasons in these matters shall support unto them, for if that by reason my opinion be not to be liked, than they may the less regard it. etc. And this first, as concerning the sinking of ground as experience hath showed, that it hath happened in sundry places, and in sundry ages of the world, my opinion is this, as in the Chapter before is showed, that in those places that it hath happened, that the substance of the ground in that place is salt underneath, The cause of the sinking of the ground. and so being soaked or mollified with water, in process of time, it is turned unto water, and then the earthy substance that is a loof upon it being ponderous and heavy, and not supported or borne up with any hard thing, than it must needs settle itself down and sink into the water: and so by that means the water standeth above the superfycies thereof, as it is showed in the Chapter going before, by the sinking of the great island called Atlantyda, etc. And furthermore, as concerning some kind of earthquakes, that happeneth in such sort that it renteth and lifteth and shaketh the ground, and possible lifteth the ground higher than that it was before, and so remaineth and standeth still afterwards, with out any settling afterwards. etc. My opinion is this, by the means before rehearsed, Of Earthquakes. that there may be some veins in the ground that may be of the substance of salt, as before is rehearsed, and yet may be enclosed with other mines round about it, as we may see by experience, how often that the veins of the ground may alter, and in a small circuit, as in some place may be hard stone, and in another place chalk, and in another place, clay, or sand, or the our of divers kinds of metals, with a number of sundry sorts of substances that I do emyt. etc. Now this my or substance of salt being enclosed round about with other substances or stuff, as before is said, Water cannot departed from any place, until the air, or some other substance doth occupy the round and the springs of water in the ground coming unto it, both soak it & molifyeth it, that it is turned unto water: & then being water it is apt to run in the veins of the ground, & yet it can not departed to go from that place, until that it doth draw air thither. And look as the air doth find vent thorough the powers in the ground, & doth repair unto that place, so the water doth decrease & runneth in the veins of the ground unto other places: & thus in process of time the substance of salt being turned unto water, shallbe diminished or gone and the room thereof filled full of air, and yet the ground aloft shall stand firm and fast, for that it is borne up or supported by rocky or stony substance. etc. Now it is possible, that some will make argument, and say, how should air come thither, for that it is so low in the ground, and that there is no place open unto the air, whereby it may come thither? But they do not consider this, that no place can be vacant, but that it is furnished with somewhat, either with earthy substance, or water, or air, or fire, & every one of them is finer in substance then the other, as the earthy substance is gross and hard, so the watery substance is thinner, and yet ponderous and heavy: so that there can be no place hollow or concave in the earth, but it is filled with water or air. For the water by his ponderousness doth descend and seek to the lower parts. And then look where as the water is not sufficient to fill the hollow place, than air doth repair thither to fulfil the rest, taking his place next above him, as we may see by experience, that if we do dig in the ground, we shall meet with springs of water: as by the ensample of the digging of wells in the ground, that when they have digged so low, and have found but a small spring, then letting it stand a certain time, thither will repair a great quantity of Water afterwards. And then this being true, that the water doth find passage through the veins in the ground, than it is a plain case, that air must the rather find passage, for that it is an Element more thinner and subtyller than water, and will soak through any small thing sooner. For the nature of air is to descend very deep into the earth, if it be not filled with other substances. So in like manner water, although it be ponderous and heavy, will ascend upwards, if the air cannot come thither by the means of the closeness or thightnesse of the thing that the water is enclosed aloft or over it, and also the water will not descend or fall down suddenly, although the air be under it being enclosed in it, that the water by his thunderousness or weight, doth cause the air to seek through the water, which will be a long time, except the water and the air be be stirred by some accidental cause. And now to return to the cause of Earthquakes, The cause of Earthquakes. my simple opinion is this. The air being enclosed in the bowels of the earth, which hath happened by the means before rehearsed, or by divers other means, which I am not able to rehearse, that the air may be enclosed in the ground or earth, and then when it shall please almighty God to bring it so to pass, for God is the worker of all things, either by one mean or another, that the waters may arise and increase in the ground, and especially after any great and continual rain, and the water being ponderous and heavy, doth seek into the earth, expelling or thrusting out the air that is near the superficial part of the earth, and so by his ponderousness settleth itself lower and lower, and then the great and continual rain doth load the superficial face of the earth with water, and doth cause the earth to swell and shut itself close aloft on the upper part of the earth, and that water in the earth, by settling itself lower and lower, and the earth by his closeness will not suffer the air to departed out of the earth, so that there is no room in the earth to hold or contain both the air and the water, but that the air in the earth is forced to rend the earth to have room sufficient. And also at that time the earth is more apt to separate itself, than it is at any other time, for that the earth is soaked and made soft by the great moisture that is in it. And by this means, in such places whereas this cause doth happen that the ground doth quake and tremble, Of the shaking of the earth. and the buildings that are near thereabout, until such time as the air doth find passage to get out of the ground, and if that it cannot find passage, than it doth split and rend the ground, casting all things that are over it, or in the way of the air, that breaketh so out of the ground over it, and possible to turn the buildings underneath the earth or ground to the great and marvelous destruction both of the people and buildings where this happeneth. etc. And by this means those places, that have been land, may become Water, being near unto the Sea or any great river. And in like manner whereas there have been any pools or rivers may be dried up, as clean as though there had never been any pool, or river, or water there, by this means: for after that the air in the earth hath rend the earth to seek passage out, than this thing happening there or near unto the water, may run or descend into that place whereas the air was before, and also in the turning up or splitting of the ground, there may be some hills or cliffs standing up much higher than the ground was before. And so by this means the places that have been dry land, may become sea and water, and in like manner that place that hath been water, may become dry land. etc. And furthermore, in like manner there may by this means before rehearsed, be islands cast up in the sea, by the means of the air breaking out of the earth. etc. for that is the property of air, to run and to seek into all places, that is not occupied or furnished with some of the elemental substances, so that rather than any hollow or concave place in the earth shall be vacant, air will seek thither, if it were in the very centre of the earth. For as is said before, if water be able to seek passage through the veins in the earth, than much rather the air shall do it, for that it is much thinner, & subtler than water, although that air will give place unto water, by his ponderousness or weight. etc. The tenth Chapter showeth the reason, how America, and all the islands and new found Countries, and Lands, became peopled, and of what posterity they be come of. etc. AND furthermore, as touching the vain arguments and opinions of some people, as touching the discovering of a number of lands and islands, that have not been found nor known but within little more than .100. Years, as all America, and a number of Countries, and great and small islands more, & none of them of any quantity or bigness, for that they are peopled: and for that they are peopled, I have hard some vain and foolish arguments thereof, why there should be people there, for that these Countries or places were never known before, except there were any more adam's then one, or any more Noahs than one. So we may see by experience, how apt a number of people are to fall into errors, using most vain and contentious arguments in those matters that are past their capacity, which is a great offence before God, and also to the evil Ensample unto the world, unto such as do hear of the same. For it is no small error for us to fall into, for to think that there was anymore Adam's in the world than one, for that it is utterly against all the canonical Scriptures: and also it is as great an error to say that there were saved any more people after the deluge or flood, more than Iew and his family, that was in the ark with him, as it is manifestly declared in Genesis. etc. Wherefore I think it not hurtful to show my opinion as concerning how all America became peopled, with all the other new found lands and islands, lying in the sea, wheresoever they be. etc. first thus my opinion is, that America is part of the great island called Atlantida, as it is further declared in the eight Chapter going before, How all the new found Countries became peopled, as all America, and all other islands. that the Kings of the island did govern a great part of Europe and Africa, and according unto some Authors, that the Kings of that island were the sons of Neptunus, then that doth signify that there was a trade or occupying of Shipping between these known parts and that great island, and then when that great island did sink, as before is declared, the Sea Atlanticus was so full of mud, All the great island called Atlantida, did not synk, but part remained. that it could not be sailed in long time afterwards. And by the Ensample of America, that all the island did not sink, but the Westermost part did remain still. Although this happened long before the coming of Christ, and as before is declared, the great store of mud and filth that did remain in the Sea, was the only cause that did let the traffic and passage between us in these known parts, and them that were unknown unto us in all this long time of this mud remaining in the Sea: so long time, that those men that were the Sea men in those days, were of long time dead before the Sea was clear of the mud. And also those sea men, Old sea men being gone, the other did never attempt to seek any thing as it is to be gathered, that were in the island, did perish by the means of the sinking of the East side of that great island. Wherefore it is to be gathered, that those that were in these parts, did never attempt to seek any land that ways to the westwards, neither those that were remaining upon that part of the island that did not sink, did never attempt to seek any land unto the eastwards. And in like manner, they could not so conveniently do it, for that they had no Shipping to go unto the Sea, but small Boats called Cannouses, which be occupied to no other purpose or use, but only to go on fishing, or else to transport themselves from island unto island, near unto the main. etc. And yet it is possible that some people might pass out of these parts by shipping although they never made any return again, but might tarry there, and inhabit in those parts. And now insomuch that it is known, that they had boats, and did transport themselves from place unto place, and from island unto island, before the finding of the main land of America. So it is not to be marveled at, why all the islands in the sea, that are of any quantity, have people in them, considering that they had in all those parts, the use of boats from the beginning after Noy, The Indians had boats asoone as we here in these parts. or what time we had Boates. etc. And now furthermore, as touching the great & firm land that lieth to the Southerwards beyond the equinoctial about .50. degrees, & is extended unto the South parts, no man in these parts doth know, and it is peopled too, and the people thereof may come out of America, for there is nothing to let them, but a narrow sea, called the strait of Magalenus, and they having the use of boats, how easily is it to be passed? So that there can be no island, lying in the sea, near unto America, that is of any bigness, but that it is peopled, whether it be to the eastwards towards us, or to the West parts in the South Sea, or the East Ocean Sea. etc. And furthermore, as it doth appear in the Scriptures, that Noy had three sons, that is to say, Sem, Ham, and Japhet, and that Sem, the eldest son of Noye, did inhabit the parts of Africa, and Cham or Ham, the second son of Noy, did inhabit the parts of Asia: and Japhet the youngest son of Noy, did inhabit Europe, and the islands in the sea, as the great. Island Atlantida, now called America, and that the Kings of that great island, were the sons of Neptunus, and the people, the posterity of Japhet, the youngest son of Noy. etc. FINIS. ❧ A Table of the contents of the Chapters of the fifth and last book called a Treasure for travailers. To the reader of the fifth and last book. The first Chapter of the fifth book, showeth the natural causes how sands & banks be engendered or made, both in the sea and rivers. etc. The second Chapter showeth the natural causes of Marish ground, and other plain meadows or ground by the sides of rivers, etc. The third Chapter showeth the natural cause of the high cliffs by the sea coasts. etc. The fourth Chapter showeth the natural cause, why the Beach, & the great bolder stones on the sea coasts is become round & smooth, without any edges or corners. etc. The fifth chapter showeth the natural causes of the rocks in the sea, etc. The sixth Chapter showeth the natural cause of the ebbing and flowing of the sea, and the ebbing and flowing of havens and rivers. etc. The seventh chapter showeth the cause of currants and streams that run in the sea, in such places where it doth not ebb and flow: & of currants or streams in the sea, there are three several sorts, in the chapter it doth appear etc. The eight chapter showeth the natural cause that the water in the Sea is salt. etc. The ninth chapter is as touching the cause of earthquakes. The tenth chapter showeth the reason how America, and all the islands, and new found lands and countries, became peopled, and of what posteriritie that they be come of. etc. FINIS Faults escaped in printing. The first book fol. pa line. faults. Correction. 3 1 20 set the situate 3 2 8 marking making 3 2 24 make mark 4 1 9 of that, or that are 5 1 11 for line for the line 5 1 12 other side Dalida. 5 1 13 ridge ring 5 1 last the height 0 5 1 last measure of the that measure 7 1 12 and the and at the 8 2 13 standings places 9 1 20 as is 10 2 8 lie by 12 1 11 there then 12 1 20 the line should the line the should 13 1 1 there though 14 2 3 thence there 14 2 23 12 into 12. 15 2 12 28 24 15 2 19 5 15 16 1 23 lack look 17 1 1 do mays 17 2 4 staff transuastorie 18 2 many transitory transuastorie 18 2 many rings wings 19 1 many transitory transuastorie 20 1 32 that their 22 2 16 part put 27 2 22 by too 28 1 7 52 32 29 2 10 and half of 29 2 22 the chapter the .8. Chapter The second book. fo. pa. line. faults. Correction. 1 1 22 unto and unto 3 1 8 90 60 7 1 13 south-west South south-west 9 1 10 32. put put 10 1 11 30. degr. 49. 50. degrees .12. 9 2 20 London land 11 1 2 54 16 12 1 13 36 360 13 1 30 Elson moore Elson north 15 1 7 Cap hill Ape hill 15 1 13 18 25 15 1 15 London London .10. mi. 15 1 the longest day the day .14. hours .35. mi. 15 15 1 minutes southeast minutes, and is Southeast 24 under the tropic of Cancer 16 1 25 0 19 1 11 East and South East & by south 19 1 30 7 98 19 2 30 Maria in Aria 21 2 11 25 52 22 1 33 20 4 22 2 2 12 4 The third book fo. pa line faults Correction. 3 1 28.29 that that that 3 2 12 of a board of board 5 1 2 be corner be from corner 5 1 3 22 32 7 1 4 level bevel 7 1 11 level bevel 14 2 9 with the within the 15 1 12 30 3. quarters 15 1 19 racking raking 15 1 32 whole hold 16 2 15 would have have 19 1 22 13. inches 10. inches The fourth book. fol. pa. lin. faults Correction 3 24 as is 4 1 last targed karged 5 1 27 must may 7 1 30 with which 7 1 53 multiply by multiply that by 8 2 23 in the mould of metal in the mould of wood. 2 31 8 2 5 led raised or highed 11 1 1 near as needs 12 2 18 30. 36. 12 2 32 weight the weight that the 12 1 23 one kind of one kind 14 2 6 by the proportion of the by proportion, the 17 1 19 hang change 18 1 22 heel heeled 18 1 3 to hold to heeled 19 1 18 collect calk 19 1 ● in, enough 19 1 24 carrying carening 19 2 30 cartienes captains The fifth book fol. pa. lin. faults. Correction 5 2 6 mould mouth 6 1 2 souffynges suffings 8 1 8 suits sorts 8 2 5 souffinges suffynges 8 2 22 sea, it sea, as it 9 1 3 Ireland England 9 2 4 souffinges suffinges 9 2 19 rounded covered 11 1 15 in at 13 1 6 beaten let 15 1 12 wast West 6 2 3 meayne main 11 1 30 tract attract 11 26 higher high or ¶ Imprinted at London for Thomas woodcock, dwelling in Paul's churchyard, at the sign of the black bear. 1578.