Mathematical Instruments
Suppl. Ch. III.

# The Description of another modern Quadrant of Mr Elton’s for taking Altitudes without an Horizon, either at Sea or Land.

This Instrument (Fig. 8.) consists of four principal Parts, viz. the Frame ABCDEF, the Index GH, a Label IK, and a Shield or Ray Plate dfg; and these consist of several Parts: the Frame has two Parts, the one a gradated Arch DE, of 30 Degrees, each Degree subdivided into 6 equal Parts; the other BC, a Chord of an Arch of 60 Degrees, divided into two equal Parts. At the Extremities, and in the Middle of which are three Holes, or Stops, a, b, c, for the Label. The Index GH turns, about the Centre of the Frame, through the whole Extent of the Arch, and has three Parts, a Nonius Plate n, Eye-Vane v, and Glass Tube t, as a Spirit Level; the Nonius Plate moves with the Index, and subdivides each of the small Divisions into ten equal Parts or Minutes; the Eye-Vane v, is to look through in a fore Observation, and the Glass Tube t is to shew by the Bubble of Air when the Index is horizontal; the Label IK moves about the Centre of the Frame, the whole Extent of the Chord BC of the Arch of 60 Degrees; having three fixed Stations thereon at 30 Degrees, 60 Degrees, and 90 Degrees, and contains two principal Parts, viz. a Lens l, and a Stool o, for a Lanthorn Q; the Lens is to form the Sun’s Image upon the Shield dfg, the Lanthorn is necessary in nocturnal Observations, the Shield is fixed in the Centre of the Frame, and has three Parts; an Azimuth Tube z, an Axis x, and an horizontal Tube t; or in backward Observations a ray Plate; the Hole in the Shield is to receive the Sun’s Image, the Azimuth Tube is to direct the Plane of the Instrument perpendicular to the Horizon, the horizontal Tube is to shew when the Label is level, the Axis is to cut the Objects in forward Observations.

### The Use of the Instrument, for either a backward or forward Observation.

If the Altitude does not exceed 30 Degrees, the Label must be placed at the Station on the Radius or longest Limb of the Quadrant. If the Altitude be between 30 and 60 Degrees, at the middle Station; and if the Altitude exceeds 60 Degrees, at the uppermost Station.

### To take the Sun’s Altitude by a back Observation.

In doing this, the Sight-Vane, or horizontal Tube, on the Shield is not used. Hold the Quadrant with both Hands so as to keep it as steady as possible, with the back Arch turned towards the Sun. When the Bubble of the Azimuth Tube is brought under the Hole in the Shield, cause the Sun’s Image to fall on the Hole in the Shield, so that it may rest in the Centre of the Sun’s Image; the Instant the Azimuth Tube and the Sun’s Image are thus regulated, see if the Bubble in the horizontal Tube on the Index (which ’till then is disregarded) leaves the open End of the Tube, or stops any where clear of the Ends of the Tube. If these happen at the same Time, the Altitude is then truly taken. But if the Bubble had remained in the enclosed End of the Tube, when the Azimuth Bubble and Sun’s Image were regulated, the Index must have been slid up; and if it staid in the open End, moved down ’till the horizontal Bubble on the Index quits the open End of the Tube, or stopt between the Ends, as was before observed; and then is the Quadrant set. In continuing the Observation for a Meridian Altitude, the Quadrant being set, as the Sun rises, the horizontal Bubble on the Index will not quit the open End of the Tube, or stop between the Ends, but hang there, or leave it after the Azimuth Bubble and Sun’s Image have been regulated, which will require the Index to be continually moved down in order to keep the Quadrant set; when the Sun is up, or on the Meridian, the Quadrant will remain set for some time; and on the Sun’s falling, the horizontal Bubble will have a reverse Tendency, inclining or running wholly to the enclosed End of the Tube.

### To take the Altitude of the Sun or Stars by a forward Observation.

In this Observation the Lens and Tube, on the Index are not used. Hold the Quadrant upright, and looking through the Eye-Vane direct the Axis, or upper End of the Shield, to the Sun or Star. If the Axis cuts the Sun or Star at the same lnstant that the Bubble on the horizontal Tube on the Shield quits the open End, the Altitude is then truely taken, and the Quadrant set. .But if it should leave the open End of the Tube before the Axis, or upper Edge of the Shield, cuts the Sun or Star, then the Eye-Vane, or the Index, must be slid down; and if it remains at the open End, or quits it when the Axis is above, the Sun or Star moved up until the Quadrant is set. In continuing the Observation for a meridian Altitude, as the Sun or Star rises, the Bubble in the horizontal Tube will always quit the open End of the Tube before the Axis cuts the Horizon; so that to keep the Quadrant lit, the Eye-Vane must on every such alteration be constantly moved down; while the Sun or Star is upon the Meridian, the Quadrant will remain set; and when the Sun or Star falls, the Bubble will act contrary to what it did in the rising, resting wholly in the open End of the Tube.

### To take the Sun’s Altitude by means of the Horizon.

Turn the back of the Arch towards the Sun, and cause the Sun’s Image to fall on the Hole in the Shield, at the same Time looking through the Eye-Vane, to cut the Horizon with the Axis.

Note, In taking the Altitude of the Stars, a small Light must be fixed in the Lanthorn; the less the better. It will be best in forward Observations of the Sun, to take the Altitude of the upper Limb, and then substract; and when the Sun is very clear, take his Altitude by a backward Observation, the forward way being chiefly intended for nocturnal Observations, and when the Sun is too much obscured to give any Shade or Image.

In the Philosophical Transactions, at Number 423, pag. 273, from whence the aforementioned Description and Use of this Quadrant is taken, you have an Account how near Altitudes of the Sun taken at Sea by this Instrument, in a Voyage to Maryland, agreed with the Altitudes of the Sun taken at the same Time by Davis’s Quadrant. Sometimes they differed only one Minute, sometimes 5′ or 6′, sometimes 16′, and once their greatest Difference was 21 Minutes. In the same Place, it is said, that Observations of the Altitudes of the fixed Scars taken by both the Instruments, and the Latitude found thereby, commonly differed about 4′ or 5′, and the greatest Difference once arose to 13′. Moreover, the Captain of the Vessel that went to Maryland declares, that he observed with his Quadrant of Mr Elton’s both by the Sun and Stars, in all the various Sorts of Weather he met with in his Voyage to and from Maryland, without regarding the Horizon, with as great Exactness as with Davis’s Quadrant when the Sun and Horizon were clear. Lastly, It is said that another Sea Captain computed the Latitude in Leghorn Road, and several of the Ports of Spain, from Observations by this Quadrant, exactly agreeing with the known Latitudes of those Places. He adds, that he made several Observations by the Instrument in his Passage home in hard Gales and a great Sea, and when it was so hazy that the common Quadrant was of no use for want of the Horizon.

Hence we may briefly observe upon this Instrument, that it is no better than Davis’s Quadrant, at least these two Captains thought so, or else they would not have used Davis’s as the Standard of Exactness, whereby to compare the others in their Voyages. At most it can only exceed Davis’s in hazy Weather, and Observations of the fixed Stars at Night, when the Horizon cannot be seen.