manner in which the direct and reflected images of the sun are brought in contact.

Suppose A, fig. 1. Plate VII. the direct image of the sun, at B; the reflected image in contact; which will count on the arch, say 31.30; then, by drawing the index toward you, bring the reflected image of the sun as at A, fig. 2, above the direct image B, and count, say thirty-two; then 31.30" subtracted from 32' leaves 30" and half is 15" the index error, as before, additive to the distance, as the arch measures too little.

For the sake of distinction, we called what is read off on the arch, "on," and that on the extra arch, "off" thus,

The index error should always be found with the same telescope, that the distance is observed with. If in taking the index error, and by turning down different screens, the index error should differ materially, it shows that some or all the screens are defective; that is, the surfaces are not ground parallel to each other; this will occasion an error in the angular distance, and as soon as convenient should be taken out and good glasses put in their place.

When the index is on nonius, and when the direct and reflected image of the sun are brought in contact in the inverted telescope, for the purpose of finding the index error, if they appear as in plate VIII. fig. 3 and 4, the instrument will want adjusting; but if they appear as in fig. 5, perhaps it will want no adjustment, or very little.

The index glass being set perpendicular to the plane of the sextant, if the index glass and horizon glass are not perpendicular to each other, the reflected image of the sun will appear on one or other of the sides of the direct image, when the index is at nonius, according to the deviation of the glasses, as is shown, Plate IX. fig. 1, 2, 3, and 4. Having therefore examined the index glass, as is directed in Epitomes of Navigation, set the index at 60°, or thereabouts, and look obliquely through the index glass towards the arch; if no notch appears in the arch between the direct and reflected arches, the index glass must be perpendicular to the plane of the sextant. It is most likely that the horizon glass will be thrown out of its perpendicularism, especially if it has an adjusting screw, which will sometimes give or come up a little. This will be discovered, as before mentioned, by seeing the reflected image of the sun on one side of the direct image.

If there be an adjusting screw on the back of the index glass, by looking directly through the telescope at the sun, the eye being screened, and moving the screw, you will discover which way it is to be turned, and make the images coincide. To effect this adjustment, set the index on nonius, turn down the screens, look through the telescope at the direct image of the sun; if you see but one image, round and well defined, the sextant wants no adjustment; if the direct or reflected image appear as before

mentioned, the index glass or the horizon glass, and perhaps both, are not perpendicular to the plane of the sextant, and the screw must be moved until but one image is perceived; this may also be performed by a screw placed on the back of the horizon glass. Some glasses have no adjusting screw, and in this case the error must be allowed, as a constant quantity.

The above figures will serve to explain the meaning of the perpendicularism and parallelism of the glasses.

* In fig. 1 and 2, the parallelism of the horizon glass is out of the way; and in fig. 3 and 4, the perpendicularism is not correct. Fig. 1. shows the reflected image of the sun below the direct image, having the same effect as if the index were pushed forward a little it consequently measures too much, and the index error must be subtracted.

:

In fig. 2. the reflected image appears above the direct image, producing the same effect as if the index were pushed back a little; the index therefore measures too little, and the error will be additive.

Fig. 3 and 4, exhibits the perpendicularism of the horizon glass out of the way, and the sun's reflected image appears either on the right or left hand side of the direct image.

Figure 5, 6, 7 and 8, both the perpendicularity and parallelism of the horizon glass are not perfect, and the reflected image appears either above or below, and at either side of the direct image.

If the index glass be exactly adjusted, it will most likely hold its adjustment better than the horizon glass; and when the ho

*This is when the index is set on nonius, that the figures, as in Plate IX, appear thus, if the adjustment of the instrument be out.

rizon glass is out of adjustment, making the sun appear as in fig. 1, 2, 3, 4, 5, 6, 7, 8, it will affect the observation; it will be well therefore to examine whether nothing be wrong, before you proceed to measure the distance ;-it is presumed, also, that the telescope is parallel to the plane of the sextant, as before ad

vised.

When there is no apparent index error, the sun will appear round and well defined, as in fig. 6, Plate VIII. yet, notwithstanding all the care that may be taken, and that the direct and reflected images may appear to coincide perfectly, yet, on account of the glare of the sun's rays, there may still exist some small index error, of several seconds, which it will be proper to obtain, as directed in Plate VII.

In measuring the distance with the above errors, you will bring the moon either a little to one side or the other of the sun, unless proper allowance is made; therefore, your observation will be erroneous. It is really astonishing to me that some, who imagine they understand the lunar method of getting the longitude, omit entirely the index error; and it must reasonably be supposed that they do not know whether the telescope is parallel to the plane of the instrument or not: this is certainly prejudicial to lunar observations; but when in good hands they are most excellent, and will come within a degree of exactness, which no one, unacquainted with the operation, would imagine.

The colour of the images will depend on the colour of the screens turned down: thus a light red and a green will make the object appear yellow. In observing the direct and reflected images of the sun for the above purpose, it will be best to make as much distinction as possible between them, by means of the screens, that the error may be more easily perceptible; and when you use the screens, in taking the distance between the moon and a star, such screens must be turned down as will render the colour of the moon most distinct from the colour of the star; for if you have them nearly of the same colour, you will not be able so readily to distinguish when they are in contact.

It will be well if a card or stiff piece of paper, be put on the telescope, when getting the index error, to protect the eye from the sun's rays.

In the subsequent pages I recommend the use of the inverted telescope, and assign my reasons for it; but when the distance between the moon and a star is taken, which distance generally is not very great, and it being difficult to use the inverted telescope, the direct telescope may be substituted; but if it can be used it will be better than the direct telescope.

I have annexed part of an arch of a sextant merely to show the difference between the arch and the extra arch in Plate X.

2 2 2 2 2 2

In setting the axis of the inverted telescope to the plane of the sextant, the axis of the telescope should be parallel to the plane of the sextant; as a deviation, in this respect, will occasion a considerable error in the observations, and is more sensible in large angles; to avoid which, a telescope is made use of with wires, as in Plate X. To make this adjustment, screw in the telescope, pull out the focus, turn the tube till the wires be parallel to the plane of the instrument; then take two objects, such as the sun and moon, or moon and star, where the angular distance must not be less than ninety degrees, because the error is more easily discovered in a great distance; bring the objects in contact at the wire which is nearest the plane of the instrument, as in fig. 1. Plate X.; then, by altering the position of the sextant a little, make the images appear on the other wire, as in fig. 1. If the contact remain perfect, as appears in fig. 1, the axis of the telescope is right; but if the limbs of the objects appear to separate at the wire that is farthest from the plane of the telescope, as at fig. 2, it shows that the object end of the telescope inclines towards the plane of the instrument; which must be rectified by tightening the screw nearest the sextant, having first slackened the screw farthest from it. If the images overlap each other at the wire farthest from the sextant, as in fig. 3, the object end of the telescope is inclined from the plane of the sextant; the contrary screw must therefore be tightened, the other being previously slackened. By repeating this operation a few times, the contact will be perfectly the same at both wires, and the axis of the telescope will be parallel to the plane of the in

strument.