Chemical and Physical Notes 75 



thermometer over that of the air, if the thermometer follows 

 the law and if the first two observations are exact. The 

 agreement with the observed difference, 5'8, is quite 

 satisfactory. But we know that no observations are free 

 from error, which must affect the first observations as well 

 as the others. In the table we have the observations made 

 at the end of each of nine consecutive intervals of ten seconds. 

 In the seventh column of the table we have the differences of 

 the consecutive logarithms of the fractional excesses remaining. 

 Theoretically these differences ought to be identical. They 

 are not ; and their variations are irregular. We may therefore 

 take the mean difference, which is 0*0669, and with it calculate 

 what ought to be the excess remaining after each interval of 

 ten seconds. The initial fractional excess, y Q , is i, and its 

 logarithm is o. Subtracting 0*0669 we get I '9331 = logj^ ; 

 and again subtracting o 0669 we get T'8662 = log j/ 2 ; and so 

 on. The logarithms obtained are found in the eighth column 

 of the table. In the ninth column we have the sum of 

 logS'O, or 0-9031, and the respective numbers in the eighth 

 column. They are the logarithms of the calculated thermo- 

 metric excesses. These are given in the tenth column. 



The first and the last entries in this column necessarily 

 agree with the observed values in the fourth column. The 

 greatest difference is o'o8, so that the actual rate of cooling 

 may be held to agree fairly well with the rate which, according 

 to theory, we ought to observe if the bulb of the thermometer 

 were a perfectly homogeneous body of infinite thermal con- 

 ductivity and of symmetrical shape, cooling in a vacuum 

 enclosed by walls having a definite and constant temperature. 

 We know that this description fits neither the thermometer 

 nor the room in which it was cooling. The shape of the bulb, 

 whether it be cylindrical or spherical, is not symmetrical in the 

 above sense, because, for purposes of observation, the thermo- 

 meter must always have a stem, and the part of the bulb 

 where it is united to the stem is exposed to different 

 conditions, as regards cooling, from the other parts of it 

 Although the thermal conductivity of the bulb of a mercurial 

 thermometer is not perfect, its degree of imperfection is not 



