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51 4. Determination of the Impulses p 1 and p 2 • From the last equations (6) and provided that the inequality (9) is satisfied, we obtain the expressions (10) By putting H m =~ 2 tl = H H -H fl2 (X b. (X2 H flt b. , which represent a mass, will be called ~avit-y: mass, and v, to which we assign the same homogeneity of a mass, will be called by the name of Hubble. 5. : In accordance with principle 4, the expression of H must reduce under Newtonian conditions to the form HNewton = 1/2 m~ v~ + 1/2 m~ v~- momo f - 1- 2 r +c.
J= 1,2,3) J where His given by (25) implying the presence of the values I(Jj which do not vanish as in the particular case of inertial motion. s~dm, i where 6~dm is the spatial part of the form w6(i). , 0:2 , 0:3. lix + i. ~cx' (r X &) X r jdm. may be computed by referring r to a co-ordinate system associated with the body. CHAPTER III INVARIANTIVE MECHANICS OF SYSTEMS OF MATERIAL POINTS § 1. Inertia, Gravity and Expansion In the case of a material point, inertia is characterized by the interdependency of mass and velocity and by the expression mc 2 of the point's energy.
AAh aa. J J ~ . aBh . 1.... a +h aa. aa. J J J j = 1, 2, 3 and the equation of the energy exchange between body and field (8) The first group of equations may be written also (9) dp 1 dt (aA 1 aal aA 1 at _ aB 1 ) axl ac +(aA 1 axl ax2 a+ 1 (aA 1 aa2 _ _ aA 2) axl x _ (aA 3 _ 3 axl aB2) a 2 + (aA 1 ax2 aa3 _ aA 1 ) ~ + 2 ax3 aB 3) ax3 a 3 together with two other similar equations. Hence, there exist an electric field, a magnetic field and a mixed field which together determine the motion of the body.