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This construction has been termed a twin tunnel, and a typical cross-section is shown on Plate XII. The tunnels continue on tangents under the streets to Second Avenue where they curve to the left by 1° 30' curves, passing under private property, gradually diverging and passing through shafts just east of First Avenue.
But Leonardo da Vinci supposed that the sky owed its blue to the darkness of vast space behind the white lens of sunlit air; and perhaps where the sea presents through the extent of its depth, as it slips over into other hemispheres, tangents with the illumined atmosphere beyond, it affords a finer filter for these blue rays, and thenceforth hoards in its heart the wealth and beauty of tint found in that line of ultramarine.
This growing bewilderment and stress of fear had kept them moving in uncertain rounds, varied by occasional abrupt tangents, until within zone of most heinous crimes, when drawn by that gravity existent between the criminal and the venue of his offense, both had landed in London, fearful for the future, without any decisive purposes or settled convictions as to their lines of action.
Over the deserted plains it tore, comet-like, a meteor preceded by a streamer of light. It swung to the banked curves with no slackening of momentum; it devoured the tangents hungrily; the night wind roared past, drowning all other sounds.
The maximum curvature as first located was 10°, but for economy of time as well as money this was exceeded in a few instances as the work progressed, but is now being by degrees reduced. The maximum grades on tangents are 116 feet per mile; on curves the grade is equated one-tenth to a degree. The masonry is of the most substantial kind, granite viaducts and arch culverts.
Nothing can be more convincing and satisfactory than all the conclusions concerning the properties of circles and triangles; and yet, when these are once received, how can we deny, that the angle of contact between a circle and its tangent is infinitely less than any rectilineal angle, that as you may increase the diameter of the circle in infinitum, this angle of contact becomes still less, even in infinitum, and that the angle of contact between other curves and their tangents may be infinitely less than those between any circle and its tangent, and so on, in infinitum?
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