PHILOSOPHICAL WRITINGS OF THE LATE DB. DALTON. 1 5 



In the Ladies^ Diary for 1791, Mr. Dalton entirely con- 

 fined himself to the mathematical department. He furnished 

 solutions to eleven of the questions, and obtained insertion of 

 those to the Jifst, ninths and fourteenth of the series. His 

 name also frequently occurs in the Diary Supplement for this 

 year, hut its pages are wholly occupied by the communica- 

 tions of other contributors. The first solution in the Diary 

 relates to the determination of x and y from two given 

 equations, which Mr. Dalton concludes is impossible in whole 

 numbers; the second furnishes an elegant determination of 

 ** the least breadth of a new cut, at right angles to a river, so 

 as to admit of the passage of a given barge ;" and the third 

 produces an exception to a property in the theory of equations 

 which the proposer, Mr. Bonnycastle, had been led to con- 

 sider general. To the Gentleman's Diary for the same year 

 he contributed twelve solutions, but the only one which 

 obtained insertion at length is that to the following difficult 

 locus which had been proposed by himself in the previous 

 Diary. 



Question 631. By Mr, John Dalton, "Suppose two 

 bodies B and C to set off together from a point A, and move 

 along two right lines at right angles to each other, the one B 

 with a uniform velocity, the other C with a velocity such, 

 that the space described may be as any power of the time ; — 

 also suppose a line BC to be drawn between the bodies, and 

 CP taken thereon equal to a given line. Required the 

 equation and quadrature of the curve which is the locus of 

 the point P." 



Answered by Mr, John Dalton, " Suppose PM perpen- 

 dicular to AC and PN to AB; put s and c for the spaces 

 described by the bodies B and C respectively in one second 

 at the beginning. PutCP = 6; AN = a;; PN = y; AC = 



