REPORT ON THE PRESSURE ERRORS OF THE THERMOMETERS. 



31 



As a verification of these formulae, in addition to the simple one described in the text above, 

 I had an apparatus constructed of ordinary lead glass of the following dimensions : Length of 

 cylindrical bulb, 745 mm. Ratio a fl : a l = 8'7 : 21'9. The weight of mercury filling 424 mm. of 

 this bulb was 167 grm. To the bulb was attached a smaller tube of which the mercury filling 

 68 mm. weighed T43 grm. 



Hence we have _f^I_ 1-187 



-~ 



* 



Also the content of the whole bulb in mercury is j -167 grm. = 293-4 grrnu Hence a pressure of 



44 



(1*187 \ 



293-4 =J 0-348 grm. of mercury. This 



ought to displace the index through (^^QQ = \ IB'^'So. Comparing this with the result of ex- 

 periment, we had the following remarkably satisfactory numbers : 



There was no glass tube in the interior of the bulb, so that the slight discrepancies between the 

 ratios of calculated to observed effects are mainly due to effects of temperature. 



APPENDIX B. Calculation of the Effect of an Aneurism. 



The above formulae contain all that is necessary for work of this kind. But there is one special 

 application about which a little farther explanation is necessary. 



In calculating, for the general table in Appendix E below, the effect of the aneurism nearest to 

 the principal bulb, which is the only one of importance, I have taken the following plan. 



I assumed the section of the aneurism through the axis to be bounded by a simple harmonic 

 wave curve complete from trough to trough, which agrees very exactly with its apparent outline as 

 seen through the wall of the tube. Hence, if 2a be the greatest diameter of the aneurism, 26 the 

 diameter of the tube, and I the length of the aneurism, its volume is 



Or, if we write n for the ratio a : 6, the aneurism adds to the volume of mercury in the part of the 

 tube containing it an amount equal to that contained in a length 



3re 2 +2n-5 , 



of the unaltered tube. 



