38 



glass. Wlien thus emptied the open branch may be removed, thor- 

 oughly cleaned, and replaced. Most of the dirt will come away with 

 the glass tube, but the mercury may easily be filtered and replaced 

 clean and bright. 



79. To dismantle the siphon. — If it is desired to take down the 

 siphon, it is first necessary to remove the short branch, carefully col- 

 lecting the excess of mercury, and then, after separating the ground 

 joint of the long arm, the latter is slowly inclined, while an assistant 

 steadily pours mercury into the open cups to replace what flows jnto 

 the -vacuum. When the tube is entirely filled, the finger may be 

 slipped over the open end while submerged in the mercury and the 

 whole tube removed. 



80. T emperatv/re compensation of siphon. — It has already been 

 mentioned that by giving the siphon barometer proper dimensions 

 the influence of temperature can be eliminated for all practical pur- 

 poses. The compensation operates so that changes of temperature 

 affecting the whole instrument uniformly produce no sensible change 

 in the level of the mercury in the short or open branch of the siphon. 

 The actual difference of level of mercury in the two branches will, of 

 course, be affected by temperature in the usual way, but not the abso- 

 lute position of the surface in the open leg. Since all measurements 

 are made only on this surface in many forms of mercurial barograph, 

 it is very desirable to realize in the design of such- instruments this 

 condition of automatic compensation for temperature. 



The physical principle utilized for this purpose is found in the 

 different rates of expansion of mercury and glass or whatever mate- 

 rial is used for the tube or envelope for the mercury. If the coefficient 

 of expansion of the envelope were zero, the mercury would rise 

 slightly in the open leg with rise of temperature, and vice versa. As 

 the theory of this temperature compensation is not stated in the ordi- 

 nary textbooks of physics and meteorology, and, in fact, does not 

 appear to be widely known, it seems worth while to present it here 

 briefly. The theory was developed by Prof. G. W. Hough ^ in 1862, 

 and later by Goulier : ^ 



Let Wj = Cubical expansion of mercury per unit temperature. 



Let g = Cubical expansion of glass per unit temperature. 



Let Vq = Volume of mercury in instrument at temperature ^c 



Let d = Diameter of tube at top of column in vacuum. 



Let Hq = Height of column, at temperature to. 



Let H = Height of column, at temperature t. 



d^^ 6?^ = Diameter of the two branches of the siphon at the level 

 of the top of the column in the open branch. 

 We assume that the pressure remains constant. Therefore the 

 barometric column for a change of temperature must change its 

 length by an amount represented by the expression 



in {t—tQ)Ho; 



otherwise its hydrostatic pressure will be altered ; that is, 



n-Ho = nh{t-to)Ho. 



3 Hough Prof. G. W. Annals of the Dudley Observatory, Albany, N. Y., Vol. I, 1866, 

 p. 88. 



^Goulier, C. M. Comptes-rendus, vol. 84, 1877, p. 1315. 



