# The finding of the amount of variation

##### February 20, 2024 9 minutes • 1881 words

## Table of contents

## How great is the arc of the Horizon from its arctick or antarctick intersection of the meridian, to the point respective of the magnetick needle?

Virtually the true meridian is the chief foundation of the whole matter: when that is accurately known, it will be easy by a mariners’ compass (if its construction and the mode of attachment of the magnetick iron works are known) or by some other larger horizontal versorium to exhibit the arc of variation on the Horizon.

By means of a sufficiently large nautical variation compass (two equal altitudes of the sun being observed before and after midday), the variation becomes known from the shadow; the altitude of the sun is observed either by a staff or by a rather large quadrant.

On land the variation is found in another way which is easier, and because of the larger size of the instrument, more accurate.

Let a thick squared board be made of some suitable wood, the surface of which is two feet in length and sixteen inches in width: describe upon it some semicircles as in the following figure, only more in number.

In the centre let a brass style be reared perpendicularly: let there be also a movable pointer reaching from the centre to the outmost semicircle, and a magnetick versorium in a cavity covered over with glass: then let the board be exactly adjusted to the level of the Horizon by the plane instrument with its perpendicular; and turn the lily of the instrument toward the north, so that the versorium may rest truly over the middle line of the cavity, which looks toward the point of variation on on the Horizon.

Then at some convenient hour in the morning (eight or nine for instance) observe the apex of the shadow thrown by the style when it reaches the nearest semicircle and mark the place of the apex of this shadow with chalk or ink: then bring round the movable index to that mark, and observe the degree on the Horizon numbered from the lily, which the index shows.

In the afternoon see when the end of the shadow shall again reach the periphery of the same semicircle, and, bringing the index to the apex of the shadow, seek for the degree on the other side of the lily. From the difference of the degrees becomes known Instrument to find variation{172}the variation; the less being taken from the greater, half the remainder is the arc of variation.

The variation is sought by many other instruments and methods in conjunction with a convenient mariners’ compass; also by a globe, by numbers, and by the ratios of triangles and sines, when the latitude is known and one observation is made of the sun’s altitude: but those ways and methods are of less use, for it is superfluous to try to find in winding and roundabout ways what can be more readily and as accurately found in a shorter one.

For the whole art is in the proper use of the instruments by which the sun’s place is expeditiously and quickly taken (since it does not remain stationary, but moves on): for either the hand trembles or the sight is dim, or the instrument makes an error. Besides, to observe the altitude on both sides of the meridian is just as expeditious as to observe on one side only and at the same time to find the elevation of the pole.

He who can take one altitude by the instrument can also take another; but if the one altitude be uncertain, then all the labour with the globe, numbers, sines and triangles is lost; nevertheless those exercises of ingenious mathematicians are to be commended. It is easy for anyone, if he stand on land, to learn the variation by accurate observations and suitable instruments, especially in a nearly upright sphere; but on the sea, on account of the motion and the restlessness of the waters, exact experiments in degrees and minutes cannot be made: and with the usual instruments scarcely within the third or even the halt of a rumbe, especially in a higher latitude; hence so many false and bad records of the observations of navigators. We have, however, taken care for the finding of the deviation by a sufficiently convenient and ready instrument, by means of the rising of certain stars, by the rising or setting of the sun, and in northern regions by the Pole Star: for the variation is learned with greater certainty even by the skilful with an instrument which is at once simple and less sensitive to the waves of the sea. Its construction is as follows.

[228]Let an instrument be made of the form of a true and meridional mariners’ compass of at least one foot in diameter (with a versorium which is either nude or provided with a cardboard circle): let the limb be divided into four quadrants, and each quadrant into 90 degrees. The movable compass-box (as is usual in the nautical instrument) is to be balanced below by a heavy weight of sixteen pounds. On the margin of the suspended compass-box, where opposite quadrants begin, let a half-ring rising in an angular frame in the middle be raised (with the feet of the half-ring fixed on either side in holes in the margin) so that the top of the frame may be perpendicular to the plane of the compass; on its top let a rule sixteen digits in length be fastened at its middle on a joint like a balance beam, so that it may move, as it were, about a central axis. At the ends of the rule there are small plates with holes, {173}Another instrument to find variation{174}through which we can observe the sun or stars.

The variation is best observed and expeditiously by this instrument at the equinoxes by the rising or setting sun. But even when the sun is in other parts of the zodiack, the deviation becomes known when we have the altitude of the pole: that being known, one can learn the amplitude on the Horizon and the distance from the true east both of the sun and of the following fixed stars by means of a globe, or tables, or an instrument.

Then the variation readily becomes known by counting from the true east the degrees and minutes of the amplitude at rising. Observe the preceding star of the three in the Belt of Orion as soon as it appears on the horizon; direct the instrument toward it and observe the versorium, for since the star has its rising in the true east about one degree toward the south, it can be seen how much the versorium is distant from the meridian, account being taken of that one degree.

You will also be able to observe the arctick pole star when it is on the meridian, or at its greatest distance from the meridian of about three degrees (the pole star is distant 2 deg. 55 min. from the pole, according to the observations of Tycho Brahe), and by the instrument you will learn the variation (if the star be not on the meridian) by adding or subtracting, secundum artem, the proper reduction [prostaphæresis][229] of the star’s distance from the meridian. You will find when the pole star is on the meridian by knowing the sun’s place and the hour of the night: for this a practised observer will easily perceive without great error by the visible inclination of the constellation: for we do not take notice of a few minutes, as do some who, when they toil to track the minutes of degrees at sea, are in error by a nearly whole rumbe.

A practised observer will, in the rising of sun or stars, allow something for refraction, so that he may be able to use a more exact calculation.

Bright and conspicuous stars[230] which are not far distant from the equator which it will be useful to observe at their rising and setting: the amplitude at the Horizon on rising being known from the altitude of the pole and from the declination of the stars, by means of a globe, or tables, or an instrument whence the variation is perceived by technical calculation. {175}

Right Ascension Declination Oculus Tauri 62° 55’ 15° 53’ N Sinister humerus Orionis 72° 24’ 4° 5’ N Dexter humerus Orionis 83° 30’ 6° 19’ N Præcedens in cingulo Orionis 77° 46’ 1° 16’ S Canis major 97° 10’ 15° 55’ S Canis minor 109° 41’ 5° 55’ N Lucida Hydræ 137° 10’ 5° 3’ S Caput Geminorum australe 110° 21’ 28° 30’ N Caput boreale 107° 4’ 32° 10’ N Cor Leonis 146° 8’ 13° 47’ N Cauda Leonis 171° 38’ 16° 30’ N Spica Virginis 195° 44’ 8° 34’ S Arcturus 29° 13’ 21° 54’ N Cor Aquilæ 291° 56’ 7° 35’ N An instrument for finding the amplitude at rising on the horizon.

Describe the circumference of a circle and let it be divided into quadrants by two diameters intersecting each other at right angles at its centre. One of these will represent the æquinoctial circle, the other the axis of the world.

Let each of these quadrants be divided (in the accustomed way) into 90 degrees; on every fifth or tenth of which at each end of each diameter and on each side let marks (showing the numbers) be inscribed on the two limbs or margins made for that purpose outside the circumference.

Then from each degree straight lines are drawn parallel to the æquator. You will then prepare a rule or alhidade equal to the diameter of that circle and divided throughout into the same parts into which the diameter of the circle representing the axis of the world is divided.

Let there be left a small appendage attached to the middle of the rule, by which the middle of the fiducial line itself of the rule may be connected with the centre of the circle: but to every fifth or tenth part of that rule let numbers be attached proceeding from the centre toward each side.

This circle represents the plane of the meridian; its centre the actual point of east or west, i.e., the common intersection of the horizon and æquator; all those lines æquidistant from the æquator denote the parallels of the sun and stars; the fiducial line of the rule or alhidade represents the horizon; and its parts signify the degrees of the horizon, beginning from the point of setting or of rising.{176}

Instrument for finding the amplitude at rising on the horizon. Therefore if the fiducial line of the rule be applied to the given latitude of the place reckoned from either end of that diameter which represents the axis of the world; and if further the given declination of the sun or of some star from the æquator (less than the complement of the latitude of the place) be found on the limb of the instrument; then the intersection of the parallel drawn from that point of the declination with the horizon, or with the fiducial line of the rule or alhidade, will indicate for the given latitude of the place the amplitude at rising of the given star or the sun.

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