The use of the two mathematical instruments, the cross staff,( differing from that in common use with the mariners:) And the Iacobs staff: Set forth Dialogue wise in two brief and plain Treatises: the one most commodious for the master, and all such as are to deal in astronomical matters: the other, profitable for the surveyor, to take the length, height, depth, or breadth, of any thing measurable.  
Set forth by Th. Hood. mathematical Lecturer in the city of London.  
Newly reviewed, and the second time imprinted.  
The Staues are to be sold in mark lane, at the house of FRANCIS cook.  
 
Imprinted at London by Richard Field for Robert Dexter. 1596.   

TO THE RIGHT honourable, CHARLES LORD HOWARD, BARON OF EFFINGHAM, LORD HIGH admiral of England, &c.  
WHen I presented this little book in writing unto you( right Honourable) I did little think that it should haue come unto the Printers hand: but the staff being shewed unto diverse men that were desirous to know the use thereof, I thought the labour would be too long to teach every one, and to writ it out continually, the pains would haue been much more. Therefore to save both my pains in writing, and my labour in teaching, I could find no better means, then to commit it unto the press. Considering then that it must abroad, I beseech your Honour, that it may appear under your name, that as it pleased you at the first to give it a friendly entertainment, so now you would also be Patron unto the same, that your authority protecting, and your wisdom allowing it, you may stay the unadvised censure of some rash conceited men. whereby I shal be both encouraged to a further study, and bound to pray for your Honours increase in all good things.  
Your Honors most humble, Thomas Hood.   

To the courteous Reader.  
I Present unto thee( gentle Reader) in one small Volume, the use of two mathematical Instruments, the one is the cross staff: the other, the Iacobs staff. In the delivery of their use, I haue done mine endeavour to lay out the matter most plainly, that thou mayst find commodity in the thing. That is all my desire, which if I may attain unto, I shall be glad. If any thing seem otherwise unto thee, accept my good will, whose purpose was to satisfy thy mind: and interpret hereof faucurably, at the least, because it is my first labour that ever came abroad. So shall I be the more willing to take farther pains, and to commit such other things unto thy sight, as I haue in hand. Farewell.  
Thine Th. Hood.   

A Dialogue touching the use of the cross staff.  scholar. 
having understood that you haue a kind of cross staff, somewhat differing from those of the common sort, I am somewhat bold to request a little conference with you about the same.  master. 
Not so bold as welcome: It is my desire to further all men what I can. I pray you therefore briefly to propound what you would haue, and I will return an answer to your contentation, so far forth as I may.  Sc. 
First, I desire to know, what end you haue generally in the thing.  Ma. 
The staff may be used to diverse purposes: but my chiefest end and intention therein, is to take the height of the sun above the Horizon.  Sc. 
May not a man do it as well by the other staff, commonly which is called Bella Stella?  Ma. 
Comparisons are odious, therefore I omit that matter, and request you to propound some other question. Yet this I say, that this staff is not so troublesone as that, which you haue name. moreover, the degrees thereof are greater then those of the other staff, though the Staues themselves be of equal length. For 5. of them are as big as 15. in the Bella Stella. Neither are you tied unto an Horizon: for it may be used both by land and sea: and without applying it unto your sight.  Sc. 
These be no small commodities. If therefore I may obtain at your hands the use of this staff, I shall think myself not a litle beholding unto you.  Ma. 
Your request is granted: Take therefore what order you think best for your instruction.  Sc. 
Because I would haue all things plainly delivered, I will keep this order in my questions. First. I will begin with the two pieces of wood: and then with the sockets: thirdly, I will request the use of the Vane: and last of all, howe the suins altitude may be found out.  Ma. 
Do so: and I will labour to fulfil your mind.  Sc. 
First therefore, what names do you give unto these two pieces of wood?  Ma. 
I call the one the Yard, the other the Transame.  Sc. 
What mean these marks that are in them?  Ma. 
They are degrees of altitude, with their minutes.  Sc. 
But how shall I distinguish the Transame from the Yard, seeing the degrees in them both be all of one quantity, neither hath the one of them any more degrees then the other?  Ma. 
It is true that there be 45. degrees in each of them. The Transame containeth the first, namely, all the degrees from 1. to 45: the Yard containeth the rest, namely, the degrees from 45. unto 90.  Sc. 
Is that of necessity that they should do so?  Ma. 
No: But by this mean I make the degrees so great as they are.  Sc. 
Then I perceive this: that from the rising of the sun, until he be raised 45. degrees above the Horizon, his elevation must be taken in the Transame. again, after that he is 45. degrees above the Horizon, his elevation must be taken in the Yard.  Ma. 
It is so.  Sc. 
May I easily know by this staff, when the sun is under 45. degrees, and when he is above 45. degrees of elevation?  Ma. 
Most easily, and readily: as you shall be taught hereafter.  Sc. 
Why is the yard cut off so close unto the 90. degree?  Ma. 
That it may the better come unto your sight: wherein the Centre of the circled is imagined from whence all the lines do come.  Sc. 
Thus much concerning the Transame, and the yard. Now for the Sockets: to what purpose serve they?  Ma. 
They be made to join the Transame and the yard together.  Sc. 
What principal note is to be observed in them?  Ma. 
They must be joined together squire wise, at right angles.  Sc. 
To what end are the notches in them?  Ma. 
The notches serve to this purpose, to see how to set the Transame, and the yard just upon his place. For the brass carrying a certain thickness with it, doth hinder my sight so, that I cannot well judge of the true place whereon they should stand, were it not for these notches, which must bee no deeper, then the thickenes of the brass, or if they be deeper, they must be both of one depth.  Sc. 
To what end serve the screws?  Ma. 
They serve to none other purpose but this, namely, to keep the Sockets fast in their places that they slip not.  Sc. 
May I put the Sockets vpon the yard which way so ever I will, without any difference?  Ma. 
No: But you must take heed of this, that the Socket wherein the Transame must be put, must always hang downward, for so it is best: otherwise there is not any great heed to be taken. And yet for avoiding of confusion, let this be your rule, that The end whereat your two Sockets close together, be next unto your sight.  Sc. 
To what end serveth the Vane?  Ma. 
It serveth to take the elevation of the sun, and also to save your sight from the beams thereof.  Sc. 
In what maner I pray you?  Ma. 
Of that I will inform you hereafter: for the maner being diuers, cannot well be set down here, without confusion.  Sc. 
Whereupon must the Vane stand?  Ma. 
Sometimes vpon the Transame, and sometimes vpon the Yard, according as the manifold use of the staff requireth.  Sc. 
Is it any matter to which hand it standeth? either to the right hand, or to the left?  Ma. 
Yea that it is: and this Rule shal always serve your turn, When the Transame standeth on the right hand of the Yard, let the Vane bend toward the left hand: and contrariwise, when the Transame standeth on the left hand of the Yard, let the vane bend toward the right hand.  Sc. 
Now let me know how I shall join the Transame and the Yard together: for to that end were the brazen sockets made.  Ma. 
They are to be joined together diversly, according as the staff is diversly used.  Sc. 
Is the staff then to be used after more ways than one?  Ma: 
Yea, for you may choose whether you will apply it unto your eyes( as you do the Balla stella) or whether you will hold it in your hand, and find the height of the sun by the shadow of the Vane.  Sc. 
Is there any general observation to be noted in these several uses?  Ma. 
Yea: For this is a general rule, that whether you apply it unto your eye, or whether you hold it in your hand, the Transame must be always perpendicular unto the Horizon, and the yard level unto the same.  Sc. 
But how shall I be assured of the perpendicularitie and the parallelitie of the one and the other?  Ma. 
At the Sea, whers your Horizon is free if you bring the Yard even with the closing of the heaven & the Horizon. it is enough: But vpon the land, or looking out at a Window of an house, or standing in the street, you may adjoin unto the one side of your Transame a Plummet of lead, thereby to find out his perpendicularitie. Yet do I not think that so necessary, because I know, that a little practise will make the eye a reasonable judge both of the perpendicularity, and of the parallelitie.  Sc. 
Let us now come unto the particular use of the staff. You say that in seeking out the elevation of the sun, I may choose whether I will set the staff unto mine eye( as I do the Bella stella) or whether I will hold it in mine hand.  Ma. 
It is so.  Sc. 
I pray you therefore instruct me first concerning the use of that, when I must set it unto mine eye.  Ma. 
This one thing is not to be neglected, that it must stand on the ball of your cheek, for that place is most convenient, because it doth not lightly yield, neither is the sight thereby distorted: Yet if any man think it méeter to apply the staff to the corner of his eye next to the ear, I will not gainsay him, because the sight is not to every man so ready in one place as it is in an other.  Sc. 
How must I in this case join, the Transame and the Yard together.  Ma. 
Put the Yard into his socket, so that the notch may stand just vpon the 45. degree. Then put the Transame into his socket in like manner, that the notch may be vpon the 45. degree.  Sc. 
Is it not material which ways the degrees stand, either upward or down ward, or on the side?  Ma. 
Let this be your rule: keep the degrees of the Yard upward, and let the degrees of the Transame be toward you, so shall you be the less deceived. Otherwise to them that are cunning, it is neither here nor there.  Sc. 
Is there any thing to be observed in the placing of the Vane, more then hath been said before?  Ma. 
This is to be noted, that the edge of the Vane must be placed just with the highest degree of the Transame.  Sc. 
Each thing being fitted in this maner, how shall I take the height of the sun?  Ma. 
First, you must know whether the sun bee more or less then 45. degrees above the Horizon.  Sc. 
How shall I know that quickly? for me thinketh that should be troublesone.  Ma. 
It is most easy. The Transam and the yard being joined together, as you haue been taught: turn the 90. degrees of the yard toward your breast( it is no matter for setting it unto your eye) and bring the Transame right against the sun, until the shadow thereof fall even with the side of the yard. If the shadow of the Transame from the top of the Vane downward be longer then the yard, it is a most certain sign that the sun is under 45. degrees high. If it be shorter, the sun is more then 45. degrees high.  Sc. 
If the sun be less then 45. degrees high, what must I do?  Ma. 
Set the staff close to your eye, keeping the yard parrallele unto the Horizon, as you haue been taught before: then let the Transame sink down into his socket, until the top of the Vane come even with the Centre of the Sunns, the number of the degrees from the top of the vane to the notch of the Socket will declare his elevation.  Sc. 
This thing is plain enough. May not his elevation yet be found out any other way by the Transame, while the Sun is under 45. degrees.  Ma. 
It may be found out otherwise in this manner: Put that end of the Transame into his Socket, which containeth the beginning of the degrees, let the first degree come even with the notch, as the 45. degree did before, and make the Transame fast with the scrue: then set the yard unto your eye, and keeping it unveil, move the Vane up and down, until the uppermost edge thereof come even with the Centre of the sun: the degree upon which it lighteth is the suins altitude.  Sc. 
Thus much concerning the sun whiles he is under 45. degrees. What must I do to find his altitude being above 45. degrees?  Ma. 
The Yard, Transame, and Vane being orderly placed, as it was taught before, set the yard unto your eye, and keeping it unveil, draw the Transame to you ward, until the Vane be even with the Centre of the sun: the degree then of the yard, vpon which the notch of the socket lighteth, declareth unto you the height of the sun.  Sc. 
Is there any more to be said concerning the use of the staff, when it is applied unto the eye?  Ma. 
No: For I haue at large declared the same: so that now it remaineth to tell you, how the staff may be used, although it be not applied unto the eye.  Sc. 
One thing let me first demand: May not I take the height of any star in the same manner as I haue taken the height of the sun?  Ma. 
Yes, that you may: Neither is there any difference in the one from the other. You may also take the distaunces of any two stars thereby, so that they be not further asunder then 90. degrees, following the self same precepts which you haue been taught concerning the Sunnens altitude. For if the two stars be less then 45. degrees asunder, they will be within the end of the Transame, and the yard. Then set the yard against the one star, and draw the Transame into his sorket, until the edge of the Vane light vpon the other star, and the degrees of the Transame will show their distance. If the two stars propounded he more, then 45. degrees asunder, it is certain, that they will he without the compass of the Transame. Then draw the Transame toward your sight, until the end of the yard light vpon the one star, and the edge of the Vane upon the other star, and the degrees of the yard will show their distance, so that you may take the distance of any two stars that are 90. degrees asunder.  Sc. 
Now let us return unto the former question: how must the Transame and the Yard be joined together, and how must the Vane be placed, if I be not disposed to set the staff unto mine eye?  Ma. 
The joining of them, is after diverse manners, according as the use doth differ. First, you may find the suins elevation in the same maner, as you did before, although you do not apply the staff unto your eye, and therefore in this case the Transame and the Yard must be joined together, as they were before, and the Vane must also stand after the same manner.  Sc. 
How then shall I find the suins elevation?  Ma. 
Set the palm of your hand close to the end of the Yard where the 90. degree is placed, and then turn the Transame vpon the sun, and pull down the Transame into the socket, until the shadow of the top of the Vane fall just upon the end of the Yard close to your hand: Then the degree of the Transame next unto the socket, is the suins elevation.  Sc. 
I perceive that in this case also I must hold the yard very level.  Ma. 
Yea, that you must: and so shall you be sure of the suins altitude.  Sc. 
May I find the suins elevation thus, if he be more then 45. degrees high?  Ma. 
Yea, even as you did before. For this is all the difference, that your hand standeth now in stead of your eye And I am of this mind, that if you take heed unto the level of your yard, you may take the sun as precisely this way, as you do with applying the staff vnioy our eat. Besides, this is one commodity, you shall not day●n your sight, and hurt it as you did before.  Sc. 
What other way is there yet to use the Staff, and how must I join the Transame and the yard together?  Ma. 
There is yet an other way to find out the height of the sun without setting the staff unto your eye. For the performance of which conclusion, you must set the yard and the Transame together thus. Put the Transame into his socket so, that the beginning of the first degree may fall 〈◇〉 with the notch: then make it fast with the scrue: put the yard 〈…〉 to his socket, in such sort that the 45. degree fall eu●● 〈…〉 notch, and set the Vane at the other end of the yard, as you were instructed before.  Sc. 
How must I use it then?  Ma. 
You must here also haue that consideration which you had before of the Suns elevation, whether he be more or less then 45. degrees, which is known by the rule given in the beginning.  Sc. 
If the sun be less then 45. degrees high, how must I hold the staff?  Ma. 
Let the Transame hang downward toward your feet, and turn the Vane which is vpon the yard to the sun until the shadow of the yard fall just with the side of the Trant same: the degree of the Transame, upon which the shadow oath Vane doth fall, declareth the height of the sun.  Sc. 
Is it material which side of the shadow I do choose?  Ma. 
Yea, For that side of the shadow must be chosen, which is made by that part of the Vane, which is next unto the end of the yard, as you may see in the figure.  Sc. 
I perceive your meaning in this. But how must I hold the staff, if the sun be more then 45. degrees high?  Ma. 
Then must the Transame lye level with the Horizon, which before did hang perpendicular, and the yard must stand upright toward your Zenith. Then turn the yard toward the sun so, that the shadow thereof fall close to the side of the Transame, mark vpon what degree of the Transame the shadow of the uppermost side of the Vane falleth, subduct that out of the 90. degrees, and the remainder sheweth the suins elevation.  Sc. 
May not the height of the stars bee found out in this manner?  Ma. 
No: By reason their beam is so weak that it cannot cast a shadow; but the beam of the sun being so strong, his height may thus be easily found out, and very readily, and also certainly, having onely this care, that the staff be kept level as it ought to be.  Sc. 
Is there any thing else to be said concerning the use of this staff?  Ma. 
It may be used to diverse other purposes( as I said in the beginning:) namely, to the description of Regions, and Countries: to the finding out of the quantities of the Eclipses of the sun and moon: with the longitude and latitude of the Planets. This staff also serveth to the correcting of the places of the fixed stars: & to the setting down of the amplitude of the rising or setting of the sun or Stars. But mine intent was onely to take the suins elevation therwith. Yet haue I  told you how to take the altitude of the stars with their distances, by the same staff: which for this time shall suffice. The other propositions I will lay forth, either in my public lectures which I red, or at other more convenient time, as my leisure serveth.  
FINIS.   

THE use OF THE IACOBS staff.  
 
Imprinted at London by Richard Field, for Robert Dexter. 1596.   

TO THE RIGHT honourable, L. John LVMLEY, BARON OF LVMLEY. &c.  
AFter that I had penned( Right honourable) the use of the cross staff, I was desired by mine acquaintance, to take the pains in the Iacobs staff. I did so: my pains were liked and called( as the former) unto the press. Without a patron I would not haue it come forth, because I would not be thought to bee without a patron. To rrouble one man with them both, I thought it not good, least I should seem forgetful of other my well-willers: among whom your good will, shewed unto me at diverse times, hath emboldened me to crave your patronage for the thing, which if it shall please your Honour to undertake, I shall account it as a special token of your loving favour, and aclowledge myself in recompense, bound to pray for your Honours daily increase in all kindes of blessings.  
Your Honours most humble. Th. Hood.   

A Dialogue touching the use of the Iacobs staff.  scholar. 
SInce my last departure from you, I haue diligently applied the cross staff, according unto the rules which you haue prescribed, and find the same to be very convenient for the purpose, which you haue set down: that is, for the taking of the height of the sun and stars, with their distances: Yet can I not stay myself here, but must once again presume vpon your courtesy.  master. 
What is it that you desire? I love not many words but you shall find me most ready to pleasure you, or any man else, as far forth as my simplo skill will afford me.  Sc. 
This is the matter: I would gladly learn the use of the Iacobs staff as well as I haue learned the use of the cross staff: May I not therefore so divide the cross staff on the one side, that it may serve my turn for a Iacobs staff, so that I be not troubled with the carriage of any more then one?  Ma. 
Yes, very well. And lo, here is one so divided, that as the one side of the Yard and Transame serveth for the Sun and stars, so the other serveth for any dimension.  Sc. 
This falleth out even as I would haue it: seeing therefore the staff is ready at hand, if your leisure serve, I pray you instruct me in the use thereof.  Ma. 
With a good will: move you the questions, and I will answer them.  Sc. 
Why do they call it Iacobs staff? Was he the first inventor of the thing.  Ma. 
I know not that: but they take occasion to call it so, by reason of those words which are written Gen. 32.10. where the Patriarch saith, That with his staff he came over jordan: Wherein I think, they misconstrue his meaning. Notwithstanding, by whom soever it was invented, the Instrument questionless is of singular use.  Sc. 
Let that pass, and declare I pray you, what affinity this staff hath with the other. For comparisons will make a thing more plain.  Ma. 
First, as in the other staff, the degrees of the Yard and Transame are all one in number, so are the partitions in this. Secondly, as the yard and Transame in that, did join together squarewise and at right angles, so must they do in this. Thirdly, there must the same consideration be had in placing of the Vane in this, that was had in the placing of the Vane in the other: that is, it must stand even with the beginning of the partitions, except some special occasion require otherwise, as is to be seen in the measuring of breadthes. Fourthly, One of the two, either the Yard or the Transame, as occasion serveth, must be parallel unto the thing measured, the other must be perpendicular.  Sc. 
Is that a rule to be noted in the Iacobs staff?  Ma. 
Yea that it is: otherwise it is most certain you commit an error.  Sc. 
Then haue I been amiss informed, as I haue seen men, that haue thought themselves to be of no small cunning in the use of the staff, who measuring the height of a thing, haue made no matter how they held their staff, so that they did see the top and the bottom of the thing to be measured, even with the two ends of their Transame.  Ma. 
Belaeue me in this, that it cannot be that their practise should be true. This one argument shall serve for a thousand. You know that the proof of the use of the Iacobs staff standeth upon the proportion of Triangles. Now those Triangles onely are proportionable which are like, and in like maner situated, which they can never be except either the yard, or the Transame be parallel or perpendicular( as occasion serveth) to the thing measured.  Sc. 
Your reason is good that it should be so: but me thinketh that the performance thereof should bee impossible.  Ma. 
Why so?  Sc. 
You know that many Fields be full of Dales and hollow places: others be full of hills and Mountaines. moreover, many things stand not upright vpon the ground, but lean either forward or backward, or else to the one side or to the other. Last of all in the breadth of a thing there is a great variety. For be it in a wall, or field, or what else whatsoever, there is for the most part either hollowness or roundness, or some such like thing which may make it impossible in my iudgement to draw either parallel or perpendicular line unto them.  Ma. 
I grant those things to bee as you say: yet do they not hinder a man from taking the measure of their length, height, or breadth. For where the place itself doth not afford a leuelnesse: it is an easy matter to imagine it level. Thus also you must think with yourself, that although Geometry be the Arte of measuring well, and generally nothing may be excluded from the compass thereof, yet must we not bee too curious in particulars, least we show ourselves either over wise, or else too foolish. The physician generally professeth to heal all diseases, but when he cometh to deal with particular bodies, he faileth in his art, and yet is not to be discommended so long as he doth that which Art requireth. It is enough for the Geometrician, if he give the just length of a streight line drawn between two places assigned. Or if he can not do it by one streight line, he may do it by many. whosoever immediately( for mediately he may find out the length of a crooked line by means of a strait line) whosoever, I say, requireth any more of him then that, he abuseth both the man and the art. Therefore, when any thing is propounded to be measured, be it length, height, or breadth, you are first of all to consider, whether the thing lye level, or stand upright, or be strait, as it is required that it should be. If it be strait, you may presently fall in hand to measure it, as your rule shall direct you: If it be not strait, but be either crooked, or leaning one way or another, it must be your principal care, first to fit the same to your purpose: as for example, in measuring the distance of a thing( for I will first begin with that dimension, and will afterwards teach you what you shall do in the rest) if the distance between two places assigned be not strait, as you see in these figures which follow it is not, then choose out two points in the distance, the one being at the one end thereof, and the other in the other, between which you may imagine a right line to be drawn, and then so hold your staff, that the yard or the Transame may be parallel, or perpendicular unto it, as occasion shall serve.  Sc. 
You haue thoroughly satisfied me in this. Tell me now wherein these staues do differ, seeing you haue declared wherein they do agree.  Ma. 
Their difference consisteth in two things especially: in their partitions, and in their use.  Sc. 
Touching the first difference, it is evident indeed, that the parts of the other staff are unequal, and that this is divided into equal portions: but maketh it any matter howe many the parts are into which this staff is divided?  Ma. 
No: The more the better, and more precise will your work be. And therfore, if you could divide them into 100000. it were the more commendable, but 1000. sufficeth in this staff, which though it be not divided into more, yet you may imagine it to be an hundred times as much as it is.  Sc. 
What is the difference in the use of the Staues?  Ma. 
The general difference is this: the other serveth for astronomical matters: this serveth for measuring of land.  Sc. 
What mean you by those words, Measuring of land? Is it to take the breadth, or length only of a field? or may it be applied otherwise?  Ma. 
The truth is this, that by this staff we may measure the length, the height, and the breadth of any thing, all the which we express by those words, Measuring of land: having relation to the word Geometry, which signifieth the same if it be construed word for word.  Sc. 
Before I do come unto the particular measuring of these three dimensions, length, height, and breadth, what general notes haue I to observe?  Ma. 
First, that whether the Yard or the Transame be applied unto your sight, it must stand close unto the ball of your cheek.  Sc. 
But which end of the Yard or Transame must stand to the sight ward?  Ma. 
That which hath the beginning of the degrees: for so it is most convenient for the readiness of your account. The second note is this: to wink with one eye. For the sight by that means will aim at your mark the better, when it is not partend but brought into one. The third observation is this: that, the distance of your mark be not over great.  Sc. 
Why do you give this note, considering that in the use of the other staff, there was no limitation made of any distance? For you measured therewith the stars in heaven.  Ma. 
The case is not all one, because the stars haue a brightness which helpeth their sight, and their beam cometh directly from the Centre of their body, unto our eye. But in terrestrial things it is not so: For in them, by reason of the weakness of our sight, we may be greatly deceived, except they be within a reasonable compass.  Sc. 
What do you call a reasonable compass, or distance?  Ma. 
It cannot well be defined, because there are so many things required therein, that they will hardly jump all together generally: as these, the clearness of the air: the goodness of the sight: the largeness of the instrument. The air may be clear, but the sight of a man may be dull. again, the sight may be quick enough, but the air may be thick. again, both the air and sight may serve the turn, but the instrument which he is to use may be so small, that he can not take any thing far distant from him. So that we cannot generally determine of the distance otherwise then thus, saying that that is a reasonable distance, which is proportionable both to our instrument and sight.  Sc. 
proceed I pray you in the matter wherein you were.  Ma. 
The fourth regard must be had unto your hands that they be steady. For otherwise you may miss of the proportion of your measure. The last note is this, to take heed unto the place wherein you make your station.  Sc. 
How shall I be sure of that?  Ma. 
Thus: You know this, that either you stand upright, or else lean one way or other. To be short, howsoever your situation be, whether it be standing, sitting, leaning, or upright, that is the place of your station, which is right beneath your eye, so directly as is possible to be judged and taken.  Sc. 
These five things you say are generally to be noted. 1. The setting of the Saffe at the ball of the eye: 2. The winking with one eye: 3. A reasonable distance: 4. A steady hand: 5. The certain place of your standing. Let us now come unto the particular use of the staff in the three dimensions. You say, the Iacobs staff serveth to take the length, the height, and the breadth of any thing: Are these dimensions found out any more ways then one?  Ma. 
Yea: The length, and the height, are found out three several ways, and the breadth two ways. The first and the second way require one station: the last way in each dimension is performed by two stations.  Sc. 
What mean you by a station? and what is it to perform a thing by one or more stations?  Ma. 
A station is nothing else but the place wherein you stand: to perform a thing therefore at one station, is nothing else but by a standing in one onely place by the help of your instrument, to take the measure of a thing. To perform it at two stations, is by standing in two several places to take your measure.  Sc. 
What general note is there to be observed, when we measure a thing at one station?  Ma. 
You know this, that the measuring of a thing by the Iacobs staff, dependeth wholly vpon proportions, whose drift and final end is this, by three numbers given, to find out the fourth. Two of these numbers are always the partes of your staff, the one being the partes of your Transame, the other of the yard: the which numbers must be placed according as the rules which follow shall direct you. The third number of proportion is some assigned measure in this manner. If you measure the length of a thing, some certain height must be assigned. If you measure the height or breadth of a thing, some certain length, or distance must be given you for your third proportional number, and this number must keep the third place in the rule of proportion, or Golden rule, or rule of three, as we do commonly term it. Then must we say thus: that, as the partes of the Transame cut off by the Yard, are unto the parts of the Yard cut off by the Transame: Or contrariwise: As the parts of the yard cut off by the Transame, are unto the parts of the Transame cut off by the yard, so is the assigned measure which is given you, unto the measure of the thing sought for. This is the chiefest note in measuring at one station.  Sc. 
What note is there to be observed in measuring at two stations?  Ma. 
There are three things specially to be noted: The first is, the making of your stations, that they be both of them in a right line with the thing to the which you level your staff, whether you go forward or backward.  Sc. 
How may that be done?  Ma. 
Choose out some mark in the thing to be measured, which may be level with your eye, then set up two staues where you mind to make your two stations, so that standing at the further staff, you may bring the other just with the mark which you do choose out: so shall you be sure that the two stations are in a right line with the mark chosen. For it is a general rule, that if three points be in one level of the eye, those three points are in one right line. The second is, that your eye be no higher at the one station then it is at the other. This is to be done by the rule which I gave you even now For if you, standing at your second station, and holding your staff level from your sight, can see the top of the staff which standeth at your first station, and also the mark which you choose, it is a certain sign that your eye is in his just height. The third note is, that the distuance between the two stations be diligently taken, and that in a right line, so near as is possible: because the whole art of measuring by the Iacobs staff, dependeth vpon a right line. This distance must be the third number of your proportion. And these be the chiefest observations that I remember. If there be any thing else, I will put you in mind thereof as occasion serveth.  Sc. 
Let us come now unto the particular dimensions, and begin first with the length? What call you the length of the thing measured?  Ma. 
It is the distance between the place whereon you stand, and the place assigned, unto which you direct your sight: and in this case we commonly say thus: How far is it from my foot, to such or such a thing? as a tree or House. &c.  Sc. 
give me now the rules whereby I may direct myself in measuring any distance given.  Ma. 
The first rule requireth, that the yard should be perpendicular to the length measured: And that is this. The yard of your staff being perpendicular unto the thing measured. If your sight pass from the top of the yard over the end of the Transame to the farther end of the thing propounded, as the partes of the yard cut off by the Transame, shall be unto the parts of the Transame cut off by the yard, so shall the height of him that measureth bee unto the length of the thing propounded.  Sc. 
Here are two questions to be propounded. First, what call you the end of the Transame?  Ma. 
That is generally called the end of the Transame, over the which your eye sight passeth wheresoever it be, whether it be in the very end of the wood itself, or any other place, where you list to set the Vane, so that your eye sight pass by that place.  Sc. 
Secondly, what call you the height of him that measureth? For some man may be, and is a great deal higher then another.  Ma. 
The height of the measure is the distance between the top of the staff and the thing measured: as in the 1. figure from y. to o. and from a. to o. is the height of the measurer: so that whether he stand upon the ground at the one end of the distance assigned, or whether he stand vpon some higher place, the maner of work is all one: this being noted as a general rule: That the height of the top of the yard from the ground, must be certainly known.  Sc. 
express the meaning of your Rule by some example.  Ma. 
Put case the partes of the Yard cut off by the Transame bee 60. and the partes of the Transame cut off by the Yard be 180. let the height of the staff from the ground be 4. foot: then I say that as 60. which are the partes of the Yard, are unto 180. which are the parts of the Transame: even so is 4. feet, which is the supposed height of him that measureth unto the length propounded. So that I conclude the length thereof to be 12. foot.  Sc. 
This is easily concluded, and dependeth, as I remember vpon the 4. p. of the 6. book of euclid: where it is said that: In equiangle triangles, the sides which contain the equal Angles are proportional, and the sides which are subtended under the equal Angles, are of like proportion. moreover I perceive( as you  told me before) that the third number of the proportion, is the assigned height.  Ma. 
It is true: and you may most manifestly perceive that in the Figure which you said concerning Euclides proposition: For the 2. Triangles a. e. i. and a. o. u. are like, because they are situated after one and the self same maner: therfore in the Triangle a. e. i. as a. e. is unto a. i. so in the Triangle a. o. u. a. o. is unto o. u. Thus you see the commodity of the staff in measuring the length of a thing. And here you must note this, That it is no matter whether the thing measured do lye in a plain or flat, or whether it be in the ascention or descension of an Hill, or whether there be any concavity or conuexity between the ends of the thing measured. So that by this rule, we may measure the breadth of any river, or of any Trench, or of any Valley between the tops of the hills, or the distance of two Ships at sea &c.  Sc. 
The first Rule required, that the yard should be perpendicular unto the thing measured. Put case the yard do lye parallel unto it, as it is in the 2. Figure, what then?  Ma. 
The yard being parallel unto the thing measured, if your sight pass from the beginning of the yard over the end of the Transame, then, as the parts of the Transame cut off by the yard, are unto the parts of the yard cut off by the Transam, so is the height assigned unto the length propounded to bee measured.  Sc. 
So then by your Rule I conclude, that if the partes of the Transame cut off by the yard be 120. parts: and the parts of the yard cut off by the Transame be 210. and the height assigned and known be 400. feet, the length to be measured must be 700. feet, as I perceive by the Golden rule, and by the proposition of euclid mentioned before.  Ma. 
You say very true: for considering the two Triangles a. u. o. and a. i.e. are like, it must needs follow, that as in the lesser Triangle o. u. is unto u. a: so in the greater e. i. must be unto i. a.  Sc. 
You said heretofore, that there were 3. ways to find out the length of any thing, whereof 2. are already set down: What is the third way?  Ma. 
The two ways already set down, require but one station. For you are not bound to remove from the place whereon you first set your foot when you begin to measure. But this third way requireth a double station, as in the 3. Figure, which is many times necessary, because that a tree, or a Wall, or an Hill, may be between our sight and the end of the thing, whose distance from us we desire to know, so that our sight cannot come unto the end thereof. The third way differeth from the former in this, that there is no altitude to be assigned and given for the third number of the proportion, but the third number of the proportion, is the distance between the two stations.  Sc. 
I pray you answer me to this: Considering that I must take 2. stations, at which is it best to begin? Is it best to begin my first station at the end of the distance propounded, and so go backward? or is it best to begin my first station a good way from the end of the distance propounded, and then come forward to make my second station?  Ma. 
That is neither here nor there: But the common use is to begin the first station, at the end of the distance propounded, and so go backward: in the which thing doing, you must take heed of that especially, which I  told you before, that you go backward in a strait line: so that the line imagined to be drawn from the one end of the distance propounded unto the other, being continued unto the second station must make but one right line: otherwise you shall err in your measure more or less.  Sc. 
What distance is best to be made between the two stations?  Ma. 
The larger the better: For it is good never to take a short station, if you may haue a large one: because your error will be the less thereby.  Sc, 
give me now the rule which I must follow.  Ma. 
The Yard being parallel unto the length propounded to be measured, and your eye at each several station, passing from the head thereof over the end of the Transame, unto something that standeth upright, at the farther end of the distance prounded: as the difference of the greater segment of your Transame shall be unto the lesser segment: so shall the length between the two stations be unto the distance propounded.  Sc. 
In this kind of measuring, must the Transame keep one place vpon the yard, without pulling it nigher, or putting it farther off from the sight?  Ma. 
The rule the I gave you even now requireth that it should do so. And then you must note this, that the farther you go backward from your first station, the lower must the Transame sink into his socket.  Sc. 
give me an example of that which you haue said.  Ma. 
Put case that at your first station the partes of the Transame cut off by the Yard were 108. at your second station, put case the partes of the Transame cut off by the Yard were 72. imagine also the distance between your two stations were 40. feet: I must seek out the difference between the several partes of the Transame cut off by the Yard: which by subduction I find to be 36.( for that is the remainder, 72. being subducted out of 108.) whereupon I conclude thus, that as the difference of the greater segment of the Transame, namely, 36. is unto the lesser segment, which is 72. so is the distance between my two stations, to the length propounded: and therfore the length propunded to be measured is 80. feet. For if 36. give 72. then 40. feet( which is the distance of the two stations) must needs yield 80. Thus haue you hitherto seen the three several ways how to measure the length of any thing propounded: It followeth now to instruct you in taking the height of any thing-propounded.  Sc. 
What call you the height of a thing?  Ma. 
The height of a thing, is the perpendicular drawn from the top thereof, unto the base whereon it standeth.  Sc. 
Then you regard not at all the crookedness of a thing.  Ma. 
No: I care not at all for the fashion thereof. For whether it lean forward or backward, to the right hand or to the left, I care not so that from the top thereof I may draw down a perpendicular line: as you see in the fourth figure.  Sc. 
Do you take all this line?  Ma. 
Your measure taketh no more then is from the level of your eye upward: and therfore this must be a general rule, that, if the thing propounded to be measured, do stand level with your feet, you must add unto the height found out, the height also of your own stature.  Sc. 
How many ways is the height of a thing measured?  Ma. 
three maner of ways, even as the length or distance was.  Sc. 
What must bee the third proportional number in the first two ways?  Ma. 
As in the measuring of lengths, the height assigned and given, was the third proportional number; so in the measuring of heights, the length assigned is the third number of the proportion:  Sc. 
give me the rules to direct me by.  Ma. 
The first rule is this: Your Transame making a right angle with the height to be measured: and your sight passing from the beginning thereof to the top of the height: as the partes of the Transame cut off by the Yard, are to the parts of the Yard cut off by the Transame, so is the length given unto the height.  Sc. 
Put case then the parts of the Transame were 60. and the partes of the Yard 36. and the length given 20. feet: the height according to the rule must be 12. feet.  Ma. 
It is so: But you must remember to add the height of your own stature: so that it shall be in all 16, feet, or 15. feet according as you shall please to allow for your own height.  Sc. 
Let me request this by the way: is there no rule for the measuring of depths?  Ma. 
It is all one with the measuring of heights. For the depth is nothing else but a rehearsed height. And therefore in the measuring of the depth of a thing, The Yard of your staff being parallel unto the side of the thing, whose depth you measure, and your sight passing from the top thereof: as the parts of the Transame cut off by the Yard, are to the parts of the Yard cut off by the Transame, so is the assigned length unto the depth of the thing.  Sc. 
I perceive your meaning. As for example: If the parts of the Transame be 5. and the partes of the Yard 13. and the diameter of the well( which is here in this example the assgned length) be 10. feet long, the depth must be 26. feet.  Ma. 
It is true, if you account from the top of your staff, and therefore that you may haue the just depth of the thing, you must take away from the aforesaid number as much as is above the thing measured: which if you suppose to be one foot in length, then is the well 25. foot deep, as appeareth in the fifth figure.  Sc. 
Thus much by the way concerning the measuring of any depth. What other rule haue you for the measuring of heights?  Ma. 
The first rule required that the Transame should be perpendicular unto the height propounded. The second requireth the Yard to be perpendicular: as in the sixth figure: so that it differeth from the other onely in the manner of holding the staff. The rule is this: The yard of your staff being perpendicular unto the thing measured as the parts of the yard are to the parts of the Transame, so is the assigned length unto the height propounded to be measured.  Sc. 
So that I may conclude thus. If the parts of the Yard be 60. and the parts of the Transame 60. and the assigned length be 250. feet: the height propounded must also be 250. feet.  Ma. 
Your conclusion is allowable: But I must put you in mind of this, to add the allowance of your stature, which if you suppose to be 4. feet, then is the whole height 254. feet: Now mark this one thing for your further learning.  Sc. 
What is that?  Ma. 
By this mean you may find out the several partes of any height propunded: as in the seventh figure you may find out how many feet are contained between the top and the nether side of the window: or generally between any parts else, or placing as many Vanes vpon the Transame, as you would measure several parts.  Sc. 
I must so place my Vanes, that from the end of the yard I may see each part propounded.  Ma. 
You say right, the rule then must be this: The Yard being perpendicular, as it was before unto the height propounded, as the parts of the yard cut off by the Transame are unto the distance of the Vanes, so is the whole height, unto the part thereof propounded.  Sc. 
Let me shield that I understand you, by propounding an example: I say, that if the partes of the Transame be 50. and the diffaunce of the Vanes be 20. partes: and the whole height of the thing measured be 37. feet, then the part propounded must be 14. feet, and 〈◇〉.  Ma. 
You understand it well. And here is yet another thing to be noted: that if you know the length of any one piece of the thing whose height you desire to know, it is sufficient to bring you to the knowledge of the whole height, as in the 8. figure.  Sc. 
What rule haue you for that to direct me in the work?  Ma. 
The Vanes of your staff must be placed as they were before, ●●●ely, in such sort that your sight passing from the end of the yard by the Vanes, you may see both the ends of the part whose length you know. The rule then is this: that as the distance of the two Vanes is unto the remnant of the Transam down unto the yard, so is the part known unto the remnant of the height propounded. So that if the distance of the Vanes be 20. parts, and the re●inant of the Transame from the nethermost Vane down ward be 30. parts: and the part of the height known be 14. feet, and ⅘ I conclude the remnant of the height to be 22. feet, and ⅕.  Sc. 
That standeth with reason, and may be proved by the example next going before this. For if the whole height were 37. feet, and the part propounded 14. feet, 〈…〉 that part being taken out of the whole, declareth the remnant to be 22 feet, and ⅕.  Ma. 
The former two rules measured the height of a thing at one station The third rule requireth a double ●●ation, as in the ninth figure. The rule is this: The Yard of your staff being perpendicular to the thing measured; as the difference of the two segments of the yard is to the distance between the two stations, so are the partes of the Transame cut off by the Yard to the height propounded.  Sc. 
What mean you by the difference of the two segments of the Yard?  Ma. 
You may easily know what that meaneth, by that which hath been taught you before, in measuring the diffance or length of a thing at two stations. Yet I will make it plain unto you here: When you make your first station, you 〈◇〉 the Transame must cut the yard in one place or other: also when you make your second station, the ●●●same must cut the Yard in another place, not the same which was before: that distance or parts of the Yard, contained bett●●me those 〈◇〉 several places, are called the different of the segnm●●s.  Sc. 
In this case I must 〈…〉 and down.  Ma. 
No but you must mo●e it only either 〈…〉 your sight.  Sc. 
When must it come toward my 〈…〉 it go farther from it?  Ma. 
That fulleth not according 〈…〉 If in 〈…〉 from the thing measured, your Transame must go farther from your fight: If you come nigher, your Transame also must come nigher your fight. And here I give you warning again, that you go forward and backward in a right line, directly upon the thing propounded.  Sc. 
Let me here also by example show that I understand your Rule. You say that as the difference between the two segments of the yard is unto the distance between the two stations, so are the partes of the Transame unto the height. Whereupon I conclude thus: that if the difference of the two segments be 23. and the distance of the two stations be 30. ●●●se, and the parts of the Transame cut off by the yard be 44. then the height must be 57. feet, and 9 / 23. as in the Figure.  Ma. 
Hitherto you haue learned how to measure the length and the height of things: now it followeth to measure the breadth.  Sc. 
give me leaure, I pray you, in this place to move three questions: and first what mean you by the breadth?  Ma. 
The breadth here to be measured, is no more, then the length of the right line, contained between the two ends of the thing propounded, without any consideration of the roundness or hollowness of the thing.  Sc. 
Secondly, how must I stand to hold my staff?  Ma. 
You must stand so, that your staff being applied unto your eye, it may be perpendicular unto the breadth propounded.  Sc. 
Last of all, when I purpose to measure the breadth of any thing, as of a wall, or such like, against which part of it must I stand? against the just midst of it? or against the one end? or else where I please, between the two ends? or without both the ends?  Ma. 
It is at your own choice.  Sc. 
In measuring the former dimensions, my sight did pass but by one end of the Transame, must it do so likewise in this?  Ma. 
That is according as you stand to take the measure. If you stand within the two ends of the thing propounded to be measured, your sight must pass by the two ends of the Transame. If you stand against the one end of the thing, or clean without it, your sight passeth but by one end of the Transame.  Sc. 
What mean you here by the ends of the Transame? are they not here also to be taken as they were before?  Ma. 
Yes: The one end of the Transame must always he that, where the partitions begin: the other end is that, upon which the Vane must stand, and by which the sight passeth. For many times it will so fall out that your sight cannot pass by both the ends of the wood, so that you shall be enforced to place the Vane in some one part or other of the Transame, that it may be a limit for your sight. And this is a general rule, that if you stand within the ends of the breadth propounded, the one end of your Transame must be on the one side of the yard, and the other on the other side.  Sc. 
But will the yard be just between them both?  Ma. 
No: Except your station be made accordingly. If you stand in the midst of the thing to be measured, then will the yard be just in the midst, between the ends of the Transame: if you stand more to the one end then to the other, the yard also will fall out in like manner, more toward the one end of the Transame, then toward the other.  Sc. 
How many ways are there to he used to measure the breadth by?  Ma. 
We may measure it two ways: either by the help of one station, or of two.  Sc. 
If I measure it by the help of one station, what must be known for the third proportional number?  Ma. 
The distance between you and the thing propounded.  Sc. 
Put case that it be hollow inward between the two ends thereof: or swell outwardly: to which part must I then measure?  Ma. 
If it be conuexe, or round outward, the best way to measure the breadth is by two stations: but if it be hollow inward, you must measure no further then from your feet to the right line, which runneth between the two ends of the thing propounded.  Sc. 
What rule is there for the measuring of a breadth at one station?  Ma. 
This. The Yard being perpendicular unto the breadth assigned, as the parts of the Yard cut off by the Transame are unto the partes of the Transame contained between the two ends, so is the distance between your feet and the thing measured, to the breadth thereof. As in the tenth figure.  Sc. 
I perceive it well: For there are here two proportional triangles cut in pieces with a line in the midst: Therefore as in the triangle A B C. the line B C. is the line A C. so is the line B F. in the greater triangle to the line F G. which is the breadth of the wall. This dependeth vpon that which went before. Now what is your rule for the measuring at two stations.  Ma. 
It is this: The Yard being perpendicular unto the thing measured, & your sight passing by the ends of the Transame( as it is required:) as the difference of the two segments of the yard is unto the distance between the two stations, so are the parts of the Transame between the two ends thereof, unto the breadth propounded: as it is in the 11. figure.  Sc. 
This also is very easy by reason of that which was taught before. So that I may conclude, that if the difference of the two segments in the yard be 30. parts: and the distance of my two stations be 40. feet: and the parts between the two ends of the Transame be 50. then must the breadth of the thing be 66. feet and ⅔. Haue you any other thing to be added?  Ma. 
No: But that I would haue you to practise this diligently, and I will hereafter further you in other things.  Ma. 
I thank you for it. Yet before I depart, I pray you let me ask you one question: You said before, that in measuring the breadth of any thing it is at my choice to stand where I will, either within the two ends of the thing to be measured, or against the one end thereof, or without both the ends, in what place I shall think most expedient. This last kind of measuring me thinketh is strange( as for the other I perceive well enough how their proportion will fall out) wherefore I pray you help me herein.  Ma. 
Set the question as you shall think it best for your own understanding.  Sc. 
Put case I were to take the breadth of a river, as in the 12. figure, unto whose brink I can not come any nigher then 40. feet, by reason of some marish grounds adjoining thereunto: what means shall I use to find the breadth thereof?  Sc. 
Put case I were to take the breadth of a river, as in the 12. figure, unto whose brink I can not come any nigher then 40. feet, by reason of some marish grounds adjoining thereunto: what means shall I use to find the breadth thereof?  Sc. 
But how must they stand in respect of the river?  Ma. 
indeed that is a special thing to be noted: They must stand so, that the right line imagined to come from the two marks, may make a right angle with the riuers side: otherwise you shall err in taking of your measure: Because that only is accounted the breadth of a thing, which maketh a right angle with the length.  Sc. 
having chosen out these two marks, what is then to be done?  Ma. 
You must set up another, which must stand also just in one right line with the two first marks, whose distance from the mark on this side the river, must either be given you, as being already certainly known: or else it must be found out by the first rule concerning the measuring of breadths.  Sc. 
Put case I either know it, or find it to be 40. feet.  Ma. 
You must choose out a convenient place, wherein you may make your station, & settle yourself about your work.  Sc. 
How must that place lye from the mark that was last set up?  Ma. 
It must lye from it so, that the line drawn from that mark unto the place of your standing, may make a right angle with the line drawn between the three afornamed marks.  Sc. 
Must I not know the just length between the place wherein I make my station, and the mark which I set up.  Ma. 
Yes: For it is the third proportional number.  Sc. 
Imagine that distance to be 60. feet.  Ma. 
Then your rule to find out the breadth is this: The Yard being perpendicular with the mark set up, and your sight passing from the head thereof by the end of the Transame unto the mark standing on the farther side of the river, as the parts of the Yard cut off by the Transame, are unto the partes of the Transame cut off by the yard: so is the distance between your station and the mark set up unto the distance between the said mark, and the mark standing upon the further side of the river.  Sc. 
But what is this to the question that I propounded? you make an answer concerning the distance of the two marks, whereas I moved a question of the breadth of the river.  Ma. 
Be not angry, I will satisfy you strait ways: first find out the distance of these two marks.  Sc. 
That can I easily do: For the parts of the yard being 30. and the parts of the Transame 36. and the distance of my station from the first mark 60. feet. The first mark must be distant from the third 72. feet.  Ma. 
Then what is the breadth of the river?  Sc. 
That must come from you, for I cannot make the conclusion.  Ma. 
Then mark this. You said the distance of the first mark from the third being on the farther side of the river is 72. feet: and the distance of the first mark from the second being on the hither side of the river, was granted to be 40. feet: then take 40. out of 72. and the remainder being 32. feet, declareth the breadth of the river.  Sc. 
I perceive now what a commodity it is to haue an instructor. For the thing which seemed unto me most strange, and altogether impertinent to my question, is by your means made most evident unto me, and greatly to the matter propounded. But must I take this course, whensoever I am driven to stand without the compass of the thing measured.  Ma. 
Yea, that you must: And sometimes also you shall be driven to the second rule, wherein two stations are required, which soever you use it cometh all unto one purpose, and will eastly afford you the breadth of a thing.  Sc. 
I can but thank you for your pains, and good will, in accepting me for your scholar.  Ma. 
And I likewise you, for making choice of me to be your master. My will is good to help whom I may: howsoever others may make more boast of their cunning.  
FINIS.