14 The Rev. J. M. Heatli on the Production of Heat 



tions, this would be of slight consequence, as the work would 

 be performed once for all. 



In conclusion, I will add one other rule — namely, for inter- 

 polation between the oceanic meteorological observations when 

 smoothed, as before suggested. This is a formula for inter- 

 polation in the case of a function of three independent variables, 

 the values of which are given at equal intervals, as is the case 

 in the mean barometer-heights in latitude, longitude, and time. 



Let A, D be the differences between successive barometer- 

 heights in latitude and longitude respectively, and 8 the dif- 

 ference in time (that is to say, between the values for suc- 

 cessive months). Then, following the former notation, 



+ ^2^?(?-1)A^ + ^(^-1)D^ + t(t-1)S-^ 



+ 2f ;/ AD + 2vTm + 2t|8A \ 

 + &c. 



The proof of this will be obvious to those acquainted with 

 the Calculus of Finite Differences. No doubt it has been 

 given before, although I do not happen to have met with it. 

 This formula enables us to pass from the regular equidistant 

 values for the middles of squares and months to those for any 

 other neighbouring time and place. 



II. On the P7'oduction of Heat hy Dynamical Action in the 

 Compression of Gas. By the Rev. J. M. Heath*. 



"TTTHEjN^ the equilibrium between the compressive and 

 ' ▼ expansive forces in a given mass of gas has been dis- 

 turbed by suddenly establishing an arbitrary, but finite, in- 

 equality (/) between them, the dynamical effect of this 

 unbalanced force will be, a gradual and continuous alteration 

 in the volume and temperature of the gas, which continues 

 until the expansive force, which depends upon these two 

 elements alone, again becomes equal to that of the compres- 

 sion, and the energy of the inequality is exhausted. At this 

 moment a new condition of equilibrium obtains, in which the 

 elements p^, v' , i^Y differ from their former values by determi- 

 nate finite quantities, hp, Sv, and Bt. 



These quantities will, of course, satisfy the equation 



V . Bp — p^8v =pv . aiBt, 



which expresses nothing but that they are the differences of 



* Communicated bv the Author. 



