PHILOSOPHICAL WRITINGS OP THE LiTE DR. DALTON. 1 1 



In the mathematical department he answers ten out of tlie 

 list o{ fifteen questions proposed, of which those to questions 

 5, 11, and 15 obtained insertion. The fifth question relates 

 to the impact of two elastic bodies ; — the eleventh to the flow 

 of water through a circular aperture ; — and the solution of the 

 prize question is here transcribed as furnishing an interesting 

 specimen of his attainments in physical astronomy. 



Prize Question, 907. By Lieut, JVilliam Mudge, " It 

 is required to determine the quantity of heat received by the 

 great comet, expected to appear in the beginning of the year 

 1789, during its passage from the aphelion to its perihelion, 

 the quantity received in one second when at the mean distance 

 of the earth being given = q ; and to compare the mean heat 

 of the earth to the greatest heat of the comet when in its 

 perihelion ; the period of the comet being 128 J years, and its 

 perihelion distance '44851, the radius of the earth's orbit 

 being unity." 



Answered by Mr, John Dalton, "Lemma 1. Suppose 

 two like bodies to revolve round the sun in concentric circles ; 

 then the quantities of heat received by each body in one re- 

 volution will be inversely as the square root of their distances 

 from the sun. For let H and h be the quantities received in 

 any small given time, as one second ; T and t their periodic 

 times in seconds; R and r their distances from the sun. 

 Then as the density, and consequently the heat of the solar 

 rays, is inversely as the square of the distances from the sun, 

 it will be H : A :: r^ : R2; and it is well known that T : < :: R» 

 : rt; and, therefore, TH : th :: r^ : R*. 



Lemma 2. Suppose two like bodies to revolve round the 

 sun, the one in a circle and the other in an ellipse, whose 

 transverse axis is equal to the diameter of the circle ; then the 

 quantities of heat received by each in one revolution will be 

 inversely as the areas of their orbits. For let the orbits be as 

 in Fig. 1, and draw SD and S e rf indefinitely near it; then 



