Handbook of Railroad Construction; For the use of American engineers. / Containing the necessary rules, tables, and formulæ for the location, construction, equipment, and management of railroads, as built in the United States.

by George L. Vose

Generally in place of writing a × b to express multiplication, we put simply a b.

The above signs may be compounded in any manner; thus,

∜([(a + b)c
d]/m]¾).

Here we have, first, the product of c by the sum of a and b; this is divided by d, and three quarters of the quotient is divided by m; and, finally, the fourth root of the last result is extracted, which is the value of the expression.

The following examples show the use of formulæ. See Chapter VI., on Earthwork, art. Average Haul:—

Required the average haul of several masses of earth. Let m m′ m″ mⁿ represent the several masses, and d d′ d″ dⁿ the respective hauls; S the sum of the masses, D the average haul, and we have

D = m d + m′ d′ + m″ d″ + mⁿ dⁿ
S.

If we make the values	m	=	100	also	d	=	100
	m′	=	200		d′	=	50
	m″	=	300		d″	=	75
	mn	=	400		dn	=	200

the sum is 1000, and we have

D = 100 × 100 + 200 × 50 + 300 × 75 + 400 × 200
1000 = 122.5 ft.