Sorry fellows, thought you all spoke engineering shorthand...for instance: when 69 implied "hp=torque x time" he got the definition backwards, resulting in a quantity that doesn't make sense physically; I wrote "hp x time=torque, which has the correct dimensions.
The constant in the handbook formulas relating horsepower, speed, and torque arises because of the particular system of measurement used, and the constant will be different for each system of measurement, e.g. metric SI, British gravitational system, the inch,pound-force,second system used here in the USA and in Britain commonly, or cgs, electrostatic, etc. will each have their associated constants. In the British common system, the HORSEPOWER is by definition 550 ft lb of work being done each second. In the SI system, the unit for POWER is the WATT, one newton meter, or joule, of work done each second. The physical definition of POWER (horse, dog, or whatever) is:
POWER = WORK per UNIT TIME.
The dimensions are (force x distance)/time
69 said that POWER = TORQUE x TIME
The dimensions are (force x distance) x time