39 



Neglecting small quantities of a second order of magnitude, the vol- 

 umetric increase in the barometric column will be the expression 



which is the change necessary to preserve hydrostatic equilibrium. 



Now, the apparent change in the volume of mercury in the tube 

 will depend upon the differential expansion of mercury and glass, 

 and is given by the expression 



Fo(m-p') (t-t,). 



When this increase is just equal to that necessary to preserve hydro- 

 static equilibrium, all the expansion will seem to take place in the 

 vacuum chamber and no change will occur in the level of the mercury 

 in the open leg. To realize this condition we have 



Vo (m -g) (t- to) = iird^m (t - to) Ho, 

 or Vo = —r^ 



The expression 



4 m—g 

 d'Ho 



is the volume of the barometric column, supposing the diameter to be 

 the same throughout as at the top. 



The cubical coefficient of expansion of mercury 771 is a very definite 

 quantity and for barometric work may be taken to be 0.0001010 

 per degree Fahrenheit. The expansion of glass is much smaller and 

 varies considerably, ranging, according to Regnault's measurements, 

 from 0.0000145 for common white tubing to 0.0000118 for the hard 

 French and crystal tubes. That is to say, the whole volume of mer- 

 cury in a siphon to be compensated must be about 



Fo=1.168^ 



if made of common tube, 



or Fo = 1.132 



Td'Ho 



if made of French crystal. 



No great exactness is necessary in the volume of Vq. It will suffice 

 to assume Ho = th.e mean barometric pressure at the place of observa- 

 tion, and the total volume of mercury should be about 17 per cent 

 more than requisite to fill a column of height Ho and diameter d. 



If the bend of the siphon is of wide bore, the open leg and bend 

 must be very short (for example: 30X0.17 = 5.1 inches); otherwise 

 Vo will be too large. For this reason, as well as for convenience of 

 construction, the bend is best made of smaller diameter than the main 

 tube, as shown in the illustration. 



311681° — 41 6 



