Self Registering Barometer. 477 
‘wards, in consequence of the corresponding expansion or contraction of other parts, 
so that the position of the index will remain unchanged, notwithstanding any change 
of temperature experienced by the frame work of the instrument. I shall accordingly 
suppose the index or pencil to be so placed, and then we need not take into account 
the effect of any expansion or contraction of the mere frame work of the instrument. 
But there are three other causes, in a barometer of this particular construction, 
affecting its indications by changes of temperature, which I shall now notice, and en- 
deavour to trace their effects. The first is, that when the mercury in the tube expands, 
by an increase of temperature, part of it will be required to descend into the cistern, 
namely, the pillar which would have been otherwise raised upon the expansion of its 
cross section ; but since the material of the tube (suppose it to be iron) expands like- 
wise, the quantity of mercury that will truly have to descend into the cistern, is only 
the column corresponding to the excess of the expansion of the mercury above the 
expansion of the tube ; the effect is, of course, reversed when contraction takes place 
by a fall of temperature. It is then, upon the excess of the expansion of the bulk of 
mercury in the tube above the expansion of the capacity of the tube, and e contra, 
that this effect depends. It is likewise to be observed, that a mere vertical lengthening 
or shortening of the barometric column, by changes of temperature, since it leaves 
the weight of the column unchanged, has therefore, no effect upon the weight of the 
cistern. The second cause is, that the effect of the capacity of the part of the tube 
which is plunged into the mercury in the cistern upon its weight, alters on three ac- 
counts—first, because the capacity of that part of the tube itself alters; secondly, 
because the level of the surface of the mercury in the cistern is changed; also, 
thirdly, the specific gravity of the mercury which it displaces, is changed; and on 
these accounts, the weight of mercury in the cistern, is virtually changed, and the in- 
dication of the instrument affected. The third cause is, that the buoyant force of the 
hydrometer is affected: first, by its own change of bulk; secondly, by the change of 
the weight of the bulk of mercury, whose place it occupies; thirdly, by the alteration 
of the portion of its pillar or stem which is immersed in the fluid, partly by the sink- 
ing or rising of the hydrometer itself; partly by the alteration of the level of the sur- 
face of the mercury in which it floats. _Upon these principles we can, in the follow- 
ing way investigate the effect of changes of temperature upon the indications of the 
instrument. 
Let us suppose the materials of which the parts of the instrument are constructed, 
to be cast iron and mercury. 
Let c = capacity of the mercury in the barometer tube B at 30 inches pressure 
and 60° temperature. 
Let c’ = bulk of same tube B which is immersed in fluid in cistern. 
ce” = bulk of fluid in the cistern. 
e” = bulk of fluid in vessel 4. 
c’ = capacity of part of hydrometer immersed in fluid in vessel A. 
