If properties of the thermal condition varying greatly from the tensions of gases had been chosen, this relation would have assumed very complicated forms, and the agreement between heat and the other energies above considered would not subsist. It is very instructive to reflect upon this point. A _natural law_, therefore, is not implied in the conformity of the behavior of the energies, but this conformity is rather conditioned by the uniformity of our modes of conception and is also partly a matter of good fortune. VI. THE DIFFERENCES OF THE ENERGIES AND THE LIMITS OF THE PRINCIPLE OF ENERGY. Of every quantity of heat _Q_ which does work in a reversible process (one unaccompanied by loss) between the absolute temperatures _T₁_, _T₂_, only the portion _(T₁-T₂)/T₁_ is transformed into work, while the remainder is transferred to the lower temperature-level _T₂_. This transferred portion can, upon the reversal of the process, with the same expenditure of work, again be brought back to the level _T₁_. But if the process is not reversible, then more heat than in the foregoing case flows to the lower level, and the surplus can no longer be brought back to the higher level _T₂_ without some _special_ expenditure. W. Thomson (1852), accordingly, drew attention to the fact, that in all non-reversible, that is, in all real thermal processes, quantities of heat are lost for mechanical work, and that accordingly a dissipation or waste of mechanical energy is taking place. In all cases, heat is only partially transformed into work, but frequently work is wholly transformed into heat. Hence, a tendency exists towards a diminution of the _mechanical_ energy and towards an increase of the _thermal_ energy of the world. For a simple, closed cyclical process, accompanied by no loss, in which the quantity of heat _Q₁_ is taken from the level _T₁_, and the quantity _Q₂_ is deposited upon the level _T₂_, the following relation, agreeably to equation (2), exists, _-(Q₁/T₁) + (Q₂/T₂) = 0_. Similarly, for any number of compound reversible cycles Clausius finds the algebraical sum _[sum]Q/T = 0_, and supposing the temperature to change continuously, _[integral]dQ/T = 0_ (4) Here the elements of the quantities of heat deducted from a given level are reckoned negative, and the elements imparted to it, positive. If the process is not reversible, then expression (4), which Clausius calls _entropy_, increases. In actual practice this is always the case, and Clausius finds himself led to the statement: 1. That the energy of the world remains constant. 2. That the entropy of the world tends toward a maximum. Once we have noted the above-indicated conformity in the behavior of different energies, the _peculiarity_ of thermal energy here mentioned must strike us. Whence is this peculiarity derived, for, generally every energy passes only partly into another form, which is also true of thermal energy? The explanation will be found in the following.