349] THE THEORY OF SCREW-CHAINS. 383 



obtain the following equations by simply adding the equations just written 

 for each separate -screw 



20 H = (1) 20! + (w2) 20, . . . + (nn) 20 n . 



If the Dynamos in the first system neutralize then their components on 

 the screws of reference must vanish or 



But it is obvious from the equations just written that in this case 



and therefore the corresponding Dynames will also neutralize. 



Given n pairs of corresponding Dynames in the two systems, we obtain 

 ?i 2 linear equations which will be adequate to determine uniquely the ?i 2 

 constants of the type (11), (12), &c. It is thus manifest that n given pairs 

 of Dynames suffice to determine the Dyname in either system, corresponding 

 to a given Dyname in the other. It is of course assumed that in this case 

 the intensities of the two corresponding Dynames in each of the ?i-pairs are 

 given as well as the screws on which they lie. 



349. Properties of this correspondence. 



To illustrate the distinction between this Dyname correspondence and 

 the screw correspondence previously discussed, let us take the case of two 

 cylindroids. We have already seen that, given any three pairs of corre 

 sponding screws, the correspondence is then completely defined ( 343). 

 Any fourth screw on one of the cylindroids will have its correspondent on 

 the other immediately pointed out by the equality of two anharmonic ratios. 

 The case of the Dyname correspondence is, however, different inasmuch as 

 we require more than two pairs of corresponding Dynames on the two 

 cylindroids, in order to completely define the correspondence. For any 

 third Dyname 6 on one of the cylindroids can be resolved into two Dynames 

 6 l and 2 on the two screws containing the given Dynames. These com 

 ponents will determine the components ^^^ on the corresponding cylindroid, 

 which being compounded, will give &amp;lt;f&amp;gt; the Dyname corresponding to 0. 



It is remarkable that two pairs of Dynames should establish the corre 

 spondence as completely as three pairs of screws. But it will be observed 

 that to be given a pair of corresponding screws on the two cylindroids is 

 in reality only to be given one datum. For one of the screws may be 

 chosen arbitrarily; and as the other only requires one parameter to fix it 



