The English academy, or, A brief introduction to the seven liberal arts grammar, arithmetick, geometrie, musick, astronomie, rhetorick & logic : to which is added the necessary arts and mysteries of navigation, dyaling, surveying, mensuration, gauging & fortification, practically laid down in all their material points and particulars, highly approved to be known by the ingenious, and as such are desirous to profit, or render themselves accomplished : chiefly intended for the instruction of young scholars, who are acquainted with no other than their native language, but may also be very useful to other persons that have made some progress in the studies of the said arts / by John Newton.

As to Observation in taking Heights, &c. Sailing the Sundry ways, &c. And other useful matters worthy of note to Navigators, &c.

AMongst the many Undertakings, that redound to the Advantage of Man∣kind, Navigation is very consider∣able; for on it depends not only the Welfare of private Persons, but of Na∣tions and Kingdoms, as being Enriched and Improved in Knowledge by it: Wherefore it is highly necessary to speak something of it in this Treatise of Arts and Sciences, that may Instruct the Unexperienced, and, per∣haps, improve the knowledge of the Elder Practitioners.

In the Treatise of Astronomy, you find the names of the Stars, and many other things necessary to be taken notice of in Navigati∣on; for on that Art much of this depends, especially in taking the Suns height or Meri∣dian Altitude, and the Elevation or height

of the Pole, as being the Computation or Distance in Latitude from the Aequator, ei∣ther North or South, or any other Imagi∣ned Parralel, as we find East and West is the distance of Longitude, where ever the Meri∣dian is found, there must consequently be computed an equal distance on either side of it; so that the Meridian thus considered, the Rumb must be so likewise, for that leading from place to place, may be termed the di∣stance run upon such a point of the Compass. And to come nearer the taking of these di∣stances and heights are the principal things to be observed in this Art as to the Carry∣ing a Ship to any Country and Port, and knowing at any time where you are, and all these (according to the greatest Proficients) are more closely, or briefly comprized. 1. In the difference of the Latitude. 2. In the difference of the Longitude. 3. The Rumbs. 4. The distance run upon the Rumb.

Now if two of these be known or given, the two that remain may be easily found, the first by Observation, and the last by Tri∣gonometry, or Arithmetical Calculation, &c. And in further consideration of these things, to find the Latitude or Elevation of the Pole, you must observe the Meridian Altitude ei∣ther of the Sun or Stars, and though there are many ways described to do this, yet what ensues is found the most plain and easy.

Do it by the Astrolabe or Quadrant in this

manner, viz. by what we call backward ob∣servation, and not troubling your Eyes with looking through the sights, permit the Sun to shine through the sight, that is next to the Center, so ordering it, that the beam may fall directly upon the hole of the other sight, by which means the thread will fall upon the right Altitude in the Quadrant, or the Index in the Astrolabe will in the same man∣ner divide the degrees of Altitude.

If the Sun shine not, and you are desirous to find its Meridian Altitude, you may do it by informing your self of the declination and Latitude; And upon this observation, if you find the declination North, then add to the Complement of the Latitude, which you will ever find to be the same with the height of the Aequinoctial, but on the con∣trary, if it be a South declination, then sub∣tract from the Complement of the Latitude, and that will at any time give you the Meri∣dian Altitude. As put the case we find in any place the Elevation of the Pole, that is the Latitude to be 52 degrees, the comple∣ment thereof to 90 degrees, is 38 degrees, which likewise is found to be the height of the Aequinoctial, and then it being granted, that on May 2. the Sun being 20 degrees, 24 minutes of Taurus, his declination North∣ward is 117 degrees, 56' 21 s. which, when you add to 38, brings the Suns Meridian Al∣titude to be 55 degrees, 56 minutes, and

12 seconds, but if this be required to be found when the Sun comes to the Aequino∣ctial, either on the 13 of September, or the 11 of March, then the height of the stars or sun, when they are upon the Meridian, will shew the true Latitude if subtracted from 90 degrees, but at other times you must find out their declinations, and if it happen Nor∣therly, subtract it from the Altitude, but if Southerly, you must add it to the Altitude, by which means you will find the height of the Aequinoctial above the Horizon, and Consequently subtracted from 90 degrees, will give you the true Latitude of the place where you make your Observation.

If by the Globe you are desirous to find the Elevation of the Pole, take the Suns Me∣ridian Altitude, bringing the Suns place in the Ecliptick, or the Stars to the Brazen Me∣ridian, and so move that Meridian with the Globe through the notches it stands in, till you find the stars, or the suns places Eleva∣ted as many degrees above the Horizon, as their Meridian Altitude is; and whilst the Globe stands in this position, you may be confident the Pole will be Elevated to a true Latitude of the Place.

As suppose you find the Suns place in the beginning of Cancer, which may be the 12 of June, and the Meridian Altitude of the sun is 62 degrees from the place where you are to make your observation, then bring

the first degree of the sign Cancer to the Me∣ridian, and Elevate the same 62 degrees a∣bove the Horizon, and you will find the Pole Elevated 51 degrees and 30 minutes.

The next thing in Navigation to be con∣sidered, is the finding the Longitude, which could it be brought to perfection, sailing would be far more easy than it is, and dis∣coverys of yet unknown Countrys, Rich perhaps as either Indias; but indeed, though many have attempted it, and gone very far, they have never brought to perfection, how∣ever, for the light of the Navigator, we will consider some things herein.

Suppose the Moon to be Eclipsed, observe how much sooner it begins at a place of known Longitude, for which search the E∣phemerides, then at the place where you stand, and observing your Latitude by the stars, as has been directed, the true hour of the night may be found; which done, observe the difference of time of the Moons beginning to be Eclipsed, or its middle or endings, at the place where you make your observation, which spaces convert into degrees and mi∣nutes, which added or subtracted from the hour of the beginning, middle or end of this Eclips at a place of known Longitude, these degrees and minutes in their difference be∣tween the hour at one place, and the hour at an other, added or subtracted from the de∣grees and minutes of the known Longitude,

you will find them give the required Longi∣tude.

If the Moon be not Eclipsed, which E∣clips cannot be expected upon every occa∣sion, then you may observe it by the Sun and Moons motion, as thus; suppose, and it is granted, that the Moon is slower in moti∣on than the Sun 48 minutes, in 24 hours, or 360 degrees, then by the help of Mathema∣tical Instruments, find the true Meridian in any place, suppose the West-Indias, &c. you must also find the hour of the Moons com∣ing to that Meridian by the Ephemerides, or other helps; and this being calculated for London, you find by those helps, that on such a day the Moon comes to the Meridian, at four in the Afternoon, and you being the same day in the Indias aforesaid, you find her come to the Meridian 10 minutes past 4, whereupon consider by the Rule of Propor∣tion, that the Sun and Moons difference in motion, being 48 minutes in 36 degrees, what will it come to in ten minutes, or if 48 gives 360, consider what ten gives, and the fourth proportional number will be 75d. and so much is the distance of that place in India from London, and the longitude of London being subtracted from that number 20 de∣grees, and 55 Remainder again subtracted from 360, what remains produces the lon∣gitude to be 305. Some other ways are laid down to prove a knowledge of the lon∣gitude,

but the whole matter being in a man∣ner in the dark, these may suffice for an Ex∣periment.

But in plain or circular Sailing, the Com∣pass is very much heeded, but sometimes there may be mistakes by the variation of the Needle, which you may Rectifie by the Globe, in this manner; let the Suns place be brought to the East side of the Horizon, and observe the Circle of Winds, and then a∣gainst the Suns place you have the point of the Compass, whereon it riseth, and so pro∣ceed to take notice upon what point it rises or sets, observe then the difference happen∣ing by the Globe, and by the Compass, and if there be any, that is the Variation, for which Variation, allowing that the Needle will ever shew the Rumb, which is the true point of the Compass, as to the steering the Ship.

If you would know how much way your Ship makes in such and such spaces of time, this you may observe by the Logline, or Minute Glass, and by the first so many knots as she runs in half a minute, so many Miles is she counted to Sail in an hour, or it may be done by hanging up a Bullet in a string, which will count the Minutes by its swing∣ing, for if the string be proportioned to 38½ Inches, it will swing about 60 times in a mi∣nute, but if longer not so many, and there∣fore it is left to your discretion, to propor∣tion

it as you make observation by the half minute glass, instead of which, this (for necessity) may serve turn.

If you would find the Suns Amplitude, and thereby the variation of the Compass, observe, That as the Proportion of the Co∣sine of the Latitude is to the Radius, the same you will find the sine of the declinati∣on to that of the Amplitude, as, It▪ being granted the Latitude of 31 degrees, 23 mi∣nutes, its Cosine, or Complement, is 38 de∣grees, 28 minutes, and the declination of the Sun 15 degrees, 10 minutes; the Am∣plitude then will be found 24 degrees, 52 minutes North, by reason the declination is so. As for the Circumference of the Com∣pass divided into 360 degrees, observe when the Sun rises and sets, how many de∣grees it is from the direct point of the Am∣plitude so much you will find the Needle va∣ry in the place.

As for this kind of Navigation it is vul∣garly proposed in three manner of ways, or Methods, especially, as relating to private Seamen as plain Sailing, Mereators way or Instruction of Sailing, and Sailing by an Arch or great Circle, called Circular Sail∣ing. The plain way of sailing is by a plain Chart, which is the most substantial, and that on which the other are grounded, and to those that sail near the Aequinoctial, they have little or no occasion for any other

way, as having their degrees of Latitude and Longitude equal, each degree divided in to 60 minutes, and each minute put for a Mile, yet somewhat exceed the English mea∣sured miles, as containing about 6000 feet; but if you are to come far from the Aequinoctial, then though you may keep your Lati∣tude in plain sailing, yet you will be at a loss for your Longitude, and therefore to be better informed, consider that as the Radius or whole sine of 90 degrees, is to 60 Miles, so you will find the Cosine of the latitude, is to the Miles contained in one degree of longitude in that latitude, so that in the la∣titude of 60 degrees, 30 Miles make a de∣gree, as sine 90 degrees to 60 Miles 10000, so Cosine 60 degrees to 30 Miles 5000. and by this rule we find, that if your departure from the Meridian was 280 Miles, and they being divided by 60, reduced into degrees and minutes of longitude under the Aequino∣ctial, it yields 4 degrees and 4 minutes, but if these 280 Miles happen to be East or west, or your departure from the Meridian should be in the latitude of 60 degrees, where 30 Miles make a degree of longitude, then divide the 280 Miles by 30, and you will find it yields 9 degrees 10/30, or one third, which is 20 minutes for the difference of longitude in that latitude. To sail by Merca∣tors Chart, is little other than coming to a knowledge of the true latitudes, Meridians,

and Elevations of the Poles, Miles, minutes, &c. as when it so fall out that one place is under the Aequinoctial, and the other near∣er one of the Poles, then we find, the Meri∣dional minutes, answerable to that place, which hath latitude, is to be Accounted for the Meridional difference of latitude, or that latitude inlarged.

Again, suppose both places are towards one of the Poles, thereupon subtract the Meridional minutes that are found answe∣ring to the lesser latitude, and the remainer will be found to be the Meridional minutes required.

Again, if we find one place to have North latitude, and the other be in South latitude, then add the Meridional minutes, apper∣taining to either place together, and you will find the sum thereof to be the Meridi∣onal minutes required, &c.

Circular sailing is held to be a very good way of sailing, as the best, shewing the nea∣rest way and distances between any two places, yet carrys with it some little diffi∣culty, so that the Seamen seldom keep to their course near this Arch, wherefore lea∣ving you to consider of what has been said, I proceed to other useful matters.