682  Mr,  E.  Buckingham  on 
on  by  no  external  forces  except  a  uniform  normal  pressure, 
we  have  de=0dv-pdv, (10) 
which  is  merely  a  statement  of  the  two  laws  of  thermo- 
dynamics for  such  a  system,  77  representing  the  entropy. 
If  the  process  is  isothermal,  we  may  write  equation  (10)  in 
the  form 
fe)i-'(S).-' «"> 
To  give  this  a  physical  meaning  we  have  to  eliminate  the 
entropy  tj,  by  means  of  the  familiar  "  thermodynamic 
relation  " 
thus  obtaining  the  equation 
(!).=-"«(»), fDi 
§  5.  By  comparing  equation  (D)  with  (A),  (B),  and  (C) 
successively,  we  get  three  equations  which,  when  slightly 
transformed  by  means  of  the  relation 
may  be  written 
'(»\— +"^ (E) 
•IS),--* (F> 
•(SX-*** (G) 
and  which  give  relations  between  0  and  the  data  to  be 
obtained  from  the  three  experiments.  Expressing  these  in 
integral  form  we  have 
log 2r  =  1    tv  ( 7?  =  7r  =  constant),     .     .      (H) 
log^-=l     (p= 77  =  constant),     .     .      (I) 
loeV=|     ^        {v=<f>  =  constant),     .     .      (J) 
Po< 
