78 DK'S. J. A. 1IAKKKK AND I'. t'llAl'ITIS ON A 



(f ) Corrections of the Scale and Vender. . 



The corrections of the scale are given in vol. 6 of ' Trav. et Me"m. du Bureau 

 International.' We need say here only that the study of this scale by M. ISAACHSEN 

 gives the corrections at each decimetre graduation, except the second, and at all the 

 even centimetres between 500 and 1400. 



The vernier is divided into twenty parts, and its total interval (0, 20) corresponds 

 to a length of 18 '980 millims. instead of 19 millims. A correction must therefore be 

 applied to the vernier readings, which is proportional to the fraction measured, and 

 whose maximum value is 20 micron. 



The measurements made to verify the equidistance of the divisions ol the vernier 

 showed that the errors of division attain 10 micron, for certain lines, but by reason of 

 their irregular distribution, and of the repetition of the observations using different 

 parts of the vernier, they have not been taken into account. 



XXXI. CALCULATION OF THE TEMPERATURES. 



The deduction of the formula employed for the calculation of the temperatures has 

 been given with all necessary details in the memoir already quoted,* therefore we 

 only give here a re"sumd of the process. 



Let V be the volume at of the gas contained in the thermometer reservoir ; 



S the mean coefficient of dilatation of the reservoir between and T ; 



a the coefficient of expansion of the gas at constant volume ; 



v the volume of the " dead space " at the standard temperature t ; 



Av and A the variations of volume and temperature of the " dead space " ; 



H the initial pressure of the gas corresponding to the temperature of the reser- 

 voir and t of the " dead space" ; 



H 4- h the pressure of the gas at the temperature T to be determined ; the tempe- 

 rature of the " dead space " being t -\- A, and its volume v -f- Av ; 



fr the internal pressure coefficient of the thermometric reservoir. 



The total mass of the gas being the same at the temperatures and T, we have 



Suppose now that we have applied to the pressures H and H 4- h the corrections 

 necessary to reduce them to what they would have been had the whole " dead space " 

 been maintained at 0, and let us call these new pressures H ' and H ' -j- h' ; we have 

 then the simplified formula 



/v _j_ ,,\ TI ' r^(l "* ^T) + ffji . ] ,-rj , , , ,., 

 ( v o 1 H i l + j-- - rl (H -h A ), 



* ' Trav, et M4m. du Bureau International,' vol. 6, p. 52, 



