Mass, Weight, and Dynamical Units

Abstract

IF the laws of dynamics were made solely for the use of engineers, as a celebrated engineer declared of rivers that they were intended to feed canals, it might be conceded to Prof.Greenhill that it would not be necessary that the more abstract notion of mass should be distinguished from that of weight, and that the fundamental equation of dynamics might conveniently be taken as P=Wf/g, where W is the weight (or mass) of the body moved expressed in pounds or tors &c., and P the force producing in it the acceleration f, and reckoned in the same units. But a pound weight as a force is a variable unit, unless it is taken at some particular place (as Greenwich), and then theorresponding value of g must be employed (though the variation of g on the surface of the earth is not so great as often to need to be taken account of by the engineer); and so the astronomer and physicist, as well as the student of abstract dynamics, are right in demanding a less arbitrary measure of force than one founded on the force acting vertically downwards on a body at the earth's surface, as well as an absolute constant belonging to each body (its mass) independent of time and place. I conceive, therefore, in spite of Prof. Greenhill's arguments, that, in the interest of clearness of thought, as well as to avoid the practical inconvenience of a variable unit of force, the notions of mass and weight must be kept distinct, and the equation W=Mg, as a special case of the general equation P=Mf, still insisted on by all teachers of dynamics, at any rate to non-engineering students; while it would be well for engineers also (me judice) to have their dynamics cast in the same mould as the rest of the scientific world.