Example 7. Levels taken at Seacombe, prior to my design for the town of New Brighton, opposite Liverpool.

Example 8. First cross section from 2300 on first line.

See Example 5. In taking cross sections there requires no alteration to the previous advice on levelling, it is merely a transverse section of a short length that is required; and the

only matter of importance is to notice the crossing of the longitudinal section and the reduced level at that point, from which must be calculated the heights of the cross section, as shown in the margin.

Problem 11.

See Example 6. Introduces another method of keeping the level book No. 2.

As before noticed, simplicity and conciseness in the book is most required for levelling; there is but little to enter beyond the heights and distances. In this example there is one-third reduction of calculation as well as columns.

The manner of proving the calculations is the same as the former examples by the back and fore sights; it requires but little study to prove its superiority.

The first column contains the distances; that is of small importance, whether it be first or last.

The second column contains all heights that are taken from off the staff at one reading; that is, back, fore, and intermediate sights.

The third column contains the reduced levels from which the section is plotted.

The fourth column is the plane of collimation, commencing, as in former examples, with the fixed bench mark, and continuing as the same, or a series of parallel proved lines, to carry on the further calculations.

The fifth column is for remarks, sketching, &c.

All the staff heights are entered into one column: the first or back sight, 0.56, is added to the given reduced number, 105.16, and the amount is carried to the next column, called the plane of collimation, 105.72; then ALL the other heights are subtracted from that number; the last height, 2.23, will be the fore sight. Then draw a line at every removal of the instrument, and proceed in like manner as shown by the example. The next removal: the back sight, 15.30, is added to the last

reduced number, 103.49, equal to 118.79, which is carried to the column of collimation; so proceed throughout.

A cross section has been purposely introduced to show that a short line may be taken at the same time.

As 7.22 was the last fore sight, the cross section proceeding from that point, the instrument is removed to a consistent distance; the assistant holding a staff on the same point, a back sight was taken at 5.70, which is added to the last reduced level 105.54, and carried to the next column, 111.24, as before; and so proceed.

We now return to the main line: 105.54, the last reduced level (that number in practice would be omitted), adding the back sight 15.80 to that number, 121.34 is carried to the plane of collimation; and so proceed.

To balance the heights and prove the last reduced number, collect all the back sights together, as 0.56, 15.30, &c.; cast them up separately.

Also the fore sights in the like manner, subtract the one from the other (as the case may be); if the product agrees with the last reduced number the book is correct.

Then proceed to cast out the intermediates taken on each remove of the instrument as in the former examples, which are all subtracted from the last number in the plane of collimation. In all cases show the working of the balance as in the former examples.

Problem 12.

See Example 7. Is a part of a course of levels taken over an exceeding rough country; they are here introduced for practice.

PLOTTING SECTIONS.

Problem 13.

By referring to the section, Fig. 3, Plate 29, it will at once show the manner a section has to be prepared for Parliamentary purposes.

The first thing is to draw a perfect straight line, as a datum line, which is a matter of the greatest importance and sometimes of difficulty, notwithstanding its apparent simplicity. (See Plotting Scales and Straight Edge, Part V.)

The whole accuracy of a section is entirely dependent on the datum line being straight. First set off all the lengths from the level book, taken from the column of distances; then place a straight edge against the datum line, and with a set square draw in all the perpendicular lines from each length, on which prick off all the heights from the reduced levels; then draw a pencil line through each point, which will form the surface or ground line, noting particularly all roads, streams, &c. &c.; then carefully draw a fine ink line, and insert from the book all necessary remarks, as roads, streams, &c.

In like manner draw the cross sections, which are usually drawn to a larger scale. The manner of keeping the book for cross sections is shown by Examples 5 and 6.

The gradients are then drawn to equalise the cuttings and embankments, as nearly as possible forming a series of ascending and descending lines, also horizontal or level lines, all of which represent the line of rails; they are distinguished by a strong black line, the inclination being boldly written underneath each, and the heights at each end.

Tunnels, viaducts, and bridges must be very minutely described, as to the heights, the span, and mode of construction, with every other particular; also the deviation of roads, streams, &c.

Every cutting or embankment exceeding five feet must have the height inserted.

PARLIAMENTARY PLAN AND SECTION.
Problem 14.

Fig. 1, Plate 30, represents the portion of a plan for a proposed railway, which must always be constructed strictly to the standing orders of the House of Lords and the House of Com