PHILOSOPHICAL WRITINGS OF THE LATE DR. DALTON. 27 



ABC, Mr. Dalton finds . . .„ ^ .^ -^ 1 s = 



' »in. A nn. B cos. C — co«. A cos. B 



" the required quantity of water ; which is a general theorem 

 in all cases." 



The second page of the Gentleman* 8 Diary for 1794 an- 

 nounces the publication of his Essays, which are said to con- 

 tain " several new theories, and what he conceives to be a 

 complete discovery of the cause of the aurora borealis." In 

 the mathematical department we find his solution to a ques- 

 tion proposed by himself in the preceding Diary, but his 

 "true and ingenious construction" to the geometrical prize 

 question is reluctantly omitted for want of room." He also 

 proposes question 699 in the list of new questions, which is 

 answered by himself in the Diary for 1795. It relates to the 

 motion of two bodies up two different inclined planes united 

 at the vertex, but the solution is rendered less suitable for 

 selection than the following, on account of its containing a 

 reference to a similar question in a former Diary. 



Question 681. By Mr, John Dalton, " Given two 

 weights W and w, connected by a string going over a pulley 

 at A, and an inclined plane AC moveable about an axis passing 

 through A ; now supposing the less weight w placed upon the 

 plane at a given distance from A, whilst the greater W hang^ 

 freely from A ; it is required to determine the velocity of the 

 plane such that W may neither ascend nor descend: — also 

 supposing the position of the plane at any instant given, to 

 determine its initial velocity to make W ascend or descend by 

 any given uniformly accelerating force within the limits of 

 possibility." 



Answered by Mr, John Dalton, " Let kb = the given 

 distance of w from A = r ; Ac = any variable distance of the 

 perpendicular distance b c from A = a? ; t? = velocity of w ; 



