1890-91.] Mr A. M‘Aulay on Quaternion Differentiation. 123 
usefully considered when certain simplifying assumptions are made. 
In Professor J. J. Thomson’s consideration of this subject ( Applica- 
tions of Dynamics to Physics and Chemistry, §§. 35 and 39), he not 
only assumes K to be a mere scalar both before and after strain, but 
he also does not consider the most general case of strain which 
involves 6 instead of 3 independent coefficients. If this last restric- 
tion had not been made, our 42 constants would have reduced to 7, 
and in his case they reduce to 4. In either of these cases the stress 
. . @ 2 
is simple enough, viz., — aK ,* 
07 TV 
* For other particular cases of the stress under consideration, see Helmholtz, 
Wiss. Abh., i. 798 ; Korteweg, Wied. Ann., ix. 48; Lorberg, Wied. Ann., 
xxi. 300 ; KirchofF, Wied. Ann., xxiv. 52, xxv. 601. 
