62 MOLECULAR FEEE PATHS 153 



to it. For, owing to that conflict of conceptions, a new 

 and interesting side of our theory has been brought for- 

 ward which is worth a searching investigation. As in 

 Part I. of this book, the speed of the molecular motion 

 and the supply of energy therein contained were considered 

 and calculated, so there remain for this Part II. the 

 investigation of the character of the motion, the deter- 

 mination of the length of the path of a molecule between 

 collisions, and the development of the consequences which 

 will result from our knowledge of these free paths in respect 

 of the different properties and phenomena that have been 

 observed in gases. 



63. Probability of Molecular Collisions 



The pioneer investigation in which Clausius 1 opened 

 out this new wide field cannot, for the attainment of its 

 first aim, viz. the determination of the length of the 

 molecular path, dispense with mathematical expedients. 

 As in Part I., we need again the calculus of probabilities 

 in order to investigate processes which are conditioned by 

 no other law than that of chance. But the demand on 

 mathematical means may be more restricted than it was 

 in the original memoir. It is not necessary to use the 

 higher analysis, and the aid of elementary mathematics is 

 sufficient ; the following calculation presupposes no further 

 mathematical knowledge than is needed for the calculation 

 of compound interest. 



Before we solve the actual question and determine the 

 probable length of the straight path traversed by a mole- 

 cule between two collisions, we follow Clausius' procedure 

 in investigating a preparatory and more simple problem. 

 Instead of the actual behaviour of the gaseous molecules, 

 which are all moving about hither and thither, let us 

 imagine the simpler case in which one particle (or a 

 certain number of particles, but all with the same speed 



1 Pogg. Ann. 1858, cv. p. 239 ; Abhandl U. Warmetheorie, 2. Abth. 1867, 

 p. 260 ; Mech. Warmetheorie, iii. 1889-91, p. 55 ; transl. Phil. Mag. [4] xvii. 

 1859, p. 81. 



