1 84 APPENDIX I. 



As we have thus n equations to determine only the relative values 

 of n quantities, the redundancy is taken advantage of to prove 

 that 



z? z?t 



= &C., 



[0,0] [i, i] 



where [o, o], [i, i], &c., are the coefficients of (o, o), (i, i), 

 &c., in the determinant 



(o, o) (o, i) . . . 

 (i, o) (i, i) ... 



When the number of forces is less than seven, it is shown 

 how the formula? admit of a special transformation, which 

 expresses the conditions to be fulfilled. 



This very elegant result may receive an extended interpreta- 

 tion. If P , /> P 2 , &c., denote the intensities of wrenches on the 

 screws o, i, 2, &c. ; and if (12) denote the virtual co-efficient of 

 i and 2, then, when the formulae of Mr. Spottiswoode are satis- 

 fied, the n wrenches equilibrate, provided that the screws belong 

 to a screw complex of the (n - ij h order and first degree. 



PLUCKER (J.) Neue Geometric des Raumes gegriindet auf die 

 Betrachtung der geraden Linie ah Raumelement. Leipzig 

 (B. G. Triibner, 1868-69), PP- J ~374- 



This elaborate work is the principal authority on the theory 

 of the linear complex. The subject is essentially geometrical, 

 but there are a few remarks on mechanics ; thus the author, on 

 p. 24, introduces the word " Dyname :" " Durch den Ausdruck 

 'Dyname/ habe ich die Ursache einer beliebigen Bewegung 

 eines starren Systems, oder, da sich die Natur dieser Ursache, 

 wie die Natur einer Kraft iiberhaupt, unserem Erkennungsver- 

 mogen entzieht, die Bewegung selbst : statt der Ursache die 

 Wirkung, bezeichnet." Although it is not very easy to see the 

 precise meaning of this passage, yet it appears that a ' Dyname J 



