OF ARTS AND SCIEN'CES. 66 



of the conducting tubes at the point of entrance to tlie bath, the pres- 

 sure p., as measured at any instant might not correspond precisely 

 with the temperature, f, observed at the same instant, since time 

 would be required for the pressure to adjust itself by an increase or 

 decrease of transpiration. This would, of course, slightly vitiate the 

 result, and the amount of the effect would naturally increase with the 

 temperature. Being a variable error, it would be partially eliminated 

 by multiplied observations. An inspection of the records of readings 

 giving p., shows that the average deviation of the pairs of readings 

 taken in the same experiment at any given temperature increases 

 nearly as the temperature from 0.03 mm. at 20"^ to about 0.1 mm. at 

 200° C. This in connection with the column headed t\p., in Table 

 VIII. demonstrates that these observed variations in p.-, were capable 

 of producing average variable errors in y of from 0.1 per cent to 0.5 

 per cent, according to the temperature. 



If the average deviation of the various groups of determinations of 

 Tj, : ?7g in Table VI. be compared with the corresponding numbers in 

 the table of errors, it will be seen that observed percentage deviations 

 increase with the temperatures, while the precision required in the 

 instrumental measurements increases much less rapidly in any case, in 

 some cases not at all. Also the observed deviations are considerably 

 greater than can be due to instrumental errors, including the ther- 

 mometer. It seems to be thus indicated that this unequal or irregular 

 heating is probably a correct explanation of the observed variations in 

 p.,, and is one of the most prominent sources of error in this investiga- 

 tion, though at the same time one which might readily be removed by 

 modifications of the apparatus which should lead to the maintenance 

 of more constant temperatures of the bath, and to the elimination of 

 any irregular heating of parts of the tube. 



3. Errors in the determination of the temperatures t of the gauges 

 would affect the values of p^, p.,, and p^, throush the reduction to 0°. 

 Calling 0.00018 the coefficient of absolute expansion of mercury (the 

 cathetometer-bar expansion was separately corrected), the correction to 

 any observed gauge reading, I, would be, of course, C = 0.00018 / t, 

 whence 



^==0.00018?, and At = ^^ 



dt ~ ' O.U0018Z 



Assuming Ac = 0.01 mm., ar.d /= 100 mm., 



_ 0.01 _ 0.01 _ „o K- 



^ ~ 0.00018 X 100 ~ 0.018 ~ • ^' 



VOL. XXI. (N. S. XIII.) 3 



