106 PROCEEDINGS OF THE AMERICAN ACADEMY 



Tail's expression * modified for the present case is 



v^/ V=UA%(l/k + l/n)/(A\-A\) ... (2) 



where 11 is the internal pressure in atmospheres, and k and n the 

 compressibihty and the rigidity respectively of the steel employed. 

 Taking k and n from Everett's tables,! viz., ^-^ 1.84x10^^ and 

 w =: 8.2 X 10", equation (2) becomes, if II = 10^ dynes, 



v'/ V = .00000073 (3) 



This result is of the same order as (1). The difference is in large 

 part due to the constants k and 7i, which Professor Everett doubtless 

 found for high grade tool steel, whereas the above tubes, being made 

 of a low carbon steel (not teraperable), are nearer wrought iron in 

 their properties. Beyond this, the absolute gauge atmosphere is not 

 vouched for ; nor are the coethcients at the end of Table I., being mean 

 values between zero and 1,000 atmospheres, free from the thermal 

 discrepancy discussed in § 19. 



Similar results might be obtained from Tables II. and III. ; but as 

 they are not an essential part of the present paper I omit them. 



When observations are made for the purpose of measurement, how- 

 ever, equation (2) may clearly be utilized to obtain serviceable values 

 of (1 / k-j- 1 1 n). For instance, A^ may be accurately found by filling 

 the tube with mercury in vacuo, and weighing. From the known 

 density of the steel tube and its weight when empty, A^ may then be 

 computed. Similarly p is capable of accurate measurement. There- 

 fore by combining (1) and (2), (1/^-+ 1/n) is measurable with the 

 same degree of accuracy with which IT is known. 



21. Digression. Direct Reading {spiral) Bourdon Gauge. — En- 

 deavoring to achieve this result I multiplied the number of coils, 

 making a helix of five turns as shown in Figure 7. The spires B, 

 C, D, E, F, do not touch one another. The end i^is provided with 

 a needle FS, moving over a millimeter scale S, supported by a firm 

 arm TES. The end A is screwed directly into the barrel. The tube 

 was originally 1 cm. in external diameter and 0.5 cm. in bore. It was 

 flattened parallel to the axis by hammering at red heat, and coiled 

 hot. The internal diameter of the cold helix was somewhat larger 

 than 4 cm., and the upper spire, with its index, extended about a 

 decimeter beyond the helix. The following little table gives the 

 results of a comparissn with the Bourdon gauge. 



* Tait, Challenger Reports, Vol. II., 1882, Appendix A, p. 26. 

 t Everett, Units and Phys. Constants, Macmillan, 1879, p. 53. The data are 

 due to Professor Everett's researches, I believe. 



