artificial horizon. Any fluid that will reflect the image of a celestial body will answer the purpose, and I have taken very satisfactory observations in a pool of water on a perfectly calm night; but when there is the slightest wind such makeshifts are not available, as so much motion is given to the surface that it is impossible to make accurate contacts. One form of artificial horizon, and that which is generally used, is simply an iron trough filled with quicksilver, and sheltered from the wind by a sloping glass roof. Now when observations are taken in an artificial horizon the image of an object reflected from a horizontal surface appears as much below the horizontal line as the object itself is above it; hence the angular distance which we measure with the sextant gives double the altitude, and must therefore be divided by two. If you will look at the diagram (Fig. 2), I think you will see this at once. The roof should be changed, end for end, between each set of observations, to obviate, as far as possible, any errors caused by defects in the glass.

If a transit-theodolite is used, all observations should be made in pairs, with the face of the vertical circle alternately to the right and left of the observer, and the mean of two such measures will be free from all instrumental errors. There are many other ways of obtaining the latitude by observations of heavenly bodies not on the meridian, but in the time at my disposal it will be impossible for me to call your attention to these. I will therefore now proceed to say something about finding the longitude, but in the first place I will say a few words about finding the time, as longitude is really nothing more or less than the difference of time between two places.

We all know that the earth revolves on its axis from west to east in twenty-three hours and fifty-six minutes nearly, and, owing to this movement, all the heavenly bodies appear to revolve in the heavens from east to west. In consequence of this perpetual revolution of the celestial bodies, the hour angle, or distance from the meridian, of any one of them, affords the measure of time. The body observed should be nearly east or west, because when on the prime vertical, errors, of latitude of the observer, and of the altitude observed, produce the least effect on the hour angle. I must here, however, observe that, owing to the uncertainty of refraction, especially in very hot or very cold weather, no observation should be taken at very low altitudes. In latitude sixty degrees and upwards one minute error of altitude must always cause more than ten seconds error of time, but in the Tropics the time may more often be correctly determined when a body is less than an hour from the meridian than when at several hours from it in high latitude.

With these preliminary remarks I will now call your attention to the diagram (Fig. 3).

You will observe that the sun is represented here as being at some distance from the meridian. We measure its altitude above the horizon with the sextant, or some other angular measuring instrument. This, subtracted from ninety degrees, will give its zenith distance, which forms one side of our triangle. We then, after having corrected the declination, subtract it (in this case) from ninety degrees, which gives the polar distance of the object, which is another side of our triangle.

Again, by subtracting the latitude from ninety degrees, we get the colatitude, which forms the third side of our triangle. Then, by a wellknown formula, we compute the angle at the pole, which is equal to the hour angle, or the distance in time of the sun from the meridian. Now if we have with us a watch on which the error on Greenwich is known, we can find our longitude by simply comparing the local time that we have thus found, with the time at Greenwich when the observation was taken. Again, in this case, the art of observing comes in. For a single observation for time is often liable to considerable error, but if we observe

a body, or bodies, east and west of the meridian, at nearly the same altitude, the mean of the result will be free from error, or nearly so.

The next observation for longitude, to which I am going to call your attention, is that derived from occultations of stars. This is the best of the absolute methods of finding longitude, and I will describe the manner in which the observation is taken.

The moon, in its monthly revolutions round the earth, frequently passes between the earth and a fixed star, so as to intercept the spectator's view of the latter. The disappearance of the star from this cause is called an immersion, and its reappearance from behind the moon is called an emersion. A list of these phenomena is given in the Nautical Almanac, with the limit in latitude beyond which a star cannot be occulted by the As the elements refer to the moon and the stars as they would be seen from the earth's centre, they serve equally for all places on the

moon.

earth's surface. When a traveller has decided to observe an occultation, he should, during the day, find the approximate local time of that phenomenon by applying the assumed longitude in time to the G. M. T. of conjunction in R. A. of the moon and star, which he will find among the elements of occultations in the Nautical Almanac. An hour before the time so found he should point his telescope to that limb of the moon by which the star will be occulted. It is necessary to take this precaution, as his assumed longitude, and therefore his time, may be considerably in error. The moon will be seen to approach the star from west to east until its eastern limb will reach the star and occult it. He must then note the instant when this takes place. After a certain interval the star will reappear on the other side of the moon. He should note this time also, but either of these observations is sufficient to determine the G. M. T., and thence the longitude. When a star is occulted by the moon's dark limb, the observation will afford the most decisive results, and indeed the phenomenon takes place so suddenly that it is quite startling. It will be thus seen that the observation is a very simple one, and is taken with a telescope, an instrument every one can use, and which is not liable to get out of adjustment. The computation, however, is somewhat lengthy; but this should not deter any traveller from taking the observation, as, if he has recorded his facts and time correctly, he can easily get it computed by some competent person on his return home.

I may here remark that the observation of the emersion would be considerably facilitated if, previous to the immersion, the star is made to travel along the horizontal wire of a transit-eyepiece, which will then indicate very nearly the place on the moon's limb where it will reappear.

I will now speak of longitude by moon culminating stars. For this observation a transit-theodolite, or small transit instrument, is necessary, which must be placed in the meridian. There are several methods of doing this, but the best is by high and low stars. It can also be approximately fixed in the meridian by computing the time of the meridian passage of a star and following it with the telescope until the time of its computed meridian passage, and clamping it in this position. If local time is not accurately known, the true meridian may be found by stars east and west of the meridian.

I have here an instrument, called a solar compass (Fig. 4), by the aid of which the telescope can be very readily placed in the meridian. It consists, as you may see, of a small telescope and level, the telescope being mounted on standards between which it can be elevated or depressed. The standards revolve round an axis, which is fastened to the axis of the larger telescope. Two pointers are attached to the small telescope to be used in approximately setting the instrument, and are so adjusted that when the shadow of the one is thrown on the other, the sun will appear in the field of view.

To use the solar compass, we take the declination of the sun, as given in the Nautical Almanac, for the given day and hour, and correct it for refraction. We now incline the larger telescope until this amount is shown on the vertical arc. If the declination of the sun is north we

depress it; if south elevate it. In south latitude this is reversed. Then, without disturbing the position of the larger telescope, bring the solar telescope horizontal by means of its level. The two telescopes now form an angle which equals the amount of the declination. Without disturbing the relative positions of the telescopes, set the vernier of the vertical arc to the complement of the latitude of the place. By moving the larger and solar telescopes around their vertical axes, the image of the sun will be brought into the field of view of the solar telescope, and after actually

bisecting it with the solar telescope, the larger telescope must be in the meridian, as the solar telescope is in fact a small equatorial.

If the instrument is to be used with stars at night, all that is necessary, to test the accuracy of the adjustment, is to get some well-known star in the field of the solar telescope, keeping the larger telescope clamped, and see if after an interval, it still continues in the centre of the field if it does, the larger telescope must be in the meridian.

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There are, so far as I know, only two of these instruments in this country, though they are frequently used in the United States. One of these is in the possession of Mr. Alfred Maudslay, and was used by him. with great success in surveying, and finding the longitude by moon culminating stars in Guatemala. The other is the one in my possession, which I have frequently used for the same purposes during the past three years.

I got both of these instruments made, with some modifications to make them suitable for star-observing, after the pattern of an instrument in the possession of my friend Mr. Josiah Pierce, of the United States Coast Survey.

In the observation for longitude by moon culminating stars, we first note the times of the passage of the moon's bright limb over the wires of a transit-eyepiece, and then the times at which the star transits over them, or vice versa, if the star transits first. Now, as the R. A. of the star is accurately known, and for practical purposes nearly unchangeable, we can by applying the interval between the transit of the moon's bright limb and the star, obtain the R.A. of the moon's bright limb at the instant of observation, and then, by means of a very short computation, we are able to find the longitude in time. Very accurate results have been obtained by this method by Mr. W. Ogilvie in the Mackenzie and Yukon region, in British N.-W. America, for which he was this year awarded the Murchison Grant by the Council of the Royal Geographical Society.

We next come to finding the longitude by the eclipses of Jupiter's satellites. This observation is taken with a telescope, and is a very easy one. It also has the advantage of giving Greenwich time at once without any calculation whatever, as the Greenwich time of the eclipses is given in the Nautical Almanac. I have found, however, by frequent trial, that the results obtained from a single observation cannot be depended upon within forty seconds or a minute, but when the immersion and emersion of the same satellite are observed on the same evening, the mean of the two results may be near truth. As a rule the first satellite is to be preferred, as its motion is more rapid than the other three. This method, though easy and convenient, is not very accurate, as the eclipse is not instantaneous, and the clearness of the air and the power employed affect considerably the time of the phenomenon.

The moon,

Another well-known method of finding the longitude is by lunar distances. The Nautical Almanac gives the predicted angular distance of the moon from the sun, planets, and certain bright stars for every three hours of Greenwich time, and if the traveller accurately measures this distance with the sextant, he has the means of determining the Greenwich time when the distance was observed. This sounds very simple, but this class of observation is open to the following objections. making her monthly circuit in the heavens, may be considered as the traveller's standard clock, but the operation of determining the exact Greenwich time by it is very much the same as it would be from a clock that had only an hour hand. Again, the moon only moves among the stars her own diameter in an hour, and therefore the observer must determine the position of the moon within the 120th of her diameter, to arrive even within half a minute of the true Greenwich time; and when he succeeds in doing this, his longitude would still be seven and a half miles in error. The observation is also a difficult one, and has often to be taken in a constrained position, and it must be exact to give anything like favourable results, as an error of one minute in distance produces twenty-five minutes in longitude, or the effect of fifteen seconds. error of distance will produce six minutes of longitude, and this, be it