Relation to Pressure and Temperature. 



485 



Finally I compared the Bourdon gauge with a form of Tait 

 gauge oi niv own, iii which the volume expansion of a suitable 



el tube due to pressure, is measured externally. Leaving 

 further description to be given elsewhere, I will here insert an 

 example of the results obtained, selected at random. 



Table 2. 

 Comparison of gauges. 



Bourdon. 



N. G. 



Bourdon. 



X. G. 





Bourdon. 



N. G. 





atm. 



cm. 



atm. 



cm. 





atm. 



cm. 



033 







p= 



500 



870 



P= 



1000 



1700 





100 



160 



600 



1045 











200 



335 



700 



1210 











300 



520 



800 



1370 











400 



690 



900 



1530 









Here the reading of the new gauge is given under N. G. 

 Constructing the data graphically, and remembering, that the 

 deviations are to be apportioned between the gauges, it appears 

 that the error must everywhere be less than 10 atm., under 

 most unfavorable conditions. 



No stress was placed on the absolute correctness of the 

 standard atmosphere employed. The results sought follow 

 equally well for an approximate standard, correctly multiplied. 



11. Yolume changes of glass tubes. — Professor Tait* has 

 given the following expression for the volume increment of a 

 cylinder subjected to internal pressure : 



nai n «}i\ 



«i— CLl\k din) 1 



where 77 is the pressure, 1/Jc and n the compressibility and the 

 rigidity of the glass, and where a and a 1 denote the inner and 

 the outer radius of the tube, respectively. In my case 

 rt = # 015 cm or less, a, = '3 cm . It is therefore permissible to 

 neglect the factor in the above expression which involve com- 

 pressibility, with an error no greater than a few tenths per 

 cent. Hence if the proper valuef of n be introduced, and P 

 be measured in atmospheres, the above expression reduces ap- 

 proximately^: to 4/710" 8 . Unfortunately this correction is by 

 no means negligible, and may in unfavorable cases amount to 

 as much as 5 per cent of the corresponding volume decrement 

 of the liquid to be tested. The case is w r orse : most of the 

 experiments are to be made between 60° and 300°, for which 

 large interval the rigidity of glass can not be said to be known. 



* Tait: Challenger Reports, 1882, appendix, p. 29. 

 f Everett : Units and phys. constants, Macmillan, 1879, p. 53. 

 \ The correction is less than the above result, since only the right sectional ex- 

 pansion affects the measurement. 



