11-14] ' Statistical Method 13 



mast miiSHiiihr lie integral In the lingo agr of the then ay of probability 

 the statement my he taken to mean that the 'expectation** of tl^ number 

 of molecules in the region in question is Q*. Any appeal to the thmj of 

 probability fropHm that a certain amount of knowledge m given, while we 

 remain in ignorance of the remaining facts. In this particular case, what is 

 is that the molecular density throughout the region Q is r; what is 



is the position of the individual molecules of the gas. 

 With this understanding it will be perauaabie to saj that the number of 

 an element of MU*BUM dxdydx selected at ramdom is vdrdydz. 

 What k meant is that the probability of finding the centos of a 



; -.--' i-. 



r- 



at 



funaiiinatrti in 

 by . , *, and the 



shaH denote bjr *, r, WL^ In the hat two 

 virtually ilia iiia j the law of groaning of the ocwrdi- 

 x, y. z- we now have to dtscoss the law of grouping of the velocities 



take some % w: fF imaginary point as origin, and diaw from this 



of the <fifierent molecules of the gas, hVJUmd to orthogonal Tfi the 

 of the 1 1 In mil j of any fine wfll be , r, a?, the 



rfnliiiiilj rf Ihi iiainniimilia^ mnliiiiili A dnvansisn of the faw of distn- 



to a ilin nniim of the law of duuity 



tn-i 



:- 



4VCPEjawU^~ ID6& t2ODGu_ ^^C CSUO dGfiDC mvC 



already explained, "if w may denote thai 

 lentanding, we can say that the number 

 fie between and u -f- u^n, r and r -I* uw, w 

 i T is the "dennity of points at the point u, w, m? 

 We shaU find it convenient to replace T by S/ f where JT is the total number 



iriniij to specify the point u, r, r at which / is mi M 1, we shaU write 



