1416 
4. Motion relatwated with the aid of the hypothesis of Forpu. 
In this § we shall give a much simpler solution of the second 
problem of $ 1 by making the same suppositions as in the preceding 
§, moreover making use of the hypothesis of Forru. Instead of (4a) 
and (46) we take the equations (7a) and (76), but further we proceed 
in exactly the same way. 
After transformation to the new, relative co-ordinates’), the 
equations of motion (2) pass, considering (7a) and (76), into: 
Nia Ahk, 
by — wy, — wa, — 2 wi) = ae 
my, mM, 
‚ (94) 
E ; : Prion: 
yy + wa, — w*y, + 2 wae, = — ——. 
my m, 
in which 
Ër _ mJ m (ny — yx) — (Eme SE my — EmyEme) 0% 
NDR — SmZm (2? + y?) — (= mz)? — (= my)? ie 
The sign = includes all n points. 
The equations (9a) are the desired equations of motion in relative 
co-ordinates, if for w we substitute the value (96). After this sub- 
stitution we get 2n—3 independent differential equations of the second 
order. 
Without introducing Förer’s hypothesis we came in $ 3 to 2n—4 
equations of the second and one of the third order. Owing to the 
hypothesis of Förp, we have found in this § 2n—3 equations of 
the second order. For this reason the equations (9a) and (90), we 
found here, are preferable to the equations (8a), (85) and (8c). 
5. Remarks. 
a. Lanen’s method of trial bodies”) gives an experimental way of 
finding inertial systems. He does not discuss however their connection 
with the total of matter in space. 
b. Neumann*) and afterwards BorTZMANN!) try to do this by 
referring the place of the material points to the principal axes of 
inertia of the total system. They do not give differential equations. 
A further consideration of this question will bring the conviction, 
4) See § 5, &. 
*) L. LANGE. Geschichtliche Entwickelung des Bewegungsbegriffs. 
) C. NEUMANN. Ueber die Prinzipien der Galilei-Newtonschen Mechanik. 
*) BOLTZMANN. Vorlesungen über die Prinzipien der Mechanik. Leipzig 1904. 
IL paas. 
va 
