528 
Proceedings of the Royal Society 
On the other hand, the nasal hones are obviously flatter and 
longer; the antero-posterior diameter of the orbital border of the 
frontal is relatively not so long ; the double curve of the posterior 
border of the occipital is not so marked, and its base is wider (Van 
Beneden) in Schlegelii than in borealis. Again, my specimen does 
not have a pair of strong tubercles projecting from the posterior 
border of the body of the hyoid, as in the Java specimen, and the 
first rib is not bicipital. 
Some of these differences may be due to the more advanced 
ossification of the Java skeleton, and the longer and stronger spines 
of the dorsal and lumbar vertebrae, which M. Yap Beneden refers 
to, are obviously due to the same cause. The greater length of the 
Java skeleton has not the importance which Yan Beneden attaches 
to it, as I have already maintained that borealis may attain a 
length of 40 feet or upwards, and the ribs in the Java specimen 
corresponded in number with those in my skeleton. 
At the time when Professor Flower wrote his description, there 
was a greater tendency, on the part of cetologists, to limit the area of 
distribution of the individual species of cetacea, than now exists, and 
to confer specific value upon specimens which, though in many 
respects similar in characters, yet came from distant seas. The 
wider range of distribution of some o ; f the species of the marine 
mammals is now more generally recognised, and the remoteness of 
the habitat of Schlegel’s Balcenoptera ought not, if the anatomical 
arrangements correspond, to bar its association with B. borealis. 
2. On Minding’s Theorem. By G-. Plarr. 
In treating, by the method of quaternions, the question which 
forms the basis of Minding’s Theorem , I had the advantage of being 
guided by Professor Tait’s paper on that subject ( T . R. S. 1880), 
and it is only by varying his method that I could hope to present 
the question under a new aspect. 
§ 1 . 
Let us apply the operator 
p( )? 
of a conical rotation, where q = p~ l , to a system of given vector- 
