of Edinburgh, Session 1870 - 71 . 
365 
ference. If the trigon were isosceles, the representation would be 
that of the motion which we have already investigated. 
If the angle A vary with a velocity proportional to PB, and B 
with a velocity proportional to AP, the exterior angle at 0 must 
have the rate of its variation proportional to AB. Now, if we 
make DCE (fig. 3), equal to half the sum of CAB and ABC, CE 
a mean proportional between AC and CB, and then inflect ED 
equal to half the sum of the same lines, the perpendicular EQ 
intercepts QD just half of AB. Thus QD is proportional to the 
rate of increase of ECD, and consequently CQ to the rate of change 
of CDE Thus the synchronous variations of the trigons ACB 
and CED would represent four connected cases, two of oscillation 
and two of revolution in a circle. 
Now, the ratio of CE to ED is much nearer to one of equality 
than is the ratio of AC to CB; and if we were to proceed again in 
the same way, we should obtain a trigon still more nearly isosceles ; 
and, after a very few operations of this kind, we shall obtain a trigon 
sensibly isosceles. That is to say, we shall have referred the 
oscillation in a given arc to the motion in just the whole circum¬ 
ference. So, seeing that the motion in this last case has been 
completely investigated, we have a complete solution of the general 
problem ; the necessary calculations being of remarkable simplicity. 
T. On the Capture of a Sperm Whale on the Coast of 
Argyleshire, with a Notice of other Specimens caught on 
the Coast of Scotland. By Professor Turner. 
In the autumn of last year, whilst spending a few days in the 
neighbourhood of Oban, I visited Dunstaffnage, and in the court¬ 
yard of the Castle saw the two halves of the lower jaw-bone of a 
sperm-whale. On inquiry, I learned that they were the relics of a 
whale captured some years ago in the neighbouring sea. From 
some of the older inhabitants of Oban I gleaned some particulars 
respecting this animal; and as no record of its capture has as 
yet found a place in zoological literature, I am induced, as the 
sperm-whale so very seldom visits our shores, to communicate a brief 
notice to the Society. 
In the month of May 1829 a large whale was seen spouting in 
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VOL. VII. 
