TRANSACTIONS OF SECTION A. 345 
entropy is greater than heat received divided by temperature of reception is thus 
removed. : 
Applying his definition of heat as a test to the internal energy of a body, the 
author showed that it consists of two distinct portions—one which falls within his 
proposed definition of heat, and one which does not. ‘The first portion is called 
the thermal energy of the body, the second portion its non-thermal energy. The 
thermal energy of a body is equal to the product of its entropy into its absolute 
temperature. This thermal energy can be increased in two ways. In the first 
place, by raising the temperature of the body without increasing its entropy. 
The increase of thermal energy in such a case takes place at the expense of 
non-thermal energy, and is quantitatively equal to the increase of the temperature 
of the body multiplied by its entropy during the increase. The thermal energy of 
a body can, secondly, be increased by a fresh supply of heat without raising’ its 
temperature. In such a case the increase of entropy of the body multiplied by its 
temperature during the increase is equal to the fresh supply of heat. Both modes 
of the increase of the thermal energy of a body can take place simultaneously. 
To use mathematical symbols, let ¢ be the absolute temperature, d the entropy, 
and H the thermal energy of a body. 
Then H = ¢¢, and dH = ¢dt + tdd, pdt represents the increase of the thermal 
energy of the body by the first mode, tdp represents the increase of its thermal 
energy by the second mode. 
Let E represent the total internal energy of the body, then its non-thermal 
energy is equal to H—H = E— ¢¢. 
This division of the internal energy of a body into a portion which is thermal 
and a portion which is non-thermal is free from the defects which attach to Helm- 
holtz’s mode of dividing it into a portion which is ‘fres’ and a portion which is 
latent or ‘ bound.’ 
The heat contained in a body does not alter its thermodynamic properties when 
radiated into space. What is generally catled radiating energy falls within the 
definition of heat proposed by the author, and is heat. Thermodynamically, the 
only difference between radiant heat (including light) and body heat—i.c., the 
thermal portion of the internal energy of a body—is that the latter is associated 
with ordinary matter, whilst the former is associated with the free ether of space. 
All thermodynamic properties of heat are contained in the statement that heat is 
the product of entropy and temperature, and this statement applies to radiant 
heat as well as to kody beat. 
The author next proposed to give a physical interpretation, readily grasped by 
the understanding, of the thermodynamic meanings of temperature and entropy. 
Two assumptions are involved in this interpretation. The first assumption is that 
body heat and radiant heat possess the same thermodynamic properties, because 
they possess essentially identical physical properties. According to this assump- 
tion, which is legitimate on logical grounds and is supported by a number of 
physical facts, the heat of a body, or its thermal energy, is that portion of its 
internal energy which possesses physical properties essentially identical with 
those possessed by radiant heat, whilst the non-thermal energy of a body possesses 
physical properties different from those possessed by radiant heat. Since radiant 
heat (including light) is known to be vibratory in nature, the thermal energy of a 
body must likewise be vibratory in nature. If radiant heat is a periodic electro- 
magnetic disturbance, then the thermal energy of a body must also be some form 
of periodic electro-magnetic disturbance. One of the simplest mechanical models 
of vibrator disturbance is presented by a stretched elastic string which has been 
put into vibratory motion. The vibratory energy of such a string is equal to the 
product of two quantities, x and e, of which x represents the number of independently 
vibrating parts of the string, and e the energy associated with each independently 
vibrating part. The properties possessed by 2 and e can be shown to correspond to 
the properties possessed by entropy and absolute temperature respectively. The 
author proposes the view—which forms the second assumption—that the vibratory 
energy called heat consists of a number of separate vibratory disturbances, and 
that entropy represents the number of separate disturbances, whilst absolute 
