(3)
Z = Cv2/abc (dynes),
(4)
so that Z is the fraction C/Mab of the centrifugal force Mv2/c, or the fraction C/Mh of its transference of weight, with h the height of the centre of gravity of the carriage above the road. A Brennan carriage on a monorail would lean over to the inside of the curve at an angle α, given by
tan α = G′μ/gMh = G′v/gMhc.
(6)
The gyroscopic action of a dynamo, turbine, and other rotating machinery on a steamer, paddle or screw, due to its rolling and pitching, can be evaluated in a similar elementary manner (Worthington, Dynamics of Rotation), and Schlick’s gyroscopic apparatus is intended to mitigate the oscillation.
6. If the axis OC in fig. 4 is inclined at an angle α to the vertical, the equation (2) § 4 becomes
N = sin θ (Aμ2 cos θ − G′μ) + gMh sin (α − θ).
(1)