Conduction of Heat in Liquids. 45 



plication of (7), it may be as well to give its form for one of the 

 liquids. The following equation is for the methylated spirit, X being 

 = x 2 pc/4:Jc as previously. 



416(12-95)- 9 2 e- x 12 ' 9 5{X 2 -3X(12'95) +f (12-95)2} 

 + 327(12-45)- 92 e- x / 12 ' 45 {X 2 -3X(12-45) + j(12-45)2} 

 -fl57(ll-95)- 9 ' 2 e- x / 11 ' 95 {X 2 -3X(ll-95) +|(ll-95) 2 } 

 +119(ll-45)- 9 ^ e -x^{X 3 -3X(ll-45) + j(ll-45) 2 } 

 +170(107) e- x l0 - 7 {X2-3X(10-7)+}(10-7)2} 

 + 100(9-7)- 9 / 2 e- x ' 9 -7{X2-3X(9-7) + |(9-7) 2 } 

 + 79(8-7)- 92 e- x ' 8 - 7 {X 2 -3X(8-7) + j(8-7)2} 

 + 67(7-7)- 92 e- X7 - 7 {X2-3X(7-7)+|(7-7)2} 

 + 53(6-7)- 9 2 e- x /6-7{X2-3X(6-7) +|(6-7)2} 

 + 38(5-7)- 92 e- x ^ 7 {X 2 -3X(5-7) +|(5-7) 2 } 

 + 26(4-7)~ 9 2 e-W{X2-3X(4-7)+}(4-7)2} 

 + 21(3-7)- 9 ' 2 e~ x 3 ' 7 {X2-3X(3-7) +|(3-7) 2 } 

 + 18(2-7)" 9 .' 2 e- x ^ 7 {X2-3X(2-7) +|(2-7)2} 

 + 16(l-7)- 9 ' 2 e- x / 1 - 7 {X2-3X(l-7) +|(l-7) 2 } 

 + 15(-7)- 9 / 2 e- x /- 7 {X 2 -3X(-7)+|(-7)2} = 0. 



The solution must of course be obtained by trial, but it is compara- 

 tively easy to form a pretty accurate idea of its value from considering 

 the value of the coefficients in square brackets. Further, when a 

 solution has been obtained for one equation, its magnitude enables an 

 idea of the magnitude of the solutions of the other similar equations 

 to be readily obtained. The necessary arithmetic is best performed 

 by finding the value of each line of the left-hand side separately by 

 means of logarithms. The first four or five lines will in each case be 

 negative, and the rest positive. The last two lines at least will be 

 found extremely small. The following table, in which the letters 

 have their previous significations, gives the results obtained : — 



