124 I'HILOSOPHICAL TRANSACTIONS. [aNNO I764. 



o'clock at night, being calm and the weather very clear and fair, then, near the 

 inouth of this harbour, a sudden light shined, at which time we saw a fiery 

 comet or meteor in the air, at first appearing in the shape of a flask or Florence 

 bottle, which as it came nearer to us still increased in magnitude, making the 

 air very hot, shooting from the northward to the south-west; sparks of fire dart- 

 ing from it, the size of a man's fist. It came very near us before it disappeared, 

 when it seemed to be of the size of a ship's boat, with a long tail extending from 

 it, attended with a noise like thunder. As it came near the water, the body 

 appeared as black as pitch, and then vanished; the tail remaining some minutes 

 before it disappeared. 



The testimony of Richard King, saith, that coming from Kitty-Vitty to St. 

 John's on Sunday the 4th of May, between the King's Bridge and the garrison, 

 he saw towards the garrison as if there was a star shooting, falling rapidly, but 

 only larger. It was as large as a man's head, and just before it came to the 

 ground it broke all to pieces, which made like large sparks of fire flying from it; 

 and in that time it was as light as ever he saw all day, and in less than 2 or 3 

 minutes there was a rumbling noise in the air, something like thunder. Several 

 other persons in St. John's were prodigiously surprised at the same light. 



XXXf^. Some New Properties in Conic Sections, discovered by Edward fVaring, 

 M.A., Lucasian Prof. Math. Cambridge, and F.R.S. From the Latin, p. 193. 



Theor. 1. — Let the ellipsis APsacRDSEx &c. (fig. 1, pi. 4) have described 

 about it the two polygons abcdef &c, pqrstv &c, having the same number of sides, 

 and which bisected by the points of contact, apbqcrds &c. i. e. making oa ^ 

 Kb, bs = EC, cc = cd, &c. pp = pq, qa = or, m = rj, &c: then will the sum 

 of the squares of every side of the one polygon, be equal to the sum of the 

 squares of every side of the other polygon; i. e. ab"^ + bc'^ -\- cd' -f de^ -\- ef^ -^- 

 &c. = pq' + qr^ + r«^ + st"" + tv' -j- &c. 



Carol. Draw the lines ab, bc, cd, de, ep, &c. pa, qr, rs, st, tv, &c. then 

 will AB^ -I- Bc' + CD'' + de" + ef' -|- &c. = Pa'' -I- aR" -j- Rs' -I- st' -f TV' 



H&c. 



Theor. 2. The same being supposed, let o be the centre of the ellipse, and 

 draw the lines oa, op, ob, oa, oc, or, od, os, &c. then will oa" -\- ob' -|- oc' -f- 

 od" -|- &c. = op' + oa' + or* -f- os' -J- &c. 



Corol. Also draw the lines oa, op, ob, oq, oc, or, od, os, &c. then will oa' -f- 

 oZ)' -I- oc' -1- o(/' 4- &c. = OJ&' -I- 09' -\- or' -f o«' + &c. 



These are also true of polygons in like manner described between conjugate 

 hyperbolas. 



Theor. 3. — Let MPaRST &c. (fig. 2) be a conic section, whose diameter is al, 

 and its ordinate ml; and let Mp = mv, and consequently Ljb = lw. Draw the 



