the first in large, and the tenths in smaller figures; the figures of the feet are often painted red, those for the tenths being always black. Figure 131 will save a lengthened description, and make the whole plainer to the reader than words can possibly do; Fig. 131 shows the whole of one foot reduced to onefourth of the actual size; and 131A shows a little above and below one-tenth of a foot full size; the figures for tenths are, it will be seen, entered alternately, when a staff thus graduated is observed through the telescope of the level, the divisions are read off by the observer himself; but when it happens to be at a distance of ten or twelve chains, every possible assistance is desirable to make the divisions more distinctly visible, and observe that here the figures are made of such lengths that at top and bottom they coincide with a full tenth of a foot, as 9.10, 0.20, 0.30, &c., which is in every case at the top of a black division, and 0.15, 0.25, 0.35 at the bottom of a black line longer than all the other hundredths between the tenths; and so it is with all the odd hundredths, the even numbers are at the top of a black line or band, and the odd numbers at bottom. It will also be observed that with the figures 3 and the 9, portions of them coincide with some particular hundredths; when the instrument is not too far from the level, and the wires of the diaphragm are clear and sharp and free from parallax, it is very easy to subdivide the hundredths of a foot, and obtain such a reading as, for instance, 1.325. Such readings are, however, by no means desirable for ordinary levelling, as they greatly increase the labour of casting out and reducing, which will be hereafter explained; but occasionally for some hydraulic observations, as for instance, obtaining the fall of the surface of a river, it is extremely useful to be able to read to such a nicety, and with short sights and the instrument in thorough adjustment in all respects, it is quite possible, as the reader will see, to obtain even closer readings of the staff than the above.

Attempts have been made to introduce more minute divisions on the staff, but they have not been successful, the result being that even at short distances the divisions became confused instead of being distinct.

The greatest fault that can be found with a staff, the joints of which, as the above, slide down into each other, is that the topmost joint becomes inconveniently narrow to receive the figures for the decimals, as well as those for the feet; as, for instance, 12, 13, &c.; after a little use, however, one gets accustomed to this; but when stowing away for carriage is not necessary, a 15 and even 20 feet staff may be made of a piece of clean, wellseasoned wood, about four inches wide from top to bottom, and

about two inches thick at the lower end, and tapering to about half an inch thick at the top. A staff of these proportions, carefully graduated, is a valuable instrument for nice work, though when longer than 15 feet, it is heavy to carry any long distance. For some hydraulic observations, such as taking levels across a deep river, a 20, and even 30 feet staff is used; to obtain a hold at the bottom of the water, the foot of the staff is armed with three short prongs or points, which stick into the bed. A 16 or 18 feet staff, of the width of the above, may also be made in two or three pieces, which are fixed one on top of the other by means of sockets, like the ferrules of a fishing-rod; for ordinary use, however, the staff made as first described will be found the most useful and convenient. The manner in which the graduations and the figures either for the feet or the tenths are shown on the staff, is of too much importance to be in any way overlooked, for whilst at short distances everything may be very clear even on a staff graduated in an inferior manner, it becomes quite indistinct at some of those longer distances at which the value of time demands that observations should be made; in the sliding staff we have mentioned, from the top joint being so narrow, it is in fact of the highest importance. It is a very good plan, on the left hand of the column of graduations, to paint the whole length of the feet alternately black and white, leaving, however, a vertical band of white three-eighths of an inch wide between the column of graduations and the alternately white and black border. This is certainly a considerable assistance in distinguishing the feet. On some staves the figures instead of being shown upright, appear sideways, which is a very good plan also where the width of the staff will admit of it.

We have already observed that the telescope of the level inverts every object seen through it, and if the instrument is so situated that when adjusted for vision, the axis bears on a point near the ground where the staff-holder is standing, he appears turned upside down. This has a strange appearance at first, but as said elsewhere, one becomes immediately accustomed to it, as it resolves itself simply into reading downwards instead of upwards; to remedy this, which some appear to consider so great an inconvenience, the figures have been painted inverted on some staves, so that they appear upright when seen through the inverting telescope; but we submit that this is neither one thing nor the other, the figures seen inverted naturally lead one to read from the top downwards, which is the proper way, whilst the figures upright would lead one to read from the bottom upwards, which would be wrong.

Having now given a description of the "level" and of the

THE PRACTICE OF LEVELLING.

273

levelling-staff, we will enter on the subject of levelling. In Fig. 132, let all the distances between the horizontal lines represent depths of three feet each, and let all the vertical lines be supposed as one chain apart. Let A be the level of the surface of still water in the pond A W, and let it be required to ascertain the difference of level between this point and that at B. Let the levelling-staff be held upright at A, and let the observer proceed with his level up the inclined ground, until he judges by the eye that the level when set up and levelled at 1, or rather the axis of the telescope, will intersect the levelling-staff at A and B ; set up the instrument, and level it roughly at first, to see that it will do so, and then perfectly, and do this in the manner we have mentioned when describing the level. When the instrument has been levelled, turn the telescope round to A, always turning round to the right instead of the left, and adjust for distinct vision, that is, so that the wires of the diaphragm come out sharp and clear on the staff, and that they appear steady and motionless when the eye is moved up and down before the eye-piece.* This done, look to the bubble to see that it has not moved, and if it has a little, then just touch either of the parallel plate screws to bring it back to the centre of its run; now read off the staff, observing whether the horizontal wire of the diaphragm intersects the staff at the edge of one of the black bands or stripes, for if in the middle of one of these, then half a hundredth will be a quantity in the reading. In our present case the drawing has been so arranged that the wire intersects exactly the top edge of the staff, which is 18 feet long; the reading will therefore be 18 feet; had the wire bisected, say 14 hundredths from the top of the staff, then the correct reading would have been 17.985. Our reading, however, is 18 feet, which is to be entered in a note-book; having made the entry, again look to the bubble to see that it has not moved from its central position. Signal the staff-holder, who will now carry his staff on to B. Now reverse the telescope so as to bear on B, adjust for distinct vision, which will be required on account of the distances B1 and A1 being very unequal; examine the level as to any slight alteration in the position of the bubble, correct it as before, if required, and read off the staff at B; the horizontal wire now intersects exactly the foot of the staff as it did before the top, and the reading will therefore be zero or nothing; then B is

See ante what we have said on the subject of " Parallax."

+ In the staff we have described, this edge would be a brass plate one hundredth of a foot thick, always fastened on to the top of the staff as a means of drawing out the top joint from the one below it.

T

evidently 18 feet higher than A, correction for curvature, &c., being at present left unconsidered.

Now let it be required to ascertain the difference of level between the point C and the same point at A as before. The difference of level is too great for us to be able to ascertain this at one setting up of the level as last done, but it may be done at twice by setting up the level at 1 and 2, and the staff at A, B, and lastly at C; the difference of level between A and B having been already ascertained, we have now to find the difference between C and B. With the level set up at the point 2, read off the staff at B, which is supposed not to have been moved from its exact position, but merely turned round, so that the figures may face the level at 2; let this reading be 15; signal the staff on to C, reverse the telescope as before, and read off the staff at C, and let this be 0.75. Had this reading been zero from 2 to C, as it was from 1 to B, then the difference would have been the total of the first reading from 2 on B, and we should have 15 feet difference of level, and 15+ 18 would be the total difference of level from A to C. But instead of zero we have 0 75, and exactly as the reading B subtracted from the reading A gave 18 for difference of level, so now the reading C=0.75 subtracted from the reading B=15, leaves 14.25 for the difference of level between C and B, and 14:25 +18=32.25, the difference of level between A and C. Let us now put d for the difference of reading between any two staves, and pursue our course on to E; at 3 we shall have 15.75 minus 0.75, equal to 15.00; at 4 we shall have 15.75-1.00-14.75; at 5 we shall have the reading on D=4.00 and on E=400; the two readings are equal to each other; then there is no difference, and from E to D is a dead level. Let us now tabulate the above readings, calling B the first reading at each setting up of the instrument, F the second reading, and d the difference between any two readings, which, as we have seen, gives the difference of level, and we shall have

62.50=d, or diff. of level between A and E.

Observe that by casting up the column d, we obtain the total difference of level between the points A and E; also, that by adding up the columns B and F, and subtracting the lesser from the greater, we obtain the same result, the total of B minus the total of F being equal to d; we might therefore have obtained the difference of level without ascertaining the differences of readings between B and F each time.

Observe also that in the above, the readings for which we have called B are Backsights, and F are called Foresights; also that we have been ascending all the way from A to D, getting a rise at each set of readings from the instrument, and that the column for which we have put d is, as far as D, called Rise; and in the columns B and F, the backsight, is each time greater than the foresight, which is always the case with ascending levels, and that the difference between the two gives us the entries for column d or Rise; where there is no difference in the readings, as between D and E, there is also no difference of level, and neither rise nor fall, and therefore zero or a blank appears in column d, which in future we shall call by the technical term Rise, as also B and F, the Backsights and the Foresights.

This much being thoroughly understood, let us pursue the levelling operation from E to F; at the setting up at 6, the backsight reads 100, and the foresight 18:00; the difference equal to 17.00, but instead of being a rise, it is a fall; at 7 we find a difference of level equal to 12:00, also a fall, and at 8 another fall of 12:00. Now if we were to enter all these in the column of rise, and add up all the readings, we should be adding rises and falls, and making no difference between the two; and inasmuch as in ascending levels, we add all the rises together to find the total rise, so in descending levels, the fall must be subtracted from the rise, to get the fall; and if the total of falls is subtracted from the total of rises, we shall obtain the difference of levels between two points on which there may be any number of falls or rises, or which is the same thing-any number of variations in the inclinations, up or down.

An additional column is required in the field-book for the differences of the readings in descending levels, and which column is called "Fall;" the difference of the readings will have to be entered in this column of Fall whenever the foresight is greater than the backsight. In the same manner with regard to the totals of the backsights and of the foresights, whenever the total of the first is greater than the total of the second, the difference of level will be a rise; and when the total of foresights is greater than that of the backsights, the difference of level will be a fall.