344 REPORT—1905. 
From the point P’ ONP appears counter-clock-wise, while from X OYZ is clock- 
wise ; therefore the direction cosines of KP’ are 
_ma—ny _ne—lz _ le—my 
NP ’ NP ’ NP 
Projecting ONQP’ on OX we have at once 
aoe rp! v—lLON ac (may 
v'=ON .1+NP’ cos h.* NP -+NP’ sin p NP 
=x cos p + JON (1— cos h) —(mz~ny) sin ¢, 
and similarly for y' and z’. 
If the rotation be left handed we have only to change the sign of @. 
10. Graphic Methods in Spherical Trigonometry, 
Sy Professor G, H. Bryan, /.R.S. 
FPRIDAY, SEPTEMBER 1. 
The following Papers and Report were read :— 
1. A Restatement of the Second Law of Thermodynamics and its Bearing 
upon our Views of Heat and Radiation. By M. Burepen, ID. 
After discussing the conceptions involved in the definition of the absolute scale 
of temperatures, the author proposed a definition of heat which, ‘like the definition 
of absolute temperature, does not depend upon the peculiarities of particular 
substances or upon hypothetical views as regards the nature of heat and tempera- 
ture.’ 
The definition of heat proposed by the author is as follows: Heat is that form 
of energy which can only be made to produce work through a fall of temperature. 
The author showed how by means of this definition of heat much of the vague- 
ness and difficulty at present attending the exposition of the principles of thermo- 
dynamics can be got rid of. The proposed definition enables us to keep definite 
count of the amount of work which is converted into heat owing to the irreversible 
nature of a process. If, in dealing with the heat received by a body, we take into 
account not only the heat which is derived through conduction or radiation from 
a pre-existing store of heat, but also the heat which is generated through friction 
or analogous causes, then the increase of entropy undergone by a body during any 
process is always equal to the quotient of the heat received by its temperature 
during the reception of the heat, no matter whether the process be reversible or 
irreversible. The great difficulty which the student of thermodynamics at present 
experiences because of the statement that in an irreversible process increase af 
