PHILOSOPHICAL WRITINGS OP THE LATE DB. DALTON. 1 ^ 



they must somewhere become equal. Secondly, when p is 

 affirmative and 6^ — x^ in the numerator ♦♦•♦♦• 

 from the nature of equations, there will always be an odd 

 number of affirmative roots, and consequently at least one of 

 them real. 



The fluxion of the area = — ydx-=- — d (— ^ y dx -^r 

 (Jj^ — a^y dx; where if /? = 1 or — ^ ; w = 2 or J, the inte- 

 gral of the first member is had in finite terms, but in other 

 cases it will require a series ; and the integral of the last 

 term = the segment ANTR of a circle whose radius =-• b 

 and ordinate NT = (6^ — x^y. Thus, if w = 2, as in Fig. 3, 



the corrected integral = d b(- — 2) -{- d x — segment 



TVN; where c? = (^'^-~f' It is also readily bad in 

 other cases where /) = a whole number, or half of one. It 

 may also be proper to observe, that c is not actually the space 

 gone over by C the first second with a variable velocity, but 

 the space which would be described in one second with the 

 initial velocity of it continued uniform." During this year, 

 Mr. Whiting commenced the publication of his Scientific 

 Receptacle, and Mr. Dalton contributed the following ques- 

 tion, and its solution, to the second and third numbers of that 

 work. Its nature conveys the impression that he was now 

 deeply engaged in those philosophical pursuits which he relin- 

 quished only with his life. 



Question 39. By Mr, John Dalton. " There is a cylin- 

 drical glass vessel, with an upright tube, open at both ends, 

 cemented into it. At the bottom of the vessel is a quantity of 

 water, into which one end of the tube is immersed, and the 

 upper part of the vessel confines a quantity of air. The 

 diameter of the cylinder is 2 inches, of the tube ^ of an inch, 

 and of the bore tV of an inch. Now it is observed that when 

 the air is of a certain temperature, and the barometer stands 

 at 30*5 inches, the water in the tube is raised just 6 inches 

 above that in the vessel, and this last is then 4 inches firom 

 D 



