the Journals of the late Reuben Burrow. 



191 



which Simpson has only given particular cases ; — ^these are done 

 by Mr. George Brown. 



" August 26. Bead about Eclipses in the following works. 



" On Projection in Turner's Exercises. 



^' Some in Lalande's Abridgement. 



" September 3. I did a couple of Questions which were pro- 

 posed by a Quaker, who had requested Mr. Atkinson, of the 

 Mayor's Court Office, to give them to Mr. Keech and myself. 



'^ Question 1 . 



" There are two given points d and n, and dqn is a string of a 

 given length fastened to the given points :- — required the point q 

 where a weight W would rest suspended from the cord. 



'^ Construction. 



" With the centre d and di- 

 stance c?B = the length of the 

 cord, describe the arc AB ; draw 

 the horizontal line dp, and per- 

 pendicular to it draw wB cutting 

 the arc in B : — ^join B^, and 

 make the < Bwg = < d^n ; then 

 nq cuts dB in the point of sus- 

 pension required. 



" Demonstration. 



" Lemma. If the weight W be in equiUbrio, it does not sig- 

 nify in what part of the line nq, the nail that fastens the cord, 

 is put ; but it is evident that when the nail falls in the hori- 

 zontal line, as at p, then dm-=mp, and consequently it must 

 always be so. 



" Now qn = qlij and .*. < dqn — < qnB + < qBn — 2^wB, 



.'. < qnB=i — < dqn. But qm is parallel to nB, and .'. < mqp 



=:qnB. Whence <^dqm=^mqp, and conseqvLentlj dm = mp, 

 agreeably to the Lemma. Q. E. I). 



'^ Question 2. 



" What velocity must a ball suspended by a string have given 

 to it so as to make it ascend to a horizontal position ? 



^' Solution. 



" Huyghens demonstrates that bodies falling from the same 

 heights acquire the same velocities, and that pendulous bodies 

 rise to the same heights from which they fall. Hence it is evi- 



