To this purpose we will assume a distribution closely resembling 
those, discussed by Gusss in his chapter IV as “other distributions 
having the same properties as the canonical.” These distributions 
have the characteristic property, that the index of probability # is a 
linear function of one or more functions /’,, /’, etc. of the coordinates: 
the functions /,, PF, ete. are subjected to the condition that their 
average value, taken over all systems of the ensemble must be a 
prescribed quantity. We might form different distributions, all satisfying 
the conditions. Now we seek the average value of # for all these 
different distributions; this average value of 9 will be a minimum 
for that ensemble where % is a linear function of #,, /, ete. This 
is proved by Gaas in his chapter XI. I shall call such a distribution 
a quasi-canonical distribution. The canonical distribution is nothing 
else but such a quasi-canonical distribution where there is only one 
function /’, and that represents the energy. As the canonical distri- 
bution is of little application, e.g. not for systems of molecules with 
finite diameter, it would perhaps have been preferable to give a 
broader meaning to the word canonical and to use it in the sense, 
in which I use quasi-canonical. As GiBBs has however used the word 
canonical exclusively for ensembles for which a= I will use 
the expression quasi-canonical for ensembles for which 
y= wp — al’, — bF, — ete. 
In the ether we cannot have canonical ensembles, and so we will 
discuss only quasi-canonical ensembles. We put: 
== eee (-) 
0 k J, J, (°) 
where, dr representing an element of space: 
del Ca =) toert) + (i - 2) | de tf) 
if (5 8 Le) i (= a =) 4 (- =) | de (10) 
RT Vy? Oy Ow Oz Oy Ow \ 
2 = (+ uo i x) dt (11a) 
Q. hk kern ars dv Ie BT oke EN 
o =((= a: 5 be x) rates Edd (11h) 
Gn hen ate Eren Je ME 
oP" be + de. id NAD) 
k, J, and d, are constants, and d, and d, are infinitely small. The 
if 
term — -—-——— has been added, that we should have only to 
