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A55065 The catholique planisphaer which Mr. Blagrave calleth the mathematical jewel briefly and plainly discribed in five books : the first shewing the making of the instrument, the rest shewing the manifold vse of it, 1. for representing several projections of the sphere, 2. for resolving all problemes of the sphere, astronomical, astrological, and geographical, 4. for making all sorts of dials both without doors and within upon any walls, cielings, or floores, be they never so irregular, where-so-ever the direct or reflected beams of the sun may come : all which are to be done by this instrument with wonderous ease and delight : a treatise very usefull for marriners and for all ingenious men who love the arts mathematical / by John Palmer ... ; hereunto is added a brief description of the cros-staf and a catalogue of eclipses observed by the same I.P. Palmer, John, 1612-1679. 1658 (1658) Wing P248; ESTC R11098 148,140 211

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Plumb-line cuts 10 degrees from B towards C I say then is the Sun 5 degrees high and 30 degrees more in all 35 degrees in like manner you may place the Sight at any other number of degrees from D toward A as you shall find most convenient for the present Altitude remembring always that how many degrees soever you remove the Sight half so many are to be added to the Altitude found But if your Reet happen to run so far under the Limb that you cannot make a center-hole for the Plumbet through the Limb and Mater without hindring the Reets motion then may you have a small plate of sheet brass in fashion of an Arm or Tongue in the point whereof you shall have a Center-hole drilled and this plate shall be so joyned with a sluce or screw about the Limb near A that the Center-hole made in this plate may lie close to the point where the Center should have been boared in the Limb in the line A B and thus you may put it on and take it off at pleasure that it hinder not the motion of the Reet or Label Of the fashion of the Sights see more Booke 4.2 CHAP. XI Of the perpetual Calender on the back-side ON the back-side of your Planisphear you may set the Calender following which consisteth of three Tables gathered round The longest would be set outtermost The first is the Table of the Cycle of the Sun that is of the Sundays Letter This is here placed in the middle It is a Cycle of 28. years in which time the Dominical Letter runs all his changes caused by the one odd day above 52 weeks in every Common year and two odd days which run over the even weeks in the Leap years To find the beginning of this Cycle add to the year of our Lord 9. because the first year of our Lord as wee commonly acount was the 10 of this Cycle and divide the sum by 28. the remainder is the year of the Cycle running and if nothing remain then it is the 28. or last year So you shall find that the Cycle now running shall end with the Julian year 1671 as in the Table and shall begin again with the year of our Lord 1672. Thus may you renew the Table when it is expired or make this very Table serve you for ever Example Enter this Table with the year of our Lord 1656. now running and you shaall find over against this year in the next space inwards 13. shewing you that it is the 13 year of the Suns Cycle so shall the 28 year forward viz. 1684 be again the 13th year of the Cycle next comming In the next space within you have the Dominical Letters F and E because it is Leap year F shall be the Dominical Letter till you come past the Intercalary day which is the day following the 24th of February and for the rest of this year the Dominical Letter shall be E for the Letters always change backwards also you shall note here that the day inserted in every 4th year is not February 29 but February 25. for February 24. being 6 Cal. Martij is repeated again in the Leap year and they write again February 25.6 Cal. Martij and the 25th of February in the Leap year is marked with the same letter F wherewith the 24th of February hapneth always to be marked Hence the Leap year is called Annus Bissextilis and note that by the Eclesiasticall Law S. Matthias day which is February 24th in common years in the Bissextile years is to be observed on February 25. Nevertheless in our Secular Law not the 24th and 25th of February but the 28th and 29th in the Leap year are ordained to be one day in the account of Law as by Statutum de Anno Bissextili made in 21 year Henry 3. may appear The second Table is of the Cycle of the Moon consisting of the Prime or Golden Number and the Epact This Table contains 19 years which is the Annus Metonicus in which space of time Meton an Astronomer about 430 years before Christ observed the Moon to finish all her variations So that every 19 year the mean conjunctions or changes should happen upon the same days of the moneth that they did happen upon 19 years before onely an hour and half sooner Yet beeause every 19 years contain not the same number of Leap years but sometime there come five Leap years in 19 years and sometimes but four therefore there may happen in this Period of Meton an error of an whole day besides the hour and half above mentioned For remedy whereof Calippus about the 330 year before Christ devised to quadruple this period of Meton making Period●s Calippica of 76 years which contains just 19 quaternions of years so containing always the same number of Leap years and days This period is therefore more perfect then Metons for after this period of 76 years the Moon runneth over the same course for her conjunctions and oppositions changing in the same year of the period always upon the same day of the moneth save onely that shee changeth sooner by six hours in the latter period then in the former But the Church still retaineth the period of Meton called the Prime or Golden number because it used to be set in Golden letters in the Kalender in a certain artificiall order throughout every moneth to guide you to the day of the Moons Priming or Changing so may you find it in red letters thus Set to the Kalender printed in large folio with the Book of common Prayer in the time of the late Queen Elizabeth To find the year of the Prime add to the year of our Lord 1 and divide the sum by 19. the remainder is the year of the Prime or if nothing remain it is the 19th or last year Thus you may find the present year 1656 to be the fourth year of the Prime and so you find it in the Table The Cycle or Period now running ends with 1671. and begins again with the year following The Epact or Concurrent is set against the Prime in the next space inwards and finisheth his Cycle in the same time It was devised to find more readily the day of the change and age of the Moon The way to find it is this Multiply the Golden number serving for your year by 11 and divide the product by 30 the residue is the Epact for your year Or having the Epact known for any year you may make it from year to year by adding 11 to the Epact of the year foregoing and casting away 30 when the sum exceeds 30. The reason whereof is that the Moon changeth 12 times in 354. days that is 11 days before the Sun hath gone his round for which cause the changes must needs happen every year 11 days sooner Observe here that the Prime changeth every year the first day of January the Epact not till the first of March The Dominical letter changeth upon the
first of January going one letter backward yearly and in every Leap year it changeth again on the Lords day next after February 24. The reason whereof is this The Calender is marked throughout with the letters of the week A B C D E F G and the same day of the year is always marked with the same letter now if the year contained even weeks then would the Dominical letter be always one and the same but because a common year contains 52 weeks and one day therefore the last day of the year must be marked with A as the first was the first day of the year following again is marked with A now put case the last of December marked A be Sunday in the year 1654. the day following viz January 1 is Munday and yet marked A and the first Sunday in 1655 must needs fall on January 7 marked with G and so G became Dominical letter for 1655. as A was for 1654. and as those 2 days marked with the same letter A coming together at every years end cause a change of the Dominical letter so in the Leap year the Intercalary day February the 25 being marked with F always as the 24th is the coming together of those two dayes marked with one letter causeth a second change of the Dominical letter for that year by like reason The third Table is a Table to find Easter for ever This is placed outmost because it is the longest It was very falsly ordered in M. Blagraves book and so it is in Grostons Tables from whence I suppose he transcribed it I have set it right and straight and taken what care I could that the Printer or Graver do not put the ranks into the same disorder in which I found them both in Blagrave and in Grostons Tables printed 8 years before him CHAP. XII Some cautions to be Observed in the making of the Instrument THough I have taught the making of the Mater first as being the base and principal part of the Instrument yet I shall advise you first to draw and cut out the Reet and fit the Label to it leaving it sufficient length to reach to the out-side of the Mater And then having your Ring ready fitted to screw on to the Mater you shall drill the centers of the Mater Reet and Label with the same drill and fasten them together with a Center-pin well fitted to the bore this Center-pin must not be too big let it be square at the head to stick in the backside of the Mater that it turn not and let the other end have a male screw upon which you shall turn a female screw to draw the plates together so that they be neither too loose nor stick too hard Then take a great needle or such a round point of hardned steel and bearing it up into some corner of the Reet close to the inside of his Limb turn about both Reet and Needle upon the Mater so that the Needle may trace out the great Meridian of the Mater and so the principall Circles of the Mater and Reet shall be sure to be Concentrique and to argree in all postures of the Reet whereas if you draw the Meridian of the Mater before you have bored the Center and fitted on the Reet you shall hardly happen to bore so true but you shall find the Circles to be a little Eccentrique and interfering one with another And to avoid the like Eccentricity in the Circles of the Ring it were best to have a sorry Beam Compass made onely for this purpose and fitted to your Center pin to draw them by yet if those be drawn from the Center of the Mater unbored there will be no perceiveable error if you devide them from the Limb of the Reet by the Label when all is pinned together These things done quarter the Meridian of the Mater with two cross Diameters and divide them as is above directed remembring to apply your Reet to the Mater often to see how the divisions of the Diameter agree and how the Meridians and Parallels which you are drawing on the Mater agree with the Azimuths and Almicanters of the Reet And thus by comparing your plates often and examining the lineaments of the one by the other as you draw them you shall avoid many slips and mistakes and proceed in your work with more confidence and contentment The second Book Of the several Projections of the SPHEAR which are represented by this PLANISPHEAR The Preface THe Sphear may be Projected fitly upon the Plain of any great Circle but the Projection will be of little use for resolving Questions in Astronomie unless it be made upon one of these foure the Meridian the Equator the Azimuth of the Nonagesimus gradus or the Horizon This Planisphear is fitted therefore to represent all those four Projections and especially the two former CHAP. I. Of the Planisphear in the Meridional Projection representing the Eastern or Western Hemisphears And of his three Modes or postures WHat M. Blagrave Book 2. Chap 15.16 calleth the first and second distinction of the Jewel I call the first and second Meridional and Equinoctial Projection of the Planisphear for which change of termes I hope the Judicious Reader will not blame me The Meridional Projection is the Eastern or Western Hemisphear projected upon the plain of the Meridian of your place which is the great and chief Meridian in every Country passing through the Zenith and Nadir of the place as well as through the Poles of the World The eye in this Projection is supposed to be placed in the East or West point of the Horizon The lineaments which belong to this Projection are the innermost Scale of the Ring and all the lineaments of the Mater and Reet except only the Zodiack of the Reet and the Stars Here the outmost Circle both of the Mater and Reet represents the great Meridian of your place and the Scale upon the inside of the Ring divided into 360 degrees serveth to divide the said Meridian for the Label laid upon any degree of the Scale of the Ring cutteth the same degree in the Meridian Circle because it is concentrick thereto This Meridian also standeth for Colurus Solstitiorum so they call that Meridian which passeth through the beginning of Cancer and Capricorn for though all the Meridians in 24. hours space do successively come into the Meridian of your place which is the Noon Circle passing over your head North and South and the Sphear may be divided into Eastern and Western Hemisphear by any of these Meridians when they become Vertical yet the Sphear is then in the best posture to be divided for our purpose into East and West when Cancer is Southing Capricorn at midnight and ♎ 0 rising full East and ♈ 0 setting full West In this Meridian at A or Oriens is the North Pole and the South Pole at B or Occidens for the words Oriens and Occidens are there placed to serve the Equinoctial