The total energy is the product QI, _i.e._ the product of the total quantity by the total intensity at our disposal. The transformed energy is Q(I - I'), the product of the total quantity by the difference of intensity at the inlet and at the outlet of the machine. The formula for efficiency thus becomes Q(I - I') / QI = (I - I') / I. If I represents a temperature, then in order that the efficiency may be positive I' must be less than I, {104} there must be a fall of temperature in the machine. If I' were greater than I, _i.e._ if the temperature at the outlet were greater than that at the inlet, the efficiency would be a negative one, and the transformer would have to borrow heat from some external source. _Entropy._--In every transformation of energy a certain portion of the energy is transformed into heat: a lamp gives out useless heat as well as light, a machine gives out useless heat as well as mechanical work. This loss of useful energy as heat occurs in every transference or transformation of energy; it is only in the case of heat passing from a hotter to a colder body that there is no such transformation. When equality of temperature is established there has been no loss of energy, but the whole of the energy has become unutilizable, i.e. untransformable. In the formula of efficiency the fall of intensity I - I' is now zero, and therefore the efficiency of the machine (I - I') / I is also zero. Since in all its transformations a certain fraction of the energy is changed into heat, there is a tendency in nature for all differences of temperature to become equalized. Hence the quantity of utilizable energy in the universe tends to diminish. Clausius called this unutilizable energy enmeshed in the substance of a body its entropy, and showed that in every transformation the amount of this unutilizable energy tended to increase. "The entropy of a system always tends towards a maximum value."