on paper the different traverses, or ascertaining by computation the difference of latitude and difference of longitude.

Proceeding up a river close to one bank, its width may be obtained by taking the bearing of a remarkable object at the water's edge some distance above on the opposite bank, and taking the bearing again when abreast of it; the course and distance traversed in the interval being known, we have two angles and one side given to obtain another side. In the same manner distances of remarkable objects on land may be obtained with an approach to accuracy; but if there is an opportunity of landing, and the bank of the river is comparatively level, the width of the river may be obtained to a much greater degree of precision by several methods. In the last number of the Journal of the Royal Geographical Society there are the following methods of measuring angles and obtaining the perpendicular breadth of the river, by Colonel Everest.

Drive two pegs into the ground (fig. 1), one at a in the direction of O, and the other at 6 in the direction of O', both at equal distances from A; will be the chord of the angle A to radius

measure a ß. Then

unity, which call Y.

αβ
A a

Then sin. Ay (1-2) and cosine 4-1-y2.

In fig. 2, let A B=c, and the perpendicular breadth of the river = p. sine A sine B

Then pc sine A cos. B+ cos. A sin. B

Mr. Galton has also published a method with a short table for rough triangulation without the usual instruments, and without the calculation. (See fig. 4 and Appendix A.)

There are several other methods, but I shall content myself by giving you one more from Hutton's "Recreations." (Fig. 3.)

Fix a peg at A, another at C, then another at D, in a straight line between B and C, continue CA and D A, and make A E and A F to A C and AD respectively; lastly, fix a peg at G, in such a manner as to be in line with A B and E F, A G will then equal ▲ B. If it be found impossible to proceed in the direction from A towards E and F, we may take only the half or the third of A C and A D, in which case A G will be the half or the third of A B.

The log-line may be used for these mensurations, or, if a person has been in the habit of counting how many paces he makes in a mile or hundred yards, he will find that he is capable of measuring a very fair base. Sometimes one is apt to forget the number of hundred paces he has taken: transferring an article from one hand or pocket to another, or using a string of beads, will prevent confusion.

In addition to the width of a river, the height of the bank, or what a flood has risen to on a previous occasion, is an object of great importance. Where floods of considerable height occur, reaches long enough to obtain a level will usually be found.

Thus, if the eye is 8 ft. above the level, an expanse of 3 miles is required

14 ft.

4

5

Should the expanse be sufficient, procure two straight poles, mark them to feet, place one of them upright by means of a plummet, at the water's edge, retire from it in a direction opposite to the greatest extent of water, and placing your eye at the water-mark left on the trees or bushes, direct your assistant to slide the second pole up the one already placed until its top comes in line with the level of the water; you will find that the height of the pole above the water nearly corresponds with the height of your eye above the present level.

In the event of the reach not being long enough, cross over to the opposite shore of the river, leaving behind your assistant with the pole placed vertically at the water's edge, having taken care to instruct him to obey your signals; place your eye, say three feet above the water's edge, and direct your assistant to raise the pole until its top comes in line with the flood mark, then having obtained the distance across the river, you have that as a base with the height of the pole, less the height of your eye above the water as a perpendicular. To compute the angle of elevation, measure the distance from the pole back to the flood-mark, and adding it to the width of the river, a base is obtained, while the angle of elevation thus got will give the height.

This method may be used for trees or buildings, and their height above the ground obtained, provided the bole or foundation can be seen from the opposite shore.

Elevations of these objects may also be obtained by means of their shadows, for as the length of the shadow of a pole is to its height, so is the length of the shadow of a building or tree to its elevation.

The variation of the compass should be obtained by bearing of the sun either at rising or setting, or by the pole star in the northern hemisphere. The mensuration of base by sound, requiring the aid of no other instrument than a watch, may be properly introduced here.

Sound, travelling as it does at the rate of 1140 feet per second, or a geographical mile in 5 seconds, affords in the absence of other means a ready means of obtaining a base. Common watches do not, but pocket chronometers invariably beat 10 times to 4 seconds. Box chronometers usually beat half-seconds. The beats of a common watch should be tested by holding it to the ear and counting the beats in a minute by the chronometer, this will be found to be good practice for actual observation, and by looking in the direction of the gun, you are enabled to commence the instant of the flash, and obtain a more minute division of time than is to be got by watching the hands of a watch. With practised observers, and firing to and fro, results quite sufficient to enable you to plot upon an inch scale will be obtained. Where there is no auxiliary watch, recourse may be had to the pulse, and if there is no wind, to a pendulum improvised for the occasion. The state of the pulse, and the number of oscillations may be determined, both previous and subsequent to the observation. Having so far shown what can be done with what may be called primitive assistance, I have now to call your attention to reflecting instruments, by means of which you are not only enabled to obtain greater accuracy in plotting your work, but fix your geographical position by astronomical observations.

On the present occasion my business is not to enter into detail respecting the adjustment, or to give in full the different methods of calulation, but

to lay down some general rules for the guidance of those who are about to undertake the exploration of a river.

In the first place geographical positions determined astronomically should not be considered as firmly fixed, unless the latitude is obtained by celestial objects N. and S. of the meridian, and the time by A.M and P.M. sights of the sun or stars E. and W. of the meridian.

With but one boat or one observer, recourse must still be had to the ground-log and compass, but, as in all probability landmarks and mountains at a distance from the river will be seen, we will now proceed to show how they can be turned to account.

The latitude and the longitude of the starting point having been ascertained, and a true bearing of any one remarkable object obtained, from which angles to others may be taken, the traveller, on arriving at his next astronomical position, and obtaining bearings and angles to the same objects, can obtain the distance between his two places of observation, either by laying them down on a chart graduated for the purpose, or by computatation, by spherical or plane trigonometry. In Mr. Simms' useful little Manual on Instruments, the length of feet in a second of latitude and longitude is given for each degree of latitude; though this will not give the distance with the same accuracy as when the figure of the earth is taken into consideration, yet it may be assumed as sufficient for geographical, if not geodetical objects.

In the diagram (fig. 5) the distance between the two astronomical stations is assumed as sixteen miles, and the bearing N. 50° W.; at A, the first station, High Peak, bore N, 27° E.; Saddle, N. 20° W.; Dome, S. 35° E. At B, High Peak bore N. 85° E.; Saddle, N. 75° E.; Dome, S. 35° E. These objects being fixed, any position on the river can be obtained by a bearing of any two of them, and the dead reckoning corrected. They can also be used in filling in the topography of the country, by obtaining what are termed transit bearings-that is to say, the bearing when a lower hill, a remarkable object, or the foot of a range comes in line with the one behind it.

With two boats and an assistant, recourse should be had to micrometical measurement, one of the boats furnished with a board twenty feet long, weighted at one end, so as to ensure its being suspended vertically,

In a little pamphlet published to accompany Rochon's micrometer, the distance is given for each angle from 1" to 38'.

At 1 mile 20 feet subtends an angle of 13′ 1′′

The value of the scale may be obtained by computation from a measured base, or, more directly, by seeing how many divisions are occupied by the sun's diameter, and dividing the semi-diameter in the "Nautical Almanac " by half their number. This instrument was used with great advantage by Admiral Fitzroy in the Straits of Magelhaen and the survey of Terra del Fuego. With three or more boats the triangulation of a river can be accurately and rapidly performed; and it was in this manner that the Yangtsekeang was surveyed by Captain Kellett in 1841 from Nankin to The last stations, on the close of a day's work, were taken up on shore, or a pole was left in shallow water, where the current was not

the sea.

likely to take it away, so that the same positions were resorted to in the morning; the base was repeatedly verified by sound, and recourse had to true bearings. When the river became wider, the triangulation was continued by vessels, which, when the effect of the flood-tide was reached, were moored. In the recent exploration of the upper course of the Yangtsekeang to Hankow, under Captains Barker and Sherard Osborn, the steam-vessels measured their distance by patent log, and obtained the rate of the current when anchored for the night, at which time astronomical observations were taken, and the dead reckoning satisfactorily worked in between them.*

The artificial horizon was used with good result on board ship by Captain Bethune at slack water, when he surveyed the entrance to this river in 1840, and in proceeding along the north coast of America, between the ice and the shore, when the distance of the land was too near for the natural horizon we constantly used it, and such was the smoothness of the water, that I have obtained good observations with the vessel going three knots.

In sounding operations, recourse is had to the station pointer, an instrument with which the position is obtained with great accuracy, by means of two angles between three objects. The centre object ought to be the nearest, and if both angles are about 60°, the position will be more difficult to fix, than if a large and a small angle are employed. This useful instrument is not sufficiently appreciated, with it a ship's position can always be obtained with much greater accuracy than by compass bearings, and without the instrument an excellent substitute may be used by protracting the angles upon tracing paper.

For surveys of more elaborate character, the theodolite must be used and stations erected along the banks of the river, and a comparatively level spot selected for the measurement of a base. The latter may be accomplished with great nicety, by placing poles from twenty to thirty feet apart along the line to be measured. Level the theodolite, and looking along the poles. place a mark on each, where the horizontal wire of the telescope intersects the pole, then stretch a light line along the base, and stopping it up to the marks, measure it with tapes or wooden battens; extend your base by well constructed triangles, and find the sides by computation, until you have attained a sufficient distance to plot from.

Though the theodolite is of great importance in trigonometrical operations, we find from experience, no matter how large it may be, that it cannot be depended upon for astronomical observations, unless great pains are taken in securing a proper foundation and protection from the wind. Its great value to the surveyor is the measurement of horizontal angles, and low angles of elevation. Unless a solid foundation is obtained, and a covering from the atmosphere, the sextant will give a more trustworthy result than the direct instrument. Reflecting instruments however as at present constituted have two great defects, viz. the mensuration of angles under 20° and above 72° in the artificial horizon, consequently to the theodolite we must be indebted for the correct elevation of those heights which cannot be reached. In taking these observations, the instrument should invariably be reversed, and when the distance is greater than ten miles, a correction for the ellipticity of the earth is necessary. A large

* See Appendix B for an account of a Running Survey of the Irrawadi.

theodolite capable of taking altitudes near the zenith is of great value to the traveller within the tropics, as there, from the rapid motion of the sun in altitude near noon-time, azimuth and latitude may be obtained in the course of half an hour.

Elevation above the level of the sea is a most important item in the survey of rivers. Barometrical measurement and strict trigonometrical surveys were for many years our only means of ascertaining the fall of water throughout a great extent of country. Barometers, though difficult to transport, have been taken to the sources of most of the European rivers, and have been carried to the upper waters of the Ganges, the Brahmaputra and the Indus. They are however too cumbersome and too fragile for the general traveller, while an extensive series of triangulation is utterly beyond his means. We have however a simple portable instrument, which owes its introduction to the scientific world in a great measure to Colonel Sykes and its present improved condition in as great a measure to Mr. Galton. I allude to the apparatus for boiling water. In its present form, the bull's-eye lamp, commonly used for astronomical observations or other purposes is so fitted that by the introduction of a lamp holding a wick supplied with spirits of wine, the water in the little boiler, which holds scarcely more than half a gill, is speedily brought to a state of ebullition. Formerly the thermometers were placed perpendicularly over the boiler, but it was found that the escape of steam prevented the eye making that close observation which is necessary. The thermometer now by Mr. Galton's arrangement is placed at right angles to the boiler, and the effect of parallax in the scale is done away with by your being enabled to see it reflected in the mercury.

Thus the means of ascertaining the height above the sea, instead of being one of the most difficult of our geodetical observations, has become as simple as it is portable.

This most desirable object brings me to another important question in our river surveys, viz. the mensuration of the quantity of water carried daily by the river to the sea. I say important, for rivers are our natural rain gauges, and through them we can obtain an accurate insight into the humidity of the atmosphere surrounding those basins which they drain. Though it may not be in the power of most travellers to obtain the measurement and observations which are requisite for great accuracy, yet it is a matter of so great importance that I cannot argue too strongly upon all who have the opportunity of making observations upon the descent of floods to do all in their power to ascertain the volume of water, and the rate at which it moves.

The value of this knowledge in a strategetical point of view need not be expatiated upon, and the necessity of fording a river, prior to an almost certain period, or the propriety of delaying an advance until by previous knowledge it is known the navigation of a river will be opened, have contributed to the success of many a campaign.

Opportunity, therefore, should be taken in a portion of the stream where it is confined by banks at the highest flood, to obtain a correct section of the bed of the river during the dry season, and to extend the measurement to the highest flood-mark, so that as the river rises the number of square feet contained in the section may be known.

The velocity of the current at the surface can be obtained by the log