Law of Molecular Force. 129 



cannot represent the actual facts. No series of experiments has 

 yet been conducted over a range sufficiently wide and accurately 



enough to enable us to determine -~^ in a useful manner ; 



so that, without a guiding hypothesis, the search for a suitable 



7V 2 » 

 form to give the right nuances to ^~^ would be a very difficult 



matter. As I wished to construct an equation to test the law 

 of the inverse fourth power, it was necessary for me to assume 



F(v) in the above equation to be of the form --g, where I is a 



constant independent of the temperature, and to take as the 

 general type of my equation, 



The approximate determination of I is an easy matter ; but 

 the determination conjointly of the final accurate value of Z, 

 and of the simplest form of the function f of two variables 

 applicable to the experimental facts, is exceedingly difficult. 

 After a prolonged trial of many different forms, I was led to 

 adopt that given by Dr. Walter, bat with his functions /3 and 



/determined to be of the forms -7==, and 1 — cT for C0 2 ; thus 



vT 



where e is the base of the natural logarithms, T the tempera- 

 ture reckoned on the air-thermometer from absolute zero, and 

 a, b, c, I are four constants having the following values : — 



I. When the unit of pressure is that of a kilogramme weight 

 per square metre, and the unit of volume is a cubic metre (v 

 being the volume of a kilogramme of C0 2 ), 



a=19-257, 6 = '02785, c='038577, Z=35*327. 



II. When the unit of pressure is that of one atmosphere, 

 and the unit of volume is that volume which the mass of gas 

 considered occupies at 0° C. and under a pressure of one 

 atmosphere, 



a=-0036976, 6 = -0552, c = '000014666, Z=*01343. 



As Amagat measured volumes in a unit suitable to the cir- 

 cumstances of his experiments, but has not given its value, I 

 have calculated it to be 34*70 of that volume which the mass 

 of gas experimented on would have occupied at 0° C. and 

 760 millim. pressure. 



Phil. May. iS. 5. Vol. 24. No. 146. July 1887. K 



