CABBS' PAPERS I AND 11 25 



The first and last steps depend merely on the infinitesimal char- 

 acteristic of the figure and the intervening step on the definition 

 of the iso-Hnes. Next, similarly, 



/dA 



\dv/ 



Vh — Vo Vb — Vp HP 



Er, \dv/^ _ Vh — Vo _ Vh — Vr _ HY_ 



Et ~ fdp\ Pt — po Pt — Pp TP 



Vt — Vo Vt — Vr TV 



Lecture XI. About anharmonic ratios and in particular their 

 independence of the choice of the secant fine VHTP inferable 

 from the physical interpretation above. 



Gases, pv = f(t). Laws of Boyle and Charles, Mariotte 

 and Gay-Lussac. f(t) = at. Practical measurement of Cp. 

 Theoretical measurement of Cv Measurements of E^ and Et. 



Lecture XII. Velocity of sound and its relation to the 

 thermodynamic constants. Experiment with standing waves 

 and lycopodium powder (Kundt's tube). 



It is found that for a gas C„ and Cp/Cv are constant within 

 close limits over a wide range of the pv diagram. The equation 



de = dQ - dW = dQ - pdv 



reduces to de = dQ = Cvdt for constant volume and integrates 

 into e = Cvt + V(v) where the constant of integration is a func- 

 tion of the volume. Similarly for constant pressure we have 

 6 = Cpt — pv -{- P(p). Comparing, and using pv = at, 



V(v) - Pip) = (Cp - C„ - a)pv/a. 



This indicates Cp — C„ — a = and F — P = 0, so that if the 

 zero of energy is taken at ^ = we have V = P = and the 

 equations of the gases are v 



€ = C,t = Cpt — pv, a = Cp — Cv 



Lecture XIII. Review of fundamental equations. Discus- 

 sion of differences between gas thermometer scale and absolute 

 temperature defined by Carnot cycles. Further integration of 



