26 AN ACCOUNT OF THE EARLY MATHEMATICAL AND 



eastern side of the islands, in the day, the winds occasioned by 

 this cause conspire with the general east wind, and they 

 oppose it on the western side, so that the velocity of the 

 general wind will be increased in the one case, and diminished 

 in the other ; but in the night, the wind blowing from the 

 internal parts towards the sea, will be felt in a greater or less 

 degree, according to its strength, and as it conspires with, or 

 opposes, the general eastern current." 



In the mathematical portion of this Diary two of his solu- 

 tions are inserted at length. One of them corrects an error 

 in Simpsoiis Fluxions relating to the treatment of a fluxional 

 equation, and the other determines the form and capacity of a 

 certain vessel which empties itself uniformly through a given 

 orifice. The list of new questions also contains one from Mr. 

 Dalton, which is answered by himself and " Amicus^' in the 

 Diary for 1795 : — its nature is remarkably indicative of the 

 present tendency of his scientific pursuits, and is by no means 

 unworthy of the author of the Meteorological Essays which 

 had just been published when this question made its appear- 

 ance. It is as follows : — 



Question 978. By Mr, John Dalton, " There is a rain 

 guage, or vessel with a circular aperture, set to receive the 

 falling rain ; — by some accident the guage has been turned 

 aside a little, so that the plane of the aperture makes a given 

 angle (5") with the plane of the horizon, and the direction of 

 the common section of the two planes is also given ; — now, 

 admitting that q = the quantity of water caught any day by 

 the guage in such a position, and that the direction of the 

 wind (S.W.) and the angle made by the falling rain with the 

 horizon (30°) are both given ; — it is required to determine, by 

 a general theorem, the quantity of rain that would have been 

 caught by the same guage if truly horizontal." 



Answer. By considering the three planes as great circles 

 of a sphere, forming by their intersections a spheric triangle 



