to accuracy would be attended with measures and calculations so intricate and laborious as to defy human perseverance. Any sure method, then, by which we can obtain a moderate approximation, with moderate expenditure of time and money, confers a real boon on the engineering profession. Such, we conceive, Messrs. Bidder and Creedy have furnished in the tables before us. The present edition, too, besides being very much enlarged in its range and more precise in its "determinations," is printed in a more convenient form than the preceding ones. They were on a broad sheet, and were tables of double entry; this is in a little book, for the waistcoat-pocket, of 4 by 24 inches, and is, besides, converted into tables of single entry. Our practical readers will understand the value of these improvements.

The principle on which the tables are based is very simple; though neither Mr. Bidder, nor his editor, (we suppose in accordance with the ordinary laxity of practice in this respect,) has given the investigations of the formulæ employed. The rules for using the tables, are, however, very neatly laid down, and the method rendered capable of instant comprehension.

The hypothesis of the construction is :that the surface of the cutting to the extent of the individual part to be computed is a plane, whose line of declivity is in the same vertical plane with the line of the railway-that, consequently, the cross section of the cutting meets the surface in a horizontal line-and therefore, again, the part of the excavation under consideration is composed of a truncated wedge and two truncated pyramids.

The data to be used are:-the breadth and length of the bottom of the cuttingthe height of the surface of the ground above the bottom of the road at each extremity-and the "rate of slope," or to speak more precisely, the angle of the slope to the horizon. Denoting by a and b the depths of the cutting at each end, and taking a chain as the unit of length, and a foot as the unit of breadth of the bottom of the cutting, then one foot breadth of the

1. For the "Middle Section."-Let Rq be the middle, or truncated wedge, having the planes Sq, Rp of which being produced would form the edge of the wedge; the wedge, therefore, being truncated by Sr. Now this may be viewed as a prism, whose opposite parallel and equal faces are SP and sp, and whose length is Ss or Qq.

Now, since RS and PQ are perpendicular to SQ, the area of the trapezoid SP is } {PQ+RS}.Qq. Now, putting with Mr. Bidder PQ=a, RS=b, SQ=66 feet, and Qq=1 foot, this expression reduces at once

to

V=(a+b).66 cubic feet,

* That is, by the number which expresses the ratio of the depth to the horizontal breadth at the top of the cutting.

=(a+b) cub

a+b cubic yards.

Multiplying this by the number of feet in the breadth of the bottom of the cutting, we obtain his rule.

2. For the" Slopes."—Next, let rQ be one of the slopes, having PQ, RS for the Fig. 2.

R

9

depths at the two ends, and Pp, Rr for the breadths respectively. Produce PR, to meet QS in E;-which it will obviously from the parallelism of the sides of the triangles PpQ, Rrs.

Then the slope of the cutting is the difference of the two pyramids E❘ RrS and El PpQ.

Now viewed as the trunk of a pyramid, and putting the rate of slope =m, so that Pp=m. PQ=ma, and Rr=m. R S=mb, we shall have the areas of the two ends, QPp and SRr expressed by ma2 and \mb2. Also, since the planes QPp, SRr are by hypothesis perpendicular to EQ, we have SQ the height of the frustrum. Whence, by the ordinary rule of mensuration applicable to the case, we get

The tables added by Mr. Creedy speak for themselves, and need no remark from us. The whole are arranged in a neat and convenient form, and are admirably calcalated to answer the purposes contemplated by the editor of this edition. We, therefore, recommend its use to those whose professional avocations render this species of calculation necessary.

To the publisher we would suggest the advantage of using stiff covers for these tables, or, still better, a binding in the common pocket-book style.

We cannot leave this subject, however,

11 m

108

cubic yards,

(a - b)2 cubic yards.

without one final remark in reference to the payment of the labourer; for we must say, after all, that in paying for actual excavations, a closer approximation ought, in justice to the workman, to be made. Time is of less importance in this It case in performing the calculations. may make a wide difference in the payment of a workman's weekly wages, whether we adopt the hypothesis here employed or not, though in the general estimate for the level of a railway it may make but an imperceptible difference. As a general rule, the surface of any small portion of the earth is a curved surface having its convexity above the assumed plane, and thereby requiring more earth to be removed than this hypothesis allows for. As a general rule, too, supposing this superfluous bulging upwards to be removed so as to render the surface plane, that plane has not in general its line of declivity in the same vertical plane with the line of road. We shall return to the subject under this aspect hereafter; when we hope to be able to point out a proper mode of estimating, very nearly, the actual' quantity of excavation under the most general circumstances that can occur.

forms assumed by the science. De Morgan's Arithmetic is the work best a lapted of all with which we are acquainted for a stu dent of the class to which our correspondent belongs. The appendices to the last edition (the fifth) confer great additional value on the work: but either of the preceding ones, except perhaps the first, will otherwise do almost equally well, the changes made in them being comparatively slight.

We cannot leave this subject, however, without reiterating advice that we have already given to others-ON NO ACCOUNT NEGLECT GEOMETRY. For one case where arithmetic beyond the very simplest kind comes into effective play, twenty cases of the necessity for geometrical operations present themselves to the operative mechanic. ED. M. M.

PROCESS OF COATING IRON AND ZINK WITH COPPER, WITHOUT CYANURET OF

POTASSIUM.

The great advantages which would arise from perfecting a plan, whereby the easily oxidisable metals, such as iron and zink, could be coated with copper at a cheap rate, induced Messrs. Elsner and Philip, of Berlin, to undertake a series of experiments, to ascertain if such could not be effected more economically than by employing the cyanuret of potassium, and in this they have been successful. For coating iron the article must be well cleaned in rain or soft water, and rubbed, before immersing it in the solution, which may be either chloride of potassium, chloride of sodium, with a little caustic ammonia added, or tartrate of potash, with a small portion of carbonate of potash. At the extremity of the wire, in connexion with the copper, or negative pole of the battery, is fixed a thin flattened copper plate, and the article to be coated is attached to the wire from the zink, or positive pole, and both are then immersed in the exciting solution, the copper plate only partially. The liquid should be kept at a temperature of from 15 to 20 centigrade, and the success of the operation depends greatly on the strength and uniformity of the galvanic current. When the chlorides are employed, the coating is of a dark natural copper colour; and with tartrate of potash, it assumes a red tinge, similar to the red oxide of copper. When sufficiently covered, the article is rubbed in sawdust, and exposed to a current of warm air to dry,-when they will take a fine polish, and resist all atmospheric influence. In coating zink with copper, the same general principles will apply as for iron-only observing that, in proportion to the size of the article, the galvanic current must be less powerful for zink. The surfaces must be perfectly smooth,

11

and for this reason it is well to rub them thoroughly with fine san 1, and polish with a brush. Tartrate of potash is the best existing liquid for coating zink. By very simple means, large articles in iron and zink may be coated with copper by the above cheap chemical solutions, which could not, at any former period, be effected from the high price of the cyanuret of potassium.—Mining Journal.

EXTEMPORANEOUS SAFETY-RAFTS.

A late frightful collision between two steamers in the Mersey, which was attended with a melancholy loss of life, has produced a communication to the Liverpool Mercury from Mr. W. G. Rhynd, of Ross, in which he suggests the following sensible plan for the preservation of passengers and crew in such cases of emergency :

"The invention is simply this-1st. The back and seat of the deck seats of steampackets are to be lined with cork, and united with strong hinges.-2nd. The elbows are made to lock into each other-i. e., the top part with the upright.-3rd. The legs, with thick cross pieces at the bottom, are made moveable.

"Directions for Use, in event of a Boat upsetting, or a Vessel sinking.-1st. Loose the arms.-2nd. Bolt the back and seat firmly together.-3rd. Take out the legs, and place them as out-riggers in the side mortices prepared for them.-4th. Run a small rope through the four uprights (holes being already prepared for them) formed by the separate parts of the elbows; thus in four minutes you have a raft eight feet (the usual length of the seats) by seven, capable of supporting ten adults hanging on outside, and some two or three children within the ropes, without going from the seat for a single article.

"This plan of raft is merely temporary; but should there be an hour's time to spare, a permanent raft may be formed of all the seats together, and the area enlarged by spars, &c.

"In the melancholy wreck of the Rothsay Castle, seven men escaped by clinging to a part of the ripped-up deck, (a natural raft ;) and who that has read the account of St. Paul's shipwreck can ever forget the touching close of the narrative so full of mercy :

And the rest, some on boards and some on broken pieces of the ship, but so it came to pass they all came safe to land.'-Acts xxvii. 41.

"The plan and model of the seat have been submitted to the Trinity Board, and met their full approval; and one of the elder brethren remarked, that he believed the plan, if generally adopted, would be the means of saving hundreds of lives."