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there are n ( n − 1) 2 different equations. These equations represent the system´s restrictions; they are the constraint equations of the sys- tem. 

Einstein must have thought that he would obtain the number of degrees of freedom of S$_{3}$ merely by substracting the number of con- straint equations from 3 n : 

If (2) is solved for n > 4, it will be seen that the values of N$_{3}$ differ from those ob- tained when S$_{3}$ was viewed as a single body. Why does this happen? Maybe because it is not all appropiate to consider the collec- tion of particles with rigid links as one body. Or more likely, because the count of the de- grees of freedom of S$_{3}$ by consideration of the individual particles was not done correctly. Which ever the reason may be, we will soon find out. 

As it turns out, there is something defi- nitely wrong with (2), and it is that 

which is absurd. 

Einstein did notice this flaw, because in his book, instead of (2) he has: 

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We cannot think of any physical or math- ematical justification for this change of signs, and although it removes the problem of get- ting a negative value of N$_{3}$ when n >> 1, it brings up a new problem. 

In the limit when n tends to infinity, the system S$_{3}$ is equivalent to a rigid body of con- tinuous mass. So it would be expected that if the limit of N$_{3}$ is taken when n tends to infin- ity, this limit should be equal to six. But this does not hold true for N$_{3}$ as defined in (4); the limit when n tends to infinity diverges. 

Einstein introduced, as a footnote, the fol- lowing correction: 

Nonetheless, the limit when n tends to in- finity of the modified N$_{3}$ is still undefined, so (5) cannot be the correct expression for N$_{3}$ either. 

When we took up the task of developing an accurate expression for N$_{3}$ , we did not take off from where Einstein left the prob- lem, but instead, we directed our attentions back to (2), which is the expression that Ein- stein must have come up with originally, in spite of the fact that it doesn´t appear in his book. We did so because, as incorrect as it may be, there is a consistent line of think- ing behind expression (2), which there is not behind expressions (4) or (5). 

Expression (3) gave us a hint of where the 

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