84 
Proceedings of the Eoyal Society 
Scymnus and Lcemargus were very much greater than those referable 
to the form of the teeth, on which systematic zoologists had hitherto 
relied in their classification. These differences, indeed, affected 
not only the relations of Lcemargus to Scymnus , but to the sharks 
generally, and called for a reconsideration on the part of the 
zoologist of the place which the Greenland shark ought to occupy 
amongst the Plagiostomata, and required the establishment of a 
separate family for the reception of the genus Lcemargus , w'hich 
family would possess the following characters: — 
LjEmargid^:. 
No nictitating membrane; two dorsal fins; no anal fin; duo- 
denum cylindrical ; both a pancreas and duodenal caeca; in the 
female no oviducts. 
Lcemargus. — Dorsal fins short, the second not quite so high as 
the first ; lower teeth oblique, truncate. 
2. Additional Note on the Strain-Function, &c. By 
Professor Tait. 
The author gave an account of the mode in which he had treated 
the Strain-Function in an elementary Treatise on Quaternions, 
soon to be published, mainly from the pen of Professor Kelland. 
The coefficients of the cubic in <p are determined easily from the 
condition that homogeneous strain alters the volume of every part 
of a body in the same ratio. 
A careful examination is bestowed upon the case of three real 
roots of the cubic ; especially with regard to the distinction between 
the results of a self-conjugate strain and a rotational one. 
The separation of the pure and rotational parts of a strain is very 
fully treated ; and as special examples, the strain of a rigid body 
and a simple shear are analysed. 
Finally, the following problems are solved : — 
Find the conditions which must be satisfied by the simple shear , 
which is capable of reducing a given strain to a pure strain. 
Find the relation between two linear and vector functions whose 
successive application produces rotation merely. 
All this is independent of the differential calculus, but as the 
following results regarding the stress-function require its aid, the 
