(E279) 
for the orthogonal substitution has the value unity; so only the 
determinant for the first partial substitution remains. This substitu- 
tion has been chosen without taking into account the form of the 
second factor. The coefficients which determine this substitution 
depend therefore only on the coefficients of the exponent; as p does 
not occur in these coefficients, the determinant also cannot be a 
function of p, and so we may omit it in what follows. 
The integral (29) can easily be integrated and yields: 
C8 
So we have only to calculate the sum of the coefficients 8. These 
coefficients may be found by the solution of the following equation 
of which they represent the 2 roots: 
a,,—B Bis Gis F Ae he, 
da: @,,—-B 43 ostinato, 
: aah | bet es Dl 
Ue ee das «dn 0 (50) 
Gnd Ono An3 » + + Gn—B 
The sum of the coefficients 8 is the sum of the roots of this 
equation, ie. the coefficient of 8". Only the product of the elements 
of the diagonal of the determinant yields terms containing 8* 1; and 
as is obvious, the coefficient of 2! will be 
Gy, + 5, 1 33 H+ + + Gan 
In order to determine this sum we have to find an arbitrary 
substitution for which the exponent assumes the form 2° and then 
we must substitute the new variables x into the second factor. A 
substitution fulfilling this condition may easily be found. The exponent 
namely may be written as follows: 
if 
EEA + 2 Foi = = (efo) 
T 2 2 
where : dd and —2ep=>— — 
‘ kr kr 
So we find for @ and 8: 
ee ” Eee 4 capes pene 31) 
feet, at a Ge Fi of RS 
Now we dn as new variables: 
afs — Phti=R- 
This substitution does not yield the accurate coefficients for f,* and 
tel 
wh 
tf. for, in order to get » quantities %, we have to take as one of 
the new variables x, = ea fn —Bf,; so we introduce moreover a 
term 2a8/,/f, which does not occur in the exponent. As however 
the exponent consists of an infinite number of infinitely small terms, 
