266 



On the Conduction of Water. 



f 



and w=HM=QL+KE+HK=< 



sin .(pi' 



+ w'. Substitute 



cos.cp ' ■ COS.(p 



these values of (0, (w), in the equation above, there results 



cos.cp 



^ 



:b^') 



t' 



(I'H^ -h'^{fd-\-cd^) 



+ [^a'H&\n.(p-h'^{p-\-'^cd)\ 



-\-':la'Hu' 



2ff'^sin.(p<V 

 cos. 9 



+ (a''^sin.(|3^ 



in which h', 8', &;c., represent the corresponding coefficients in the 



left member. But as before, i'=cos. (w-q?)^. Wherefore it only 



remains to supply the places of the letters A, 6, &z,c., in (3), by the 



corresponding accented ones h', h\ k,c. This furnishes the equa- 



-e'4-/'cos.(6j-(p)x / /e'+/cos.(^-(p)x^ ^ 

 tion y- ' 



cos.cp' 



h' 



■\-b't' 

 + eV 



■\-f't'u' 



-\-m't'^ 

 .-\-n'u'^, 



^n' 



± 



A'4-5'cos.(w — (p)x +wt^cos.(co — (p)^x" 



2?i' 



— [*' 4- sin. (w-(p)x]' 



in which the coefficients h', h', &c. are simpler than A, i, Stc, and 

 in which {ji') being equal to (a'^), is never zero. This equation, 

 to be general, supposes the possibility of drawing. a tangent to a 

 conic section parallel to a given line, a problem which is evidently 

 impossible in the case of the hyperbola, when the line parallel to 

 which the tangent is required to be drawn makes a less angle with 

 the principal axis, than the asymptote does with the same axis. 



Art. VIII. — On the Conduction of Water ; by Prof. C. Dewey. 



In Vol. xxviii, p. 151, of this Journal, are some details on this 

 subject. In that paper, the inadequacy of Dr. Murray's experi- 

 ments on this subject was shown. It is certain that when the vessel 

 containing the water and thermometer is formed of zee, the power of 

 water to conduct caloric downwards cannot he shown, as the heated 

 water, when its temperature is below 40° Fahr., will become heav- 

 ier, and thence sink to the bulb, and cause the temperature to be 

 higher. If the vessel is not made of ice, and the water on the ther- 

 mometer is cooled to near 32° Fahr., it will be equally impossible 

 to show its conduction of caloric from particle to particle, for the 



