(598) 
dp dp 
Ent 
and when the symbol 4 denotes a certain affinity the momentaneous 
system of velocities of the system of masses is indicated by 
hence we have 
D= [Mx | Ux], pO= fp'dm. 
The evaluation of the static sum of the forces of inertia of an 
arbitrary order called forth during the motion of the system of mass 
at any epoch and the evaluation of the energies of higher species 
inter alia considered by J. Somorr also lead to the integral p®. 
It does not raise the slightest difficulty to find the integral p™ for 
a simplex of constant denseness with the vertices a,, a,, .., Om 
We can put 
pA, a; = A, a; = © And 
where all points inside the simplex are obtained, when to the 
numerical quantities 2,, À,, .., 4, are given all positive values 
compatible with the condition 
EN a 
If we think the simplex broken up into elements of the shape of 
the parallelotop, i. e. of the (2—1) dimensional analogon to the 
parallelepiped of our space, and with edges parallel to the edges of 
the simplex starting from a,, then a slight calculation to be found 
(l.e.) on page 147 gives us 
dm = (n—1)! M da, da,... dan, 
where J/ indicates the mass of the entire simplex. Hence we find 
p”) = (n—1)! M I (A, a, + 2, a, +... + dna,)'da, da,... dy. 
The polynomial theorem gives 
=, vy! 
CASAS eem An) = DRE 
Jd Ara, ae. An” 
Pl 
with 
DI Dare Dn == Oee dd > ?P, try, t---+m=—n. 
On the other hand we find according to a wellknown theorem 
of LiovviLLe under the above conditions for 4,, 4,,...4n: 
