44 Mr. Drach on Sir D. Brewster's Deductions 



Secondly. For the maximum and minimum times : 



^ = 0=B + 2C(*+T)+3D(* + T) 2 , 



,_ t C . /C 2 -3BD. 

 * l ~~ L ~3D + V WW~~ ' 



the first corresponds to a minimum, the second to a maximum ; 

 the former being nearer than the latter to the morning mean. 

 Thirdly. If A, T be the temperature and epoch, and t 

 not great, 



» = ( A + ^^ T2 ) + ( B + + 3 2 D C T f)^(^ + 3DT)^ + D .^ 



is the equation for some time on each side of T ; neglecting 

 the small quantity D t 3 , it is that of a parabola, having v for 

 an absciss and t for an ordinate. 



Fourthly. Beginning at noon, T = 0, tt=A + Btf+C* 2 

 + D tf 3 + &c. Taking the mean of homonymous hours (the 

 unit of t being one day), that is, taking the mean of t + £ and 

 t — i» we obtain 



„, +# = A + B(< + i) + c(^ + i- + l) + &c . 

 = A + T + Te + ( B + t) ' + C ' 2 + &c - 



rj 



Whereof the mean = A + — + B t + C t* &c. For the 



16 



mean of the twenty-four hours, we add — t and + t, there- 

 fore 



24A 2C 12* f8 2E 12< f* 

 General mean = _ + _ 2^ _ 2 + — . 2^ . ^ 



650 C 60810 E A , C | Q 



= A + 12^576 + 18757? = A + H + &C * 

 Now C, D, &c. being small, it is evident this nearly agrees with 

 the homonymous mean, the chief error B*+ C( — — TT = p^ ) 



indicating very nearly a progressively uniform error, so that 



5 1 



by combining t and — t this error = — — C = — C must very 



nearly vanish. 



