476 Professor STEVELLY 07 a new 
nitely long scale, and would therefore be useless ; but if s” were double of s, the mul- 
tiplier of sh’ would be unity and the scale of the instrument would be precisely the 
same as that of the common barometer; between these, any desired length of scale 
may be obtained by proportioning the pillar of the hydrometer to the cross section of 
the upper part of the tube B. But of course the formula affords the more correct 
rule for constructing the instrument, so as to suit the use for which it is intended. 
I shall, however, give one other example of a particular construction of it, before I 
proceed to examine the effects of changes of temperature upon the indications of 
this barometer. 
If the internal cross section of the upper part of the tube B be made equal to the 
external cross section of that part of it which dips into the cistern, that is if s=s’; 
and if the cross section of the vessel 4 near the surface of the fluid it contains be so 
large that s” shall be nearly equal to s’—s’”; then will (@) become 
sh= oh" ~ cin ant Yap aago2y7 
that is, the scale of this instrument will bear to the scale of the common barometer, the 
ratio of the internal cross section of the upper part of the tube B to the cross section 
of the stem or pillar of the hydrometer. Now, these conditions may be obtained 
while the passage for the mercury through the lower part of the tube B, shall be as 
small as is necessary for getting rid of the irregular oscillations, before alluded to ; 
and since the cross section of the vessel 4, must be always pretty large, this rule will 
be sufficiently exact to enable a workman to guess at the size that the instrument will 
be when constructed, as also to know before hand, pretty exactly what length of scale 
an instrument of which he had only made the tube B and the hydrometer stem would 
require ; or, vice versa, what relative magnitudes he should give these, in order to pro- 
duce an instrument with a required length of scale; all these considerations also will 
enable an intelligent person before hand to calculate with sufficient exactness the cost 
of a rerequired instrument constructed on this principle. 
Let us now suppose the pressure of the atmosphere to remain unvaried, but the 
temperature to change, and let us endeavour briefly to investigate the manner in which 
the indications of the instrument are affected, and the allowances to be made, correc- 
tions to be applied, or the precautions to be adopted in consequence of that change. 
Any person who has attended to the subject of compensating pendulums, will rea- 
dily perceive, that there is a certain position in the frame which supports the cistern, 
depending upon the materials of which the hydrometer is constructed, and upon its 
dimensions, as also upon the frame, and scale, or whatever supports the sheet of paper 
on which the curve of barometric oscillation is to be delineated ; at which position, if 
the index or tracing pencil be fixed, any alteration of temperature will move it as 
much upwards, in consequence of the expansion or contraction of one part, as down- 
