Example of Case 3: Modification 3: fig. 12, plate IV.

Example of Case 3: Modification 4: fig. 13, plate III.

Objections may possibly be urged against the hypothetical generation of intermediate ground by means of middle sections, and it is difficult to free this subject wholly from exception; but with a given number of transverse sections taken in the field, if close attention is paid to the inclination of the ground as developed by the end sections, and occasionally where it is very complex, if the figures are simplified by introducing additive or deductive solids, we have not yet met with any other practical method, giving results equally satisfactory.

Various expedients are known to engineers for facilitating the computation of the areas of cross sections, to attempt an account of which, though it might be interesting to students, would prolong this paper to an inconvenient length.

The above examples embrace, as we have stated, specimens of the principal varieties of excavation and embankment; and a little attention to the calculations and the modes of deducing the middle sections between those usually taken in the field, will enable any one to apply the "Prismoidal Process" to the mensuration of earth work upon canals, roads or railroads. When the mean areas are computed, it will be much more expeditious to get out the cubic yards from a table of cubic yards previously made out (supposing the stations regularly 100 feet,) for each foot and tenth of mean area, from 0.1 up to the largest which commonly occur: such or similar tables in manuscript are in the possession of many engineers, but those who have them not can in a few days construct a set by simple addition, and verify them by observing how the cubic yards for the preliminary areas of the first hundred, are subsequently repeated in the same decimal place.

Indeed, Mr. Macneill's tables (if extended to tenths of feet) might be used; by constructing a supplemental set to show by inspection the height or centre cutting in level ground, of two sections with the given base and slopes, to be respectively equivalent in area, to the end sections of any given length of excavation or embankment; or these heights could be ascertained by the aid of an ingenious formula given by Mr. Macneill, and being found might then be wrought with in entering the tables according to the directions laid down: either of these proceedings, by determining a true mean cut

fing at each end, would obviate the necessity of a middle section, but neither, it is believed, would be altogether as satisfactory.

We desire to be understood as suggesting the application of the preceding process only to those exact calculations, required by the Final Estimates of sections; for running estimates or those on lines of location, less accurate but more speedy methods will answer every purpose. Oldtown, Md., November 20th, 1839.

TO THE EDITOR OF THE JOURNAL OF THE FRANKLIN INSTITUTE.

In the Railway Magazine, (London,) for August, 1839, I observed a formula for calculating the area of a cross section of excavation in, or embankment on, sloping ground. I shall feel indebted to any of your correspondents who will furnish me with a solution by which its correctness may be ascertained.

E
2

Having the bottom width_given, if excavation, (or top width, if embankment,) = E; the depth at from the centre, on each side, =D and d respectively; and the ratio of the side slopes = r; the following is the formula given,

E (D+d)

=area.

2

J. M. H.

Philadelphia, Jan. 1, 1840.

Telford Premiums to be awarded by the Institution of Civil Engineers of

London.*

The Committee on Publications of the Franklin Institute having received the following circular from the Institution of Civil Engineers, lay it with pleasure before the readers of the Journal, believing, that to many of them it will be a subject of interest. COM. PUBLICATIONS.

Institution of Civil Engineers, established 1818, incorporated 1828.

The Council of the Institution of Civil Engineers give notice that they will award, during the ensuing session, Telford Premiums to Communications of adequate merit on the following subjects:

1. The nature and properties of steam, especially with reference to the quantity of water in a given bulk of steam in free communication with water at different temperatures.

2. An account and drawings of the original construction and present state of the Plymouth breakwater.

3. The ratio, from actual experiment, of the velocity, load, and power, of locomotive engines on railways.

1st. Upon levels.

2nd. Upon inclined planes.

4. Drawings and description of the outfall of the King's scholars' pond sewer, and of other principal outfalls of the Westminster sewage; also, the *The premiums of this Institution are awarded to Foreigners as well as English

men.

inclination, dimensions, and forms, of the sewers, and the observed velocities of water in them.

5. Drawings and descriptions of the sewage under the commission for Regent street, especially of the outfall at Scotland yard.

6. Drawings and description of the best machine for describing the profile of a road, and also for measuring the traction of different roads.

7. The alterations and improvements in Blackfriar's bridge.

8. The explosion of steam boilers.-Especially a record of facts connected with any explosions which have taken place; also, a description, drawings, and details, of the boiler, both before and after the explosion.

9. Drawings, sections, and descriptions, of iron steam vessels.

10. The comparative advantages of iron and wood as employed in the construction of steam vessels.

11. The comparative advantages and disadvantages of hot and cold blast in the manufacture of iron, with statements of the quality and quantity of materials employed, and produce thereof.

12. The causes of, and means of preventing, the changes in texture and composition which cast iron occasionally undergoes when in continued contact with sea water.

13. The properties and chemical constitution of the various kinds of coal. 14. A memoir of Sir Hugh Middleton, with an account of his works. 15. A memoir of Arthur Woolf, with an account of his works.

16. An account of the various methods lately employed for preserving timber from dry rot, and other sources of decay.

17. On the best gauge for the width of railways, with the result of the experience furnished by existing railways.

The communications must be forwarded to the House of the Institution, No. 25, Great George street, Westminster, on or before the 31st of March, 1840.

It is not the wish of the Council to confine the Telford Premiums to communications on the above subjects; other communications of distinguished merit and peculiarly deserving some mark of distinction will be rewarded.

Copies of this paper, and any farther information, may be obtained on application to the Secretaries.

THOMAS WEBSTER,Secretaries.
CHARLES MANBY,

25, Great George street, Westminster, June 25, 1839.

Telford Premiums.

The Council of the Institution of Civil Engineers have awarded the following Telford Premiums:

A Telford medal in silver and twenty guineas to John Edward Jones, for his description, plan and drawings of the sewage of Westminster.

A Telford medal in silver to Charles Hood, for his paper on warming and ventilating buildings.

A Telford medal in silver to Charles Wye Williams, for his paper on the properties and application of turf and turf coke.

A Telford medal in silver to Edward Woods, for his paper on the forms of locomotive engines.

A Telford medal in bronze, and books suitably bound and inscribed, of the value of three guineas, to Lieut. Frederick Pollock, Madras Engineers, for his description and drawings of the Coffre Dam of Westminster bridge.