24 



AN ACCOUNT OF THE EARLY MATHEMATICAL AND 



gantly investigated by Mr. Gough and Ferdinando (Mr. John 

 Ryley). The prize is an extension of question 648, already 

 noticed, by requiring " their velocities and the time of vibra- 

 tion" when the pendulum and vessel are " put in motion by 

 the force of uniform gravity." Mr. Dalton first points out 

 the intimate connexion between the two questions, and then 

 investigates, ab initio, the required expressions in a very 

 elegant manner. His solution to the remaining question 

 furnishes an excellent specimen of geometrical composition, 

 and is here selected as a proof that Mr. Dalton was not in- 

 sensible to the attractive charms of the Greek geometry. 



Question 665. By Mr, Thomas White. " From a given 

 point P without a given circle, to draw a right line PAC 

 cutting the circle in A and C, so that taking therein PB in a 

 given ratio to BC; from B drawing BD to meet the circle in 

 D, parallel to a right line EF given in position without the 

 circle; and through 1) and C drawing a right line DQ meet- 

 ing EF in Q; the two parts thereof DC and CQ may obtain 

 a given ratio : — and to shew the limits of possibility." 



Answered hy Mr, John Dalton. '^Composition, Let fall 

 PT perpendicular to FE, from P draw any right line PO, on 

 which take PM : 

 MN in the given 

 ratio of PB : BC; 

 and MN : NO in 

 the given ratio of 

 DC : CQ;— join 

 OT parallel to 

 which draw No, 

 Mb meeting PT 

 in o and b; then 

 draw oC and 6D 

 parallel to FE cut- 

 ting the circle in 



Fig. 5 



