BY HEAT OF METALS AND ALLOYS. 879 



to reduce the temperatures indicated by the common mercurial thermometer to those 

 indicated by a thermometer of the second kind mentioned above. I have since found 

 that Recknagel* and PoGOENDORFFf have given a similar investigation. 



Let M B denote a mercurial thermometer in which A is the freezing-, B the boiling- 

 point, the capacity of the tube between A and B being divided into 100 parts of equal 

 capacity. 



Let M' B' denote a thermometer of material absolutely uninfluenced by heat, having 

 exactly the dimensions of A B when at 0° C; A', B' its freezing- and boiling-points, and 

 the capacity of A', B' divided into 100 parts of equal volume. 



Let V be the capacity of M A at 0°, 100 K the capacity of A B at 0°. Since the ther- 

 mometers are exactly alike at 0°, the capacity of M' A' will be V. Let the capacity of 

 A'B'=100 mV, and, therefore, m the cubic expansion of mercury for 1° in terms of the 

 indications of thermometer M' B' ; g the cubic expansion of glass for 1°. 



When the thermometers are at the same temperature, let the ends of the columns 

 of mercury stand at T, T', f, i being the number of degrees between A and T, and A' 

 and T' respectively. 



The capacity of MA will now be V(l-f^!5'), and that of AT wiU be K^ (1+^0' an^^ 

 the volume of the mercury in MT will be V(l+m^). Hence 



V(H-mO=V(l+5r^)+K^(l+^0- 

 Therefore 



V(m-^X=K^(l+^i^). 



But t and t are both 100 at the same time. Hence 



V(m-^)100=K100(l+yl00). 

 Therefore 



But g is very small and t very nearly equal to t. Hence 



^=^—^^(100—^) very nearly. 



g varies from 0-000023 to 0-000028. Taking the higher value, 



at 50° C, ^-^=0-000028 x 50 x 50=0°-07 C, 

 at 25° C, #-^=0-000028 x 25 X 75=0°-052 C. 



Hence the expansion of mercury is not proportional to its ascent in the tube of a ther- 

 mometer, and the diiference of rates is a perfectly sensible quantity, too large to neglect 

 in many researches. Part of the increased rate of expansion of various bodies at high 

 temperatures is due to this error of the mercurial thermometer, which indicates tempe- 

 rature between 0° and 100° too high as measured by the true expansion of mercury. 

 * Pogobndoeff's ' Annalen,' vol. cxxiii. p. 115. t Ibid. vol. xli. p. 372. 



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