OF ARTS AND SCIENCES. 



49 



could be placed astraddle the bar, and thus make a very close con- 

 uection. 



After the water had boiled one hour the bar reached a permanent 

 state. I then took the following observations of the temperatures of 

 tlie different points, as shown by the deflections of the galvanometer. 

 The temperatures are expressed in centimeters of the galvanometer 

 scale, and consequently give the excess of the temperatures above that 

 of the air. 



These average values are laid off as ordinates of a certain curve 

 whose abscissas are the corresponding lengths of the bar. We can 

 find an equation to satisfy these seven known points of the form : — 



In drawing the curve I found that the sixth point would not come 

 in the symmetrical curve, and so I threw it out ; thus we shall have a 

 curve of the fifth degree, the constants of whose equation can be 

 determined from the following equations : — 



y^Ax^-^-Bx^-^Gx^ + Dx'^Ex^F Eq. (1) 



F=1A. 



4.7 — ^_|_ 5_|_ c -{- D -\- E -\- F. 

 2.9 = 32 ^4- 16.5+8 (7+4 D -\- 2 E -^ F. 

 2.1 = 243 ^ + 81 ^ + 27 O + 9 i) + 3 ^ + i^. 

 1.4 = 3125 ^ + 625 ^+ 125 G-\-2bD-\-bE-\-F. 

 0.4 = 6561 X 9 ^ + 6561 ^+729 C+81 D -\- ^ E -{- F. 



Solving these equations, we find the coefficients A B C D E F, and 

 substituting in Eq. (1), we get the equation of the first curve : — 



y = —.000238 x^ + .00598 x* — .0799 x" + .701 x"" — 3.326 x + 7.4. 



The next step is to determine the second curve, or the rate of cool- 



VOL. XVI. (N. S. VIII. j 4 



