380 General Theorem relating to Regular Polygons. 
sum of the triangles, that is the figure B B' B" B'" B lv , is equal 
to the sum of the products, that is, to 
i (pp' +p'p" + p"p"' +p'"p iy + p™p) sin ec 
which has been proved equal to 
- ( r 2 sin a -}- | v 2 sin a cos ex) 
that is, to n (l r 2 sin ^ -f J v 2 sin 2««), 
which is the theorem in question. 
Coroll AH y. — If two circles have the same centre, and a re- 
gular polygon be described about the outer circle, and from any 
point in the circumference of the inner circle perpendiculars be 
drawn to the sides of the polygon, the figure formed by joining 
the bottoms of the perpendiculars will have an invariable mag- 
nitude. 
For then the expression for the area will be composed of con- 
stant quantities. 
Art. XXIV . — Letters from Dr Oudney ; from Mr Bowdich ; 
andfrom Captain Parry. 
I. 
Qln the London Quarterly Review, many interesting details have 
been published regarding the African Journey of our friend 
and pupil Dr Oudney. The Letters we now lay before our 
readers form part of a series, which we intend to continue as 
opportunity offers.] 
Dr Oudney to Professor Jameson. 
My dear Sir, Murzouk , June 6. 1822. 
i intended writing you long ago, but my time has been so 
occupied with such a variety of objects, that really I could not. 
I am much disappointed in the climate of Fezzan, and agreeably 
so. The temperature under cover is not much greater than in 
other places on the same parallel of latitude. Now it is June, 
and the maximum daily heat is seldom above 90°. The mini- 
mum is about 80° or 78° Fahr. The air is dry, as, indeed, seve- 
ral of my instruments shew too well, for the ivory on several 
