200 



THE CIVIL ENGINEER AND ARCHITECT'S JOURNAL. 



fJvLV, 



Greater Heights. 

 35, 56 

 .56, 39 

 39, 45 



Tab. Nos. 

 2575 

 2787 

 2159 



Total 7521 

 Mult, by difF. of slopes 2 



Subtract 



15042 

 3392 



3392 



11,650 Answer. 



If the sections were at unequal distances apart — say 2, li, 3 

 chains — each tabular number would have to be multiplied by the 

 corresponding distance. The above e.vample would tlien be modi- 

 fied as follows : — 



Tab. Nos. Distance. Product. Tab. Nos. IJislante. Product. 



2575 X 2 = 5150 295 X 2 = 590 



2787 X li = 3716 3.30 y, H = 440 



2159 X •' = 6+77 223 X 3 = 669 



Total 1 5343 



30686 

 Subtract 6796 



Total 1699 

 4 



6796 



23890 Answer. 



To extend the large table where either height e.\ceeds 60, take four 

 times the tabular number for half the given heights. For instance, 



the tabular number for {lOO, 20 } is four times that for {50, lo} • 



To extend the small tahh\ where either height exceeds Ha, add the 

 tabular numbers for any two heights which together make up the 

 given height. For instance, the tabular number for 60 is the sum 

 of the tabular numbers for 50 and 10, or of those for 55 and 5, &c. 



To find the tabular number in the greater table. Look for either 

 height in the horizontal row of inde.\ figures, and for the other 

 height in the vertical row of indices. Tlie tabular number re- 

 <iuired is beneath the one inde.x and opposite the other. In the 

 f-mall table used for le^•el-lying ground, only one inde.x figure is 

 used : the tabular number required is opposite it in the column 

 designated by the given widtli of the formation level. For other 

 widths than those given in the table, multiply the number to " base 

 1 foot" by the given width. — Exatnjile : The number for height 27 

 to base 22 is 22 X 33. 



Measurement nf slopes. — The slopes on railways are measured by 

 the horizontal distance corresponding to one foot vertical rise. If, 

 for instance, the rise of one foot correspond to a horizontal dis- 

 tance of 25 feet, the slope is 2.i (to one). The same mode of mea- 

 surement is adopted here for the natural inclination of the ground 

 as for the artificial inclination of the sides of the embankment or 

 cutting. 



Change of the natural slope may occur in sidelong ground where 

 the s\irface is very irregular. The sections ought to be taken so 

 near that the difference of slopes at two successive sections may 

 not be considerable. Now, by using exclusively the greater of 

 these natural slopes with the actual heights, the result would be 

 too large : by using the smaller of them, too small. But as the 

 results obtained in these two ways will not in general widely diifer, 

 the truth may be taken as a mean between them. 



The difficulty arising from change of natural slope may however, 

 in general be avoided. For the upper surface of the ground being 

 undulating and irregular, the natural inclination is represented by 

 equalising lines drawn so that the small curvilinear areas in excess 

 and defect may balance each other. These e(pialising lines being 

 in some degree arbitrary in position, nuiy in general be drawn at 

 the same inclination for several sections together. 



*jf* These tables, arul the method of usiny them, ore original and copyright. They are 

 published separately bv Weale, Holborn. 



10 



i 

 11 



12 



i 

 13 



i 

 14 



15^ 

 i 

 16 



17 



is' 



19' 

 20 

 21 



22 



23 



i 

 24 



25; 



26^ 



27* 

 28* 

 29* 

 30* 

 31* 

 32* 

 33* 

 34* 

 35* 



36 ; 



37' 

 38' 

 39 

 40 



41 



J 



42' 



43 



44; 



45 



46 



47 



48' 



49 



50 



51 



52 



53 



54 



55 



