VOL. LXV.] PHILOSOPHICAL TRANSACTIONS. 651 



of heat. By comparing these last 3 years with that first given, when the clock 

 was in some degree foul, it seems as if it were most affected when the work 

 is clean. Though that is not quite certain ; for the differences, which decreasing 

 gradually in the following table, would justify this conclusion, it may be ob- 

 served increase again in the last instance. For hence it appears that July and 

 August are the months for greatest acceleration, and Jan. and Feb. for retarda- 

 tion ; contrary to the affection of metalline rods, but agreeable to the effect to 

 be expected from moisture on wood. Yet this difference is not so great in any 

 degree, nor (what is more material to observation) by any means so sudden in its 

 changes, as what is occasioned by heat on metals. And even this perhaps might 

 be obviated by a strong coat of varnish on the rod, or some preparation of the 

 wood itself". One thing it may be proper to mention, as an accidental experience 

 Mr. W. h ad the last year ; that a clock so fixed, with a pendulum of so simple 

 construction, is not easily affected by any tremulous motion of the building to 

 which it is fastened. In the months of March, April, and part of May, he had 

 occasion to make alterations in the top of his house, in order to gain more rooms 

 in it ; and notwithstanding the great jarring necessarily consequent on taking off 

 the old rafters, and laying on a new leaded roof, and new joists and floor over the 

 observatory itself, the clock seemed not to have been disordered at all by it. 



XX Fill. Of Triangles described in Circles and about them. By John Stedman, 



M.D. p. 296. ^,«,,ij. 



Prop. 1 . An equilateral triangle inscribed tvilhin a circle is larger than any 

 other triangle that can be inscribed within the same circle. — Let abc, fig. 15, 

 pi. 12, be an equilateral triangle, inscribed in the circle adcb ; and let ade be 

 a triangle supposed larger than abc. Let ade be drawn with one of its angles 

 at the same point with one of the angles of the equilateral triangle, suppose at 

 A, and then its other two angles will fall either on the segments adb and aec, or 

 one of the angles on the segment bc. First, let one of its angles fall at d, 

 between a and b ; and the other at e, between a and c ; and draw the line be. 

 In the triangles abc, abe, the triangle abf is common, and the two remaining 

 triangles bfc, afe, are similar ; for the angle afe is equal to its opposite angle 

 bfc ; and the two angles eac, ebc, are equal, being subtended by the same 

 segment ec, and so the two remaining angles ae*", bcp, must be equal ; there- 

 fore the sides are proportional, and bc and ae, subtending equal angles, must 

 be homologous ; but bc is equal to AC, which is greater than ae ; consequently 

 the triangle bfc is greater than afe, and so the equilateral triangle abc is 

 greater than the triangle abe. In the same manner, the triangle abe may be 

 proved greater than ade ; for ahe is common, and the two triangles adh, bhe 

 are similar, and their sides proportional ; and ad and be, subtending equal 



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