On comparing the three forms, it will be observed that the first requires eight columns, as compared with six in the second, and four in the last. That the method of filling in the distances is continuous from the starting to the finishing point in the first, whilst in the other two the distances are only continuous for one "plant" of the instrument, and an addition made of these at the end. An advantage claimed for the first form is that it checks every level filled in when added up at the bottom of the page, whilst there is no such check on the intermediate levels in the other methods. Against this it may be fairly claimed for the second and third forms that there is less figuring required, and that they are more simple than the first. It will be observed that the Reduced Levels and Remarks are the same in all three cases; that in the first form the first row of intermediate figures have to be subtracted from the figures under the head of back-sight, or the latter are subtracted from the former, the result being placed as a rise if the intermediate sight is less than the back, and as a fall if more. The next figures in the Inter. column are either deducted from those previously placed in the Inter. column, or else the previous Inter. column figures are subtracted from them, and the result placed as a rise or fall. These rises or falls are added to or subtracted from the figures in the Reduced column all the way down the page. At the bottom of the page, or sooner termination of the levelling, an addition is made of the Back, Fore, Rise and Fall columns, as shown, and the difference between the Back and Fore must agree with the difference between the Rise and Fall shown in the addition, and this difference must also agree with the difference of the Reduced Level at the finish and at the commencement. In the second form, taking the starting point as being 100 feet above the datum line, and the reading for the back-sight being 8.59, it is obvious that the height of the instrument itself must be 100 + 8:59 = 108.59 feet above datum, and placing these figures in a column to itself, called Height of Instrument, every other reading of the staff placed on the chosen stations during the first "plant" are entered as fore-sights, and subtracted from the figures in the Height of Instrument column, the result being the Reduced Level. On fixing the instrument again, we read for the back-sight 12:43, which must be added to the figures 102:55 in the Reduced Level column, and the result placed in the Height of Instrument column. All other readings whilst the instrument remains in its second position are booked as fore-sights, and these are each subtracted from the figures last placed in the Height of Instrument column. For the sake of clearness, the figures that have to be added at the bottom of the page are underlined, because all that are in the Distance and Fore columns are not to be added together, but only those indicated by the underlining which forms a part of those columns. In practice this underlining is unnecessary in the levelling book, because the eye easily rests on the figures to be added together, as they are in a line with the figures in the Back and Height of Instrument columns. Besides the underlined figures in the Fore and Distance columns, the Back column figures must be added at the foot of the page, and the method afterwards explains itself. If the levelling is to be continued further, the totals at the foot of one page are carried forward to the next. The third form is simply a modification of the second, whereby two of the columns there used are dispensed with. Instead of having two columns for backand fore- sights, all the level readings are entered in one column, and the first entered after each "plant" of the instrument is a back-sight, and the last the foresight. A line is drawn across the first three columns after taking the fore-sight and removing the instrument. These lines serve to distinguish the proper figures to add together at the foot of each page. Thus, only the figures in the Level Readings column immediately over the lines ruled are added together for the total fore-sights, and only those immediately under the lines are added together for the total back-sights, the rows between these extremes not forming a part of either addition. The Height of Instrument column is dispensed with, and the figures really forming the height of the instrument are entered in the Reduced Level column. These are not to be plotted, but are merely used as a basis each time for ascertaining the levels of other stations which have to be plotted. There is little fear of confusing these figures with those in the Reduced columns, which have to be plotted, as the line drawn immediately over them, together with the blank space in the Distance column alongside, sufficiently distinguishes them. The plotting of the levelling just given will be shown later on, after plotting instruments have been explained. A very interesting pamphlet on "Hints on Levelling Operations, as applied to the reading of distances by the law of perspective, and the saving thereby of chainmen in a level survey," by W. H. Wells, C.E., was published in 1879 by E. & F. N. Spon, from which the following remarks are drawn. The image of the staff, or any portion of it, seen in the telescope of a level will diminish as the distance the staff is moved from the telescope increases, according to the laws of perspective. If when the staff is held, say, 100 feet from the telescope, the portion of the image of the staff contained within the space A B, Fig. 695 (being the horizontal D E с Fig. 695.-SHIFTING ARRANGEMENT IN THE DIAPHRAGM OF A TELESCOPE. cross web), and C (being the lower edge of the diaphragm), be 150 foot, a datum is obtained from which can be ascertained any distance that the staff is afterwards moved, by reading the portion of its image enclosed within the vertical space DC. For instance, if the staff be now moved, and, on directing the telescope to it, it is found that the portion of the staff image contained within the space D C is 210; the distance to the staff will be found by a simple proportion sum, thus-As 150: 2'10 :: 100: 140; that is, the staff in its new position is 140 feet distant from the telescope. Instead of using the lower edge of the circular diaphragm, a more accurate outline of a portion of the staff image is obtained by fixing a second horizontal web either near the bottom or top of the diaphragm, as shown dotted at E F. If this second web is a fixture in the diaphragm, the surveyor must ascertain his own datum at a distance of 100 feet, by carefully measuring out that distance on the ground, the staff being placed at one extremity and the telescope at the other, and then reading the portion of the staff image enclosed between the lines A B and E F. A note of this reading is made in the survey book, and all further levelling operations may be proceeded with without using the chain. All the surveyor has to do after reading the staff in the ordinary way is to read and enter in a proper column in his survey book the portion of the staff image contained between the lines A B and E F. The distances can be worked out after the day's operations are finished, and this is done by a series of proportion sums. The form of book must necessarily be altered to suit the particular method. The following would appear to be quite clear, although it is open to the objection of having many columns. Datum distance, reading, say, 1'50 of the staff image = 100 feet. In this form, a line is drawn between the distances at C and J, to show the position of the instrument, and these are ruled in the survey book, whilst the operations are going on; the distances may afterwards be filled in. A line is also drawn under the Level Readings Fore column at F, as well as in the Distance column, and this distinguishes between the position of the instrument and the last sight taken by it each time of fixing. The example above shown is the first two "plants" of the level in the Levelling given previously in other forms of keeping the level book, and taking distances in the ordinary way. It will be noticed that the reading of the second cross web at F, after moving the instrument, is 15:20, and with a 14-foot staff the instrument could not have D Fig. 696.-STAFF ReadingS OBTAINED FROM A Levelling. been used in this way for distance reading, unless it had been placed at a lower level. There are, no doubt, times when shorter sights must necessarily be taken as a consequence of working by this system, but there is a much greater advantage obtained from having no chainage to do, and all the distances read are horizontal ones. Where great accuracy is desired, the distances may be chained and checked by the staff distance readings. Fig. 696 shows the position of the instrument when the preceding readings were taken. It is plain that the distances, as worked out in the level book, will be those between the position of the instrument and the different stations on which the staff was held on either side of it, and this must be borne in mind when plotting. If the distance between B and C was required, then 49'33 12.66 = 36.67 feet. Similarly the distance between any other two stations may be obtained. An objection to having the second cross web fixed in the diaphragm at any convenient distance from the usual horizontal cross web is the fact that a series of proportion sums must be worked out before the distances are obtained. But this objection may be removed if the instrument maker fixes to the instrument a properly arranged diaphragm, in which the second cross web can be moved and regulated by the surveyor himself, by means of a thumb-screw placed either above or below the diaphragm of the instrument. Having this shifting arrangement, the surveyor may bring 1 foot of the staff image in the space between the two cross webs at 100 feet distance, or any other portion convenient to himself. If he make the former arrangement, there will be no proportional sum to find the distances, or only such as can be made mentally in a moment. For instance, if the space between the cross webs read 2'15 after such an adjustment were made, the distance from the staff will be 215 feet; if '65, it will be 65 feet. If by means of the regulator two or more whole feet of the staff image is contained between the two horizontal webs at 100 feet distance, more accurate readings will be obtained. Another advantage of this regulator is in the facility it affords for reading the distance to the other side of a river or other large obstruction, when the staff figures are beyond the limits of vision. In this case, the regulator is adjusted until either the whole staff, or a portion whose length is known, placed on the opposite side of the obstruction, is enclosed between the cross webs. Without further touching the regulator, a staff is now held on the same side of the obstruction as that on which the instrument is, but 100 feet from it, and the figures enclosed within the horizontal webs then noted. A proportion sum then gives the width of the obstruction. For instance, if the regulator be adjusted to include the whole of a 14-foot staff between the horizontal webs, when the staff is placed on the opposite bank of a river and the reading of the distance between the horizontal webs (the regulator not having been moved) on a staff 100 feet distant from the instrument on the same side of the river is 1'45 foot; the distance across to the opposite side is as 145 14'00 :: 100: 965.52 feet. If in addition to the regulator for adjusting the space between the two horizontal webs, a scale of equal parts be fixed outside the telescope, and a point conveniently attached to the adjusting arrangement be made to move along the scale, the amount of the space may be shown on the scale. When the two webs coincide and there is no space between them, the pointer on the scale would indicate zero. Any other position of the second cross web would be read on the scale of equal parts. With this arrangement no staff would be required on the other side of the river. The telescope may be directed to any suitable object such as a tree or a house, and the space between the horizontal webs carefully adjusted until the object selected is exactly enclosed therein, and the reading on the scale of equal parts noted. The instrument is then moved backwards to a suitable distance, and from this new position the space between the horizontal webs is again made to enclose the same object within it. The reading on the scale of equal parts is noted, and as the distance is increased the reading will be less than that first taken. The distance of the first position to the object is found by the following proportion sum. As the number of equal parts of the scale first read minus the number of equal parts of the scale next read is to the number of equal parts of scale at first observation so is the distance that the telescope was moved to the distance required. For instance, if at the first point of observation 8 equal parts were noted as the space between the horizontal webs enclosing the object, and at the second point of observation 120 feet back from the first |