891-92.] Dr W. Peddie on Transformation of Energy. 253 
Note on the Law of Transformation of Energy and its 
Applications. By W. Peddie, D.Sc. 
(Read May 16, 1892.) 
The investigation of the relations which subsist amongst various 
physical quantities, and which are exemplified in the different trans- 
formations of energy, is one of the most interesting investigations in 
the whole range of physics. On the other hand, the mathematical 
methods which are usually employed for this purpose are of such a 
nature as to be unavailable to any who are unacquainted with higher 
mathematical methods. It is one of the objects of the present note 
to point out how these relations may be worked out by means of the 
most elementary methods. For the notation of the calculus, though 
used below as a matter of convenience, is quite unnecessary, since 
we might use, e.g., small and capital type of the same letter to 
denote quantities of the same kind of different magnitudes. 
The first relations of this kind which were investigated were 
those exemplified in the transformation of heat into mechanical 
work. In any such transformation, the dynamical principle of 
conservation of energy holds good ; but it was found necessary to 
introduce another principle — the Second Law of Thermodynamics — 
before the problem could be fully solved ; and this principle is not 
explicitly dynamical, but is based upon an axiom in agreement with 
experience. Further, when we pass from thermo-mechanical trans- 
formations to transformations between two forms of energy of which 
heat is not one, no law corresponding to the Second Law of Thermo- 
dynamics has been formulated. On the contrary, it is generally 
stated that, in these cases, this method reduces to- the use of the 
principle of conservation alone — a principle which is often not suffi- 
cient for the purpose. A second object of this note is to show that 
the application of the principle of conservation to a certain cycle 
of reversible transformations directly expresses the principle of 
degradation of energy and leads to the generalised analogue of the 
Second Law. 
Let us denote the quantities which fix the physical condition of 
