36t 



THE CIVIL ENGINEER AND ARCHITECT'S JOURNAL, 



[^December, 



)seA 



j\'(>. i. Mr. Sopwitli's: this on trial seemed altotjetlier too com- 

 plicated, and the suljdivi.sions too minute. Mr. Bourne's remarks 

 on this staff seem decidedly judicious — page 21 1 of the work before 

 (juoted: "Several attempts liave been made at improvements in 

 tliis (Mr. (Jravatt's) staff, but their success is very problematical. 

 Mr. Sopwith, for instance, has introduced one in which distinctive 

 figures are attached to every-other 100th of a foot; the mechanical 

 construction also differs from this, — it is more elaborate, which 

 consequently makes the staff more expensive. It is very neat, 

 however, but is subject to injury in windy weather." 



A'o. 5. A staff of my own invention, constructed with cylinders 

 of block-tin, the largest 3d inches diameter, to slide one within 

 another, which seemed to afford great strength and lightness, and 

 fonned besides a case to carry plans in, — the particular object 

 aimed at being, by obtaining a surface of 9 to 11 inches, to mark 

 every 100th of a foot by a dot and figure, running in a spiral line 

 from bottom to top; it should of course revolve slowly during 

 observation. On actual trial, however, Mr. Gravatt's staff seemed 

 jireferable. 



Ao. 6. A staff which, on actual trial, seems capable of being 



read with more distinctness at short distances tlian any staff now 



in use, and with facility at between four to five times the usual 



distance; it is graduated by an application of the upiight vernier, 



the principle of which is usually expressed 



in the formula, 



(« — 1) L = nV; 



., L-V=L-^L=liL = 'L. 



n n 



* L and V being the length of a division on 

 the staff and vernier respectively. And 

 since to propose any form of sliding ver- 

 nier would have been at once rejected, as 

 introducing the old vane in a new form, I 

 have got over the difficulty in the following 

 manner; — 



By inspecting the diagram, it will be seen 

 that there are 9 rows, or columns of stars 

 or dots, which it is impossible to confuse 

 in a lateral direction one « ith another. The 

 initial position of the first star in the first 

 of these rows is zero on the staff; the 

 others follow in regular succession at in- 

 tervals of lOOth-foot between each; then, 

 all the stars in any one row are y^Tiths of 

 a foot from centre to centre, while the 

 lines dravvn across mark -njtlis of feet as 

 usual: one star will therefore be found at 

 every -^th-foot, which is useful to recol- 

 lect in graduating a staff in this manner. 



In reading such a staff, we first read the 

 feet and rnths of feet as usual; then, sup- 

 pose the cross-hair of the diaphragm to 

 occur anywhere within some particular 

 •jijth, observe whicli dot or star it inter- 

 sects, then count dots or stars upwards, in 

 its vertical line, until a coincidence with a 

 horizontal line is found: the numbers so 

 counted will represent smiths of feet, and 

 consequently gives us the second decimal 

 place. '^ 



E^FjFy^-^^-'P^ The great advantage gained is simply this: 



vJ Cr that wliereas in all the staves now extant, 



14* I ♦ M W6 'ire obliged to distinguish between';hun- 

 J^HH^B ■ I dredths, to obtain tlie second place; in this 

 levelling staff, we attend to no subdivisions 

 less tlian -j-lj^ths-foot apart, to obtain equal 

 accuracy. On trial, it will be found that this staff can be read 

 with facility at yj-mile sights: I found it practicable at 35 and 

 40 chains, witli a 12-in. focus. 



I sliouid reconimend the horizontal lines to be put in in Ver- 

 million, as the contrast between black and vermillion will be 

 found distinct at the utmost distance at which any staff can be 

 read. 



♦ ♦ 



♦ U 



♦ 



♦ 



'Royal Agricultural College, 

 Cirencester, November 9th, 18+9. 



J. D. Pembebton. 



PRESSURE TO SUSTAIN BANKS OF EARTH. 



On the Maximum Amount of Resistance, acting in any direction, 

 required to sitstain Banks of Earth, or other materials, vith Sloping 

 Tops and Faces, and the effects of Friction between the Face of the 

 Rank and the Back of a Retaining Structure. By J. Neville, Esq., 

 Dundalk, County Surveyor of Louth. — (I'aper read at the Koyal 

 Irish Academy.)* 



If CDE be any bank with a sloping face CD, and a sloping top 

 DE; CE tlie position of the plane of repose, CF tliat of the plane 

 of fracture, and the arrow R that of the resistance: put 

 c = the angle of repose; 

 c =; the complement of the angle of repose; 

 fi =: the angle DCE contained between the plane of repose snd 

 the face of the bank; 



5 := the supplement of the sum of the complement of the angle 



of repose, and the angle which the given direction of the 

 resistance makes with the face; 



6 := the angle KDF, contained between the face produced and the 



top of the bank; 

 f ::= the angle DCF, contained between the plane of fracture and 



the face; 

 h = the length of the fare CD; 

 w = the weight of a cubical unit of the bank; 

 R = the resistance. 



Then, when tlie resistance is a maximum, 

 tan3v'(tan 6 tan 5) 



tao If = 



V(iiaeiaaS) + -v/Ktan /8 + tan S) x (taa fl— tan (3)] 

 wh^ tan B sin i8 tan B 



R = 



2 cos S 



1 



(I) 



(2) 



V A/[taii 5 (tan 6 — tan ;8)] + ^/[tan 9 (tan 5 + tan fl)] 



Equation (1) furnishes the following geometrical construction 

 for finding the fracture CF. Draw any line GH at right angles to 

 the face produced, cutting the slope DE at H and the line DG; 

 making the angle GDK=5 at G : on GH describe a semicircle 

 cutting the face produced in I : draw Dc parallel to the plane of 

 repose CE, meeting GH in e: draw eO parallel to KI, meeting the 

 circumference in O: make I L equal «0 ; draw I/' parallel to Le, 

 and CF parallel to T)f: CF is the fracture requiring a maximum 

 resistance to sustain the hank CDF. 



If the top lying between F and D be loaded with a given weight, 

 the values of ip and R are rigorously determined from the equations 

 by producing the top ED torf, so that tlie triangle CDrf, multiplied 

 by w and the length of bank acted on, may be equal to the given 

 weight, and then substituting the new values of h, 5, 6, and 8, cor- 

 responding to the face Crf and top Erf, in the equations, in place of 

 those to the face CD and top ED. 



When the resistance is generated by the pressure of the bank 

 against a structure at the face, 5 may be taken equal 2c'. Thus, 



tan 3A/(iaii 6 tan 2c') 

 tan 0= ^ 



^/(tan e tau 2c') + ^/[(tan B- tun j8) x (tan + tan 2c')] 

 wA' sin B tan ;8 tan 8 

 ¥ ' cos 2c 



V[tan 5 (tan B — tan /3)] + V[lan 8 (tan 2c' + tan B)} 





(3) 



m 



* ' Proceedings of the Royal Irish Academy,' Vol. W. Part 2. 



-i Equatioug (3) and (4J dvteiniirie the diieclioD uf the fracture CF, and value of the 



