ie lone 
Il.—Additions to the paper ‘On the Establishment of the Elementary Prin- 
ciples of Quaternions, &c.,” in the Transactions of the Royal Society of 
Edinburgh, Vol. XX VIT. By G. Piarr, Docteur és-Sciences. 
(Read 7th May 1877.) 
Page 190, to the alinea (beginning with): “the sole condition to be satisfied, 
is,” &c. (ending with): “...the versor of the expression may then become 
what it may,” add : 
provided this versor does not differ from the versor of the product 
px [ax (ap) 
made by successive multiplication (according to the definition of multiplication 
of more than two vectors), the quaternions w+, w—o being likened respec- 
tively to the products 
pa and @p 
by a proper choice of the vectors p and a. 
Page 191, to the fourth line from above, add: 
Tt will be easily found that, in virtue of the value = —1, the versor of the two 
products px|@x(wp)| and (pa) x (wp) become equal; both being equal to 
unity. 
Let us designate the unit vectors of p, o, o, 7, respectively by p’, a’, o’, 7’. 
Then for the calcul of the versor [@ x (a@p)| we admit, by an anticipation, not 
founded on }=—1, besides p°=) and p’o’=7’: 
ore g=tt, he= +1, 
2°) —p'7’= o’ f On =p: 
and taking from pages 187, 182: 
o'p’= cos u—7’ sin wu 
w =p COS uUto”’ sin u, 
we have: 
p' Xa x a'p!=p'(p’ cos u+o" sin u)(h cos w—7’ sin w) 
VOL. XXVIII. PART J. K 
