278 M. Achille Cazin on Internal Work in Gases. 



formula (12). Making, in this latter as in the preceding cal- 

 culation, n Y = 4i'7 atmospheres and n' = 0*989, we find 



T,— T f =a3°-46, 



which number is a little less than that deduced from formula 

 (12); but the difference is so trifling that the approximation of 

 formula (14) is justified. 



All the preceding formulae follow the course of the phenomena; 

 but they can never give very exact numbers, on account of the 

 uncertainty which prevails as to the value of some of the con- 

 stants, such as a, A, K, and C^. Thus Messrs. Joule and 

 Thomson have taken, from Mr. Rankine, 



log ^ =2-5111438 and T = 274, 



instead of 2*4365685 and 273, which I have adopted. 

 Consequently formula (14) gives with these numbers 

 T,-T' = 4°*09. 



On page 336 of the memoir just quoted may be read that 

 the cooling observed with a difference of pressure of 60*601 

 pounds on a square inch was 5°049 at the temperature of 

 12°*844. 



This excess of pressure is equivalent to n l — n , = 4*216 atmo- 

 spheres, if we assume for one atmosphere a pressure of 14*373 

 pounds per square inch. 



Formula (14) gives the preceding number with the constants 

 of Mr. Rankine very well ; but with those which have been used 

 in the preceding calculations we obtain under the same circum- 

 stances 4°*65, a smaller number. 



It is possible that in the experiments of Messrs. Joule and 

 Thomson the thermometer may have been placed at too small a 

 distance from the orifice for the vis viva of the jet to be com- 

 pletely converted into heat. Let us see what in fact was the 

 mode of operating. 



In the large apparatus described in volumes cxliii. andcxliv. 

 of the Transactions of the Royal Society, the gas contained in a 

 gasometer is withdrawn by a pump and forced into a long ser- 

 pentine tube surrounded by water. At the end of this serpen- 

 tine tube is a wooden cylinder into which cotton is pressed, 2*72 

 inches in length and 1*5 inch in diameter; and beyond, a tube 

 is adjusted which reconducts the gas to the gasometer. The 

 pump maintains the regular circulation, and keeps the pressures 

 p l and // constant on each side of the porous partition. The able 

 physicists took the most minute precautions in order to obtain 

 regular effects. A thermometer placed very near the partition 

 received the gas after its expansion in the form of a multitude 



