32fl 



THE CIVIL ENGINEER AND ARCHITECT'S JOURNAL. 



LNOVBDBEE, 



A long scale of equal parts (H) is formed at the edge of a 

 groove, and another (V) slides in contact with this, as shown in 

 the figures. H represents the horizontal measurements commonly 

 taken witli the chain, and should e.xtend from to about 150 feet. 



(kltuiff 



£1 

 Zf 



n 

 nf 

 6 



£ 



Z 



fl 



A 



3. 26 

 . 2S 

 30 

 3Z 

 3i 

 3G 

 .38 

 r,o 



IZ 



a 



Pip. S. 

 Slide arranged for determining 

 tlie Widlh of a Cutting. 



Fig. 4. 

 Slide arranged for determining 

 the Width of an Embankment. 



If the instrument be made of box, H may contain 10 feet to the 

 inch, and each foot may be divided into 5 equal parts. The slide 



V corresponds to, and must at least contain as many feet as are 

 marked on the levelling-staff. The scale on V, as shown in the 

 figures, is for a slope of 1 J to 1 ; for l^ foot on H is equal to 1 foot 

 on V. Other slides will be required for other slopes. 



In the example of a cutting previously calculated, we found that 

 '( n' ■= 42-5 feet. Bring 0, on slide V, opposite 42-5 on H (fig. 3). 

 The staff is set up at/', and the reading is found to be C-S. Refer 

 to V with 6-5, and opposite this point we find x = 32'8 on H, 

 without any calculation. 



But the measured distance y is 22-00 ; .". y is not = .r. 



Again, the staff is set up at other points, and the trial repeated 

 till we come to the point c', where the reading of the staff (/»') is 

 10-7 feet. Refer to V with 10-7, and opposite it we find 26-5 on H, 

 which differs only by the 4^t\i of a foot from the result previously 

 given by calculation. 



As r k has to be auhtracted from a a' in cnttinff>.; it is necessary 

 for the scales V and H to be numbered in apjumte directions, as in 

 fig. 3. But in eiiiha)ilcni(/iiti', rh must he arldvd too n', and the scales 



V and II must increase in the same direction, as in fig. 4. This is 

 the reason why the slide has two scales, differently numbered. 

 Fig. 4 corresponds to the numerical examide given al)Ove for an 

 embankment : on V being placed opposite 59-9 on II ; and 10-05 

 on V falls opposite 75 on H. 



AVe liave hitherto supposed that zero on the scale V is placed 

 opposite a a', the horizontal width at the level of the line of col- 

 limatinn. Now, the value of a o- is dependent on the accidental 

 position of the level, and must he calculated in the field. Sup- 

 pose, however, that the half-\vidths at the levels of the centre- 

 pegs have been determined, and registered previously to commenc- 

 •og: operations. In the example of a cutting (fig. 1), we supposed 



B A to be = K =:t 26-2 : .•. the half-width, supposing the ground 

 to be level, = r K = 1 1 X 26-2 := 39-3 ; and h was taken = 2-13. 

 And the result is the same, 



whether we place 2-13 (or h) on V opposite 39-3 on H, 

 or on V (q)posite 42-5 on H. 



The first method will be found the best, because all the half- 

 widths at the levels of the stakes may have been previously deter- 

 mined in the office. The same may be said of fig. 4. 



It will be found convenient to have an index capable of sliding 

 along 11, inde])endently of V, and capable of being fixed at plea- 

 sure. This may be formed partly of a piece of horn, or other 

 transparent substance, having a line ruled parallel to the divisicms 

 of the scales. This will be of great service where the ground ia 

 very sloping, and it becomes inconvenient to hold the levelling- 

 staff on every peg. 



If, in figs. 1, aiul 2, the ground had been so low that the top of 

 the staff c' e fell below the line of coUimation, it would have been 

 necessary to have shifted the level, and a a' would have taken a 

 new position and value. It will, however, be found an easy matter 

 to determine B o, and therefore also a a\ in all cases ; and on V 

 must then be placed ojiposite this value of a a' on H. 



Or, calculation may he avoided even in this case. Fig. 1. Sup- 

 pose the first reading at a to be 2-15, and the half-width at the 

 level of A, 39-3 feet. Bring 2-15 on V opposite 39-3 on H. Let 

 the staff be held at any point, and take the reading 9-55, suppose. 

 Slide the index along H to point to 9-55 on V. 



Remove the level to a new position D', and adjust it, and sup- 

 pose the back sight taken in the ordinary way to be 3-2. Move 

 the scale V, so that the index points to 3-2 on V ; and the instru- 

 ment is adjusted for the cross-section at A, so long as the level is 

 not disturbed. 



The index will be found very serviceable where it is not conve- 

 nient to commence levelling from every centre-stake. Suppose 

 the centre-pegs to be one cliain apart, and that the gradient rises 

 5 in every chain. 



We have seen that the distance Bn of the horizontal plane 

 through a a' from B is := H -|- A (fig. 1), as the gradient is sup- 

 posed to rise 5 feet in a chain, at a point corresponding to B ; but 

 a chain from it, the new value of n B becomes (K -|- h — S) ■ 

 and the new lialf-width a a' becomes }- (K 4- /') — '' S. 



If we take an embankment (fig. 2), the new value of a B be- 

 comes (K — A -^- S) at the distance of one chain ; 



and the new value of the half-width a a' = r (K — h") -\- r 5. 



Thus, in a rising gradient, S for every chain, we must move the 

 slide by the scale H, a distance r 5 ujjwards for cuttings 1 



and a distance r 5 downwards for embankments J 

 But r 5 on the scale H is the same in magnitude as 5 on the scale 

 V, and therefore it will be most convenient to employ the index in 

 moving the slide V upwards or downwards, through a space 5 for 

 every chain. 



It may be useful to remark that for a rising gradient the slide V 

 has to be moved in that direction in which the numbers of the feet 

 on V increase, as denoted by the arrows, whether the case be one 

 of cutting or embankment. If there be a falling gradient, the 

 slide V must be moved in the opposite direction. 



It will be found convenient to be provided with the height of 

 each stake above some common datum; the half-width, supposing 

 the ground to be level ; the numbers and distances of the stakes, 

 with particulars respecting the gradients, slopes, &c. Also, vacant 

 columns must be prepared to recei\'e the half-widths on each side, 

 as they are determined, and the corresponding reading of the 

 level. The point on H to which the zero on V is opposite, ought 

 also to be registered. This last is very useful where a number of 

 consecutive side-stakes are determined without starting from the 

 centre ; and doubts might otherwise arise as to whether the proper 

 correction had been made for the gradient in every case. 



As this slide-rule has been used where the ground was remark- 

 ably uneven, both for determining the widths of cuttings and em- 

 bankments, and the limits of embankments at the ends of viaducts, 

 I can strongly recommend it to the attention of those practically 

 engaged on such work, as it avoids much trouble and uncertainty, 

 and the result is as accurate as can he desired by the most fastidi- 

 ous. An addition to the widths above found must be made to 

 allow for the ditches and fences. 



67. John's CoUet/e, Cambridge, Francis Bashfobth. 



Oct. 2l' 1848. 



