(446) 
mined period we must give g a determined value p and then take 
the square of the amplitude for ou vibration. So we find: 
2 
=| Dm (| 2 
Ay ="? | & fo sin (rop) En T° | = f, cos (rop) 
t—0 = 
In what follows we may omit the limits as all summations are 
to be executed between O and 7”; and we may omit the constant 
factor T° 
quantities A, for different values of p: So we get: 
A, = J fy fw {sin (cep) sin (te'p) + cos (tvp) cos (te'p) } 
Afi ff LOS (U OPT Ene eee ae 
For this quantity A, we seek the mean value for all systems of 
the ensemble. To this purpose we have to multiply the value of 
equation (27) with the probability that the quantities 7,....j, have 
a determined, arbitrarily chosen value and consequently we have to 
integrate according to df, df, between the limits — o and + oe 
| df Joti—fo 
To that purpose we will represent — by eS and we get: 
di T 
Prijs (fe) 
a krt ae 4 an 
Ay ==" he Sof v cos (v—v') tp df, ..+.dfn - (28) 
D 
=. 
If we bring the factor e outside the integral sign as well the 
exponent of e as the other factor under the integral sign are homo- 
geneous quadratic functions. By the introduction of other variables 
we may transform both functions to terms of 7 squares and in the 
same time it is possible to choose the variables in such a way, that 
all coefficients which occur in the exponent are unity. So we may 
bring the integral into the following form: 
lp jens APN) 8 » 
fi EE (8, PUB, Pa? +B; Ps Bn Gn") A dy,... dp, (29) 
where A represents the determinant of Jacot. The linear substitution 
required to get this form may be thought to be executed in two 
operations: 1s* a substitution which yields 
Ai HA 
for the exponent and: 
a1, Yas = As om == s+ e+ Cnn An “= 2 ds ta he Sas Ph oe 2 An—1 jn Zn Yn 
for the other factor; 2°¢ an orthogonal substitution in consequence 
of which both functions assume the form they have in equation (29). 
The determinant of Jacosi for the total substitution is the product 
of the determinants for the partial distributions. The determinant 
as it is only our aim to determine the relative values of 
ee EE 
