1819.J 



THE CIVIL ENGINEER AND ARCHITECT'S JOURNAL. 



13 



purpose, applicable to all bases and slopes, and extending to very 

 great ciitthiys and evili(nil<iiient<i of ISO feet vertical section; I 

 again turned my attention to the subject, and discovered a very- 

 simple means of successfully performing the operation; and 

 having for some time submitted the method to the test of private 

 use, which is quite satisfactory, I now offer its advantages to the 

 public. The scale is made, of the usual materials and length of 

 12 inches, so as to fit into boxes or sets of scales now generally 

 employed, thereby ensuring its portability and general utility. 

 As most working sections are plotted to a scale of 20 feet to 1 inch, 

 I have constructed the graduations to this standard. 



The application of the scale is as follows, all dimensions being 

 in feet : — 



Having divided the section, as before described, in the usual 

 manner, produce the perpendiculars B D beyond the gradient 

 to A, and through D draw the lines U C, so that the angle B D C is 

 always 60 degrees. This is very easily done, as every draughtsman 

 is provided with such an angle. Then with the compasses make 

 IDC, 1AD= IDB; 2DC, 2AD = 2DB; and so on through- 

 out. The section is then ready for measurement. 



To find the Mean Area of the Sides:— With the scale marked A C, 

 measure across from A to C, and note the graduation from O of 

 the scale. This measurement, multiplied by the slope, is the mean 

 area, or the cubic yards, due to 1 foot of length. 



To find the Mean Area of the Middle. — Apply the scale marked 

 A B to the distance A B, and note the graduations from O of the 

 scale. This measurement, multiplied by the base (in feet), is the 

 mean area, or the cubic yards, due to 1 foot of length. 



The sum of these two measurements multiplied by the length in 

 feet will give the cubic yards contained in the prismoid. 



The process above detailed, when put into a formula, appears 

 thus — 

 [(AB X base -f AC X slope) = mean area] X length = cubic yds. 



From the above statement it appears, that there are two mea- 

 surements of this scale, set against two measurements of the 

 heights, and their respective tabular numbers ; tlie remaining pro- 

 cess being the same by both methods: thus showing, that besides 

 the greater accuracy due to the coincident measurements of quan- 

 tity, a saving of time is effected by not having to refer to tables. 



Having thus described the use of this general scale, I beg to 

 refer to the particular scale already herein noticed, and fully de- 

 scribed in my work, page 210. Tliis is constructed on the same 

 principle of coincident measurements; and is adapted for the use 

 of any railway, by simply altering the graduations of the part 

 called " sectional areas," which can be easily done by means of tlie 

 rule given in the volume. 



To Measure a Cutting hy the Scale. — Apply the zero of the scale 

 of "'sectional areas" vertically to the gradient or formation line, 

 and read oft' where the surface line intersects; put tliis in column 

 1 or 2, as the case requires: then, at the smaller end of the pris- 

 moid, upon the scale of vertical yards, with zero on the surface 

 line, observe where the gradient intersects, then place the .same 

 point of intersection on the gradient at the other end, and read off 

 above the zero on the scale of "differential areas," where tlie sur- 

 face line intersects; put this in column 4, and then, having mea- 

 sured all the lengths by the scale of horizontal yards, and inserted 

 them in column 6, proceed as in the use of the tables. To save 

 time, it is desirable to take a pair of dividers and mark off at each 

 division the difference of the heights in succession, and then the 

 differential scale above zero need only be applied. The arrange- 

 ment of the columns used for this scale is as follows : — 



[(Col. 1 -j- col. 2 = ) col. 3 — col. 4 = ] col. 5 X col. 6 = col. 7 = 

 cubic yards in the prismoid. 



The scales above described can be had by applying to Mr. Elliot, 

 268, High Holborn. 



CAST AND WROUGHT IRON BRIDGES. 



On the Strength of Materials as applicable to the construction of 

 Cast or Wrought Iron Bridges. Tart III. — " 0)i the Transverse (tr 

 Cross Strain."-* By George Buchanan, Esq., F.R.S.E., President 

 R.S.S.A. — (From a paper read at the Royal Scottish Society of 

 Arts.) 



The President stated that he proposed now to complete the 

 third branch of the subject — namely, the transverse strength of 

 MATERIALS, but would iirst advert to one or two points connected 

 with the preceding expositions, namely : — 



First, the Conway Tubular Bridge, in regard to which it was 

 gratifying to observe, that it had now been in operation for up- 

 wards of three months, the regular traffic of the line going on, 

 and trains passing and re-passing daily, everything connected with 

 it proceeding in the most satisfactory manner, and this truly won- 

 derful design crowned with complete success. He then exhibited 

 a drawing of the great Britannia Bridge, now in progress of ex- 

 ecution across the Straits of Alenai. This was exactly on the 

 same principle as the Conway Bridge, but on a still more magnifi- 

 cent scale, the Straits liere being so much wider, and the bridge, 

 in order to keep the navigation free from obstruction, being ele- 

 vated 102 feet above the surface of the water at the highest 

 equinoctial tides. The breadth across the Straits at high-water 

 is about 1,160 feet; and, including the banks to the abutment 

 piers of the bridge, 1,490 feet. This space is divided into four 

 spans by a massive pier in the centre of the water-way, termed 

 the Britannia Tower, 45^ feet thick, and two small piers or tow ers 

 in the water at each side, 32 feet each, forming two spans in the 

 centre, 460 feet in length each, and two half spans, one on each 

 side, 230 feet. * 



Secondlv, having been particularly requested by the Society, at 

 the last meeting on this subject, to extend and complete his expe- 

 riments on the tensile and compressive strengths of different 

 stones, he would now state the result of these experiments. The 

 mode of trying the direct tensile strength was formerly exhibited 

 by appending weights to the substance till it was actually torn 

 asunder. In this way the strength of the different stones, by 

 careful and repeated experiments, was found at an average as 

 follows, viz. : — 



Craigleith stone 



Hailes 



Redliall 



Humble 



BinDie 



Breaking weight. 

 453 lb. 

 336 



28:i 

 27S 



Several other specimens had been prepared of marble, whinstone, 

 Caithness and Arbroath pavement, and the results on these would 

 be afterwards communicated. 



The compressive strength of these substances, or their power to 

 resist crushing, being generally far beyond their tensile strength, 

 could only be tried conveniently by mechanical power, and he 

 showed the apparatus nhich had been used for the purpose, con- 

 sisting of a combination of two levers, giving an increase of 

 power of 30 to 1. The sjiecimens, consisting of nearly exact cubic 

 inches of the material, being placed near the centre of motion, 

 and the upper lever brought down with a plate of metal to fall ex- 

 actly on the stone, the weights were applied at the extreme end of 

 the lower lever until the stone gave way. On trying, at the meet- 

 ing, with this apparatus a piece of Hailes stone, it bore 3,540 lb., 

 and then gave way with a violent crash. A specimen of Craig- 

 leith stone was next tried, the side of the cube being about one- 

 eighth part more than a square inch. This carried upwards of 

 6,500 lb., when the sides began to skirt oft', and with 6,81011). it 

 suddenly gave way, and was crushed to powder. In all these ex- 

 periments it was' obser\ed that when any part of the stone re- 

 mained entire, it exhibited the same appearance noticed by Hodg- 

 kinson in the fracture of cast-iron ; pieces breaking olt' at the 

 sides at certain angles, and leaving a nucleus of a conical shape. 

 Specimens of these were preserved, and may be shown at another 

 meeting. By experiments of this kind, carefully made and re- 

 peated, he had found the compressive strength of the different 

 stones as follows : — 



Craigleith, gave way to a pressure of 4,iH)0 lb. 



Huml)ie .. .. a.74U 



Hailes .. .. a, .WO 



Redhall .. .. 3,32" 



Binnie .. .. 2,t52ll 



In regard now to the transverse strain, this, as formerly ex- 

 plained, is of a compound nature, both the tensile and compres.sive 

 forces being brought into play. A beam supported at the one 



* For the two previous portious ol this paper, see "Journal," vol. xi., p. 125, aud 153. 



