=Thickness of Lining Masonry.=--It is obvious, of course, that the masonry lining must be thick enough to support the pressure of the earth which it sustains; but, as it is impossible to estimate these pressures at all accurately, it is difficult to say definitely just what thickness is required in any individual case. Rankine gives the following formulas for determining the depths of keystone required in different soils: For firm soils ( _r_²) _d_ = √(0.12----), ( _s_ ) and for soft soils, ( _r_²) _d_ = √(0.48----), ( _s_ ) where _d_ = the depth of the crown in feet, _r_ = the rise of the arch in feet, and _s_ = the span of the arch in feet. Other writers, among them Professor Curioni, attempt to give rational methods for calculating the thickness of tunnel lining; but they are all open to objection because of the amount of hypothesis required concerning pressures which are of necessity indeterminate. Therefore, to avoid tedious and uncertain calculations, the engineer adopts dimensions which experience has proven to be ample under similar conditions in the past. Thus we have all gradations in thickness, from hard-rock tunnels requiring no lining, and tunnels through rocks which simply require a thin shell to protect them from the atmosphere, to soft-ground tunnels where a masonry lining 3 ft. or more in thickness is employed. Table II. shows the thickness of masonry lining used in tunnels through soft soils of various kinds. The thickness of the masonry lining is seldom uniform at all points, as is indicated by Table II. Figs. 46 and 47 show common methods of varying the thickness of lining at different points, and are self-explanatory. [Illustration: FIGS. 46 and 47.--Transverse Sections of Tunnels Showing Methods of Increasing the Thickness of the Lining at Different Points.] =Side Tunnels.=--When tunnels are excavated by shafts located at one side of the center line, short side tunnels or galleries are built to connect the bottoms of the shafts with the tunnel proper. These side tunnels are usually from 30 ft. to 40 ft. long, and are generally made from 12 ft. to 14 ft. high, and about 10 ft. wide. The excavation, strutting, and lining of these side tunnels are carried on exactly as they are in the main tunnel, with such exceptions as these short lengths make possible. Table III. gives the thickness of lining used for side tunnels, the figures being taken from European practice.