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flaw in (2) may be. Not in the signs, but rather, in the lack of a term. A term that shouldn´t be a constant, but dependent of n . A term that added up to the other two would not only make N$_{3}$ possitive for n >> 1, but actually equal to six. So there must be an aditional source of degrees of freedom which Einstein missed to consider. If we could iden- tify where this source of degrees of freedom was, we would have our problem solved. 

A group of n particles may rotate in space without dissatisfying the condition that the distances between the particles remain con- stant. However, it is meanigless to talk about rotations without first establishing an ade- quate reference frame. To do so we arbi- trarily selected three particles from S$_{3}$ ; the points were the centers of mass of these par- ticles are located generate a plane P in three- dimensional space. And the vector v , which is orthogonal to P , designates an arbitrary direction in space. We must point out that we are defining v as a fixed vector, and that it is perpendicular to P in its original position, but as S$_{3}$ rotates, this perpendicularity rela- tion will be lost. Therefore, it is convenient to make a copy of P , which we will call P ´, and hold this copy fixed in the original position of P . Thus v will allways be orthogonal to P ´. By considering the plane P ´ and its normal vector, we are defining a three-dimensional coordinate system. 

Now, if we choose two particles, different from the ones used to generate the plane, the line that joins their centers of mass is a possi- ble rotation axis for S$_{3}$ . And since the num- ber of ways in which pairs may be chosen from a set of n − 3 particles is 

<img src='content_image/369891.jpg'>

There will be an equal number of such axes. Each of this axes forms with the di- rection of the vector v an angle ϕ$_{i}$ which is a function of time and determines a possi- ble rotation of the system. In general, the different ϕ$_{i}$ will not hold relations of linear independence. 

We believe that the number of ϕ$_{i}$ allowed to S$_{3}$ for a given value of n is the term miss- ing in Einstein’s calculation, and we propose that the number of degrees of freedom for the system S$_{3}$ is given by: 

<img src='content_image/369897.jpg'>

However, (2) seems to be the correct ex- pression for n = 2. It also works for n = 3 and n = 4, which is not surprising, since for this value of n the last term in expression (7) is equal to zero, so (7) and (2) are equivalent. 

Once we had developed this expressions, we were curious on wether, by following the 

