# EQUATORIAL

, *Universal,* or Portable OBSERVATORY,
is an instrument intended to answer a
number of useful purposes in practical astronomy, independent
of any particular observatory. It may be
employed in any steady room or place, and it performs
most of the useful problems in the science of astronomy.
The following is the description of one lately invented,
and named the *Universal Equatorial.*

The principal parts of this instrument (sig. 2, plate viii.) are, 1st, The azimuth or horizontal circle A, which represents the horizon of the place, and moves on a long axis B, called the vertical axis. 2d, The Equatorial or hour-circle C, representing the Equator, placed at right angles to the polar axis D, or the axis of the earth, upon which it moves. 3d, The semicircle of declination E, on which the telescope is placed, and moving on the axis of declination, or the axis of motion of the line of collimation F. Which circles are measured and divided as in the following Table:

Measures of the several circles and divisions on them. | Radius Inches | Limb divided to | Non. of 3.0 gives seconds | Divid. on limb into pts.of Inc. | Divid. by Non. into pts.of Inc. | |

Azimuth or horizontal circle | } | 5.1 | 15′ | 30″ | 45th | 1350th |

Equatorial or hour circle | } | 5.1 | 15′, or 1 m. in time | 30″ | ||

2″ | 45th | 1350th | ||||

Vertical semicircle for declination or latitude | } | 5.5 | 15′ | 30″ | 42d | 1260th |

4th, The telescope, which is an achromatic refractor with a triple object-glass, whose focal distance is 17 inches, and its aperture 2.45 inc., and it is furnished with 6 different eye-tubes; so that its magnifying powers extend from 44 to 168. The telescope in this Equatorial may be brought parallel to the polar axis, as in the figure, so as to point to the pole-star in any part of its diurnal revolution; and thus it has been observed near noon, when the sun has shone very bright. 5th, The apparatus for correcting the error in altitude occasioned by refraction, which is applied to the eye-end of the telescope, and consists of a slide G moving in a groove or dove-tail, and carrying the several eye-tubes of the telescope, on which slide there is an index corresponding to five small divisions engraved on the dove-tail; a very small circle, called the refraction circle H, moveable by a finger-serew at the extremity of the eye-end of the telescope; which circle is divided into half minutes, one whole revolution of it being equal to 3′ 18″, and by its motion it raises the centre of the cross-hairs on a circle of altitude; and also a quadrant I of 1 1/2 inc. radius, with divisions on each side, one expressing the degree of altitude of the object viewed, and the other expressing the minutes and seconds of error occasioned by refraction, corresponding to that degree of altitude. To this quadrant is joined a small round level K, which is adjusted partly by the pinion that turns the whole of this apparatus, and partly by the index of the quadrant; for which purpose the refraction circle is set to the same minute &c, which the index points to on the limb of the quadrant; and if the minute &c, given by the quadrant, exceed the 3′ 18″ contained in one entire revolution of the refraction circle, this must be set to the excess above one or more of its entire revolutions; then the centre of the cross-hairs will appear to be raised on a circle of altitude to the additional height which the error of refraction will occasion at that altitude.

The principal adjustment in this instrument, is that of making the line of collimation to describe a portion of an hour circle in the heavens: in order to which, the azimuth circle must be truly level; the line of collimation, or some corresponding line represented by the small brass rod M parallel to it, must be perpendicular to the axis of its own proper motion; and this last axis must be perpendicular to the polar axis. On the brass rod M there is occasionally placed a hanging level N, the use of which will appear in the following adjustments:

The azimuth circle may be made level by turning the instrument till one of the levels be parallel to an imaginary line joining two of the feet screws; then adjust that level with these two feet screws; turn the circle 180°, or half round; and if the bubble be not then right, correct half the error by the screw belonging to the level, and the other half error by the two foot screws, repeating this operation till the bubble come right; then turn the circle 90° from the two former positions, and set the bubble right, if it be wrong, by the foot screw at the end of the level; when this is done, adjust the other level by its own screw, and the azimuth circle will be truly level. The hanging level must then be fixed to the brass rod by two hooks of equal length, and made truly parallel to it: for this purpose, make the polar axis perpendicular or nearly perpendicular to the horizon; then adjust the level by the pinion of the declination semicircle: reverse the level, and if it be wrong, correct half the error by a small steel screw that lies under one end of the level, and the other half error by the pinion of the declinationsemicircle, repeating the operation till the bubble be right in both positions. To make the brass rod, on which the level is suspended, at right angles to the axis of motion of the telescope, or line of collimation, make the polar axis horizontal, or nearly so; set the declination semicircle to 0°, and turn the hour-circle till the bubble come right; then turn the declination- | circle to 90°; adjust the bubble by raising or depressing the polar axis (first by hand till it be nearly right, afterwards tighten with an ivory key the socket which runs on the arch with the polar axis, and then apply the same ivory key to the adjusting screw at the end of the said arch till the bubble come quite right); then turn the declination-circle to the opposite 90°; if the level be not then right, correct half the error by the aforesaid adjusting screw at the end of the arch, and the other half error by the two screws that raise or depress the end of the brass rod. The polar axis remaining nearly horizontal as before, and the declinationsemicircle at 0°, adjust the bubble by the hour-circle; then turn the declination-semicircle to 90°, and adjust the bubble by raising or depressing the polar axis; then turn the hour-circle 12 hours; and if the bubble be wrong, correct half the error by the polar axis, and the other half error by the two pair of capstan screws at the feet of the two supports on one side of the axis of motion of the telescope; and thus this axis will be at right angles to the polar axis. The next adjustment, is to make the centre of the cross hairs remain on the same object, while the eye-tube is turned quite round by the pinion of the refraction apparatus: for this adjustment, set the index on the slide to the first division on the dove-tail; and set the division marked 18″ on the refraction-circle to its index; then look through the telescope, and with the pinion turn the eye-tube quite round; then if the centre of the hairs does not remain on the same spot during that revolution, it must be corrected by the four small screws, 2 and 2 at a time, which will be found upon unscrewing the nearest end of the eye-tube that contains the first eye-glass; repeating this correction till the centre of the hairs remain on the spot looked at during a whole revolution. To make the line of collimation parallel to the brass rod on which the level hangs, set the polar axis horizontal, and the declination-circle to 90°, adjust the level by the polar axis; look through the telescope on some distant horizontal object, covered by the centre of the cross hairs: then invert the telescope, which is done by turning the hour-circle half round; and if the centre of the cross hairs does not cover the same object as before, correct half the error by the uppermost and lowermost of the 4 small screws at the eyeend of the large tube of the telescope; this correction will give a second object now covered by the centre of the hairs, which must be adopted instead of the first object; then invert the telescope as before; and if the second object be not covered by the centre of the hairs, correct half the error by the same two screws as were used before: this correction will give a third object, now covered by the centre of the hairs, which must be adopted instead of the second object; repeat this operation till no error remain; then set the hour-circle exactly to 12 hours, the declination-circle remaining a 90° as before; and if the centre of the cross hairs do not cover the last object fixed on, set it to that object by the two remaining small screws at the eye-end of the large tube, and then the line of collimation will be parallel to the brass rod. For rectifying the nonius of the declination and Equatorial circles, lower the telescope as many degrees &c below 0° or Æ on the decli- nation-semicircle as are equal to the complement of the latitude; then elevate the polar axis till the bubble be horizontal; and thus the Equatorial circle will be elevated to the co-latitude of the place: set this circle to 6 hours; adjust the level by the pinion of the declination-circle; then turn the Equatorial circle exactly 12 hours from the last position; and if the level be not right, correct one half of the error by the Equatorial circle, and the other half by the declination-circle: then turn the Equatorial circle back again exactly 12 hours from the last position; and if the level be still wrong, repeat the correction as before, till it be right, when turned to either position: that being done, set the nonius of the Equatorial circle exactly to 6 hours, and the nonius of the declination-circle exactly to 0°.

The chief uses of this Equatorial are,

1st, To find the meridian by one observation only: for this purpose, elevate the Equatorial circle to the co-latitude of the place, and set the declination-semicircle to the sun's declination for the day and hour of the day required; then move the azimuth and hourcircles both at the same time, either in the same or contrary direction, till you bring the centre of the cross hairs in the telescope exactly to cover the centre of the sun; when that is done, the index of the hour-circle will give the apparent or solar time at the instant of observation; and thus the time is gained, though the sun be at a distance from the meridian; then turn the hour-circle till the index points precisely at 12 o'clock, and lower the telescope to the horizon, in order to observe some point there in the centre of the glass; and that point is the meridian mark, found by one observation only. The best time for this operation is 3 hours before, or 3 hours after 12 at noon.

2d, To point the telescope on a star, though not on the meridian, in full day-light. Having elevated the equatorial circle to the co-latitude of the place, and set the declination-semicircle to the star's declination, move the index of the hour-circle till it shall point to the precise time at which the star is then distant from the meridian, found in the tables of the right ascension of the stars, and the star will then appear in the glass.

Besides these uses, peculiar to this instrument, it may also be applied to all the purposes to which the principal astronomical instruments are applied; such as a transit instrument, a quadrant, and an equal-altitude instrument.

See the description and drawing of an Equatorial telescope, or portable observatory, invented by Mr. Short, in the Philos. Trans. number 493, or vol. 46, p. 242; and another by Mr. Nairne, vol. 61, p. 107.

EQUIANGULAR *Figure,* is one that has all its
angles equal among themselves; as the square, and all
the regular figures.

An equilateral figure inscribed in a circle, is always Equiangular. But an Equiangular figure inscribed in a circle, is not always equilateral, except when it has an odd number of sides: If the sides be of an even number, then they may either be all equal, or else half of them will always be equal to each other, and the other half to each other, the equals being placed alternately. See the demonstration in my Mathematical Miscellany, pa. 272. |

Equiangular, is also said of any two figures of the same kind, when each angle of the one is equal to a corresponding angle in the other, whether each figure, separately considered in itself, be an equiangular figure or not, that is, having all its angles equal to each other. Thus, two triangles are Equiangular to each other, if, ex. gr. one angle in each be of 30°, a second angle in each of 50°, and the third angle of each equal to 100 degrees.

Equiangular triangles have not their like sides necessarily equal, but only proportional to each other; and such triangles are always similar to each other.

Equicrural *Triangle,* is one that has two of its
sides equal to each other; and is more usually called an
Isosceles triangle.

, Equuleus, or Equus *Minor,* a constellation
of the northern hemisphere. See EQUULEUS.