Seif- Registering Barometer. 473 
force of a hydrometer ; and I also conceive that a hydrometer floating in mercury is 
to be preferred, although almost any other fluid may be made to answer. ‘This me- 
thod of suspending, or, to speak more correctly, of weighing the cistern, was suggested 
to me by having long since observed that a most simple, cheap, and sensible instru- 
ment for weighing, may be constructed on the hydrometrical principle, by using an 
index, or the wire of a microscope attached to the vessel in which the hydrometer 
floats, for noting the position of the mark upon the stem of the hydrometer, instead 
of using the surface of the fluid for that purpose, as is usually done. 
The following description of a barometer constructed upon these principles will, I 
trust, be readily understood. 
Let B be a barometer tube, which may be of iron, turned accurately cylindrical, 
internally, where the upper surface of the mercury rises and falls , externally, where it 
dips into the cistern ; its shape and dimensions, in other respects, is of no consequence. 
This tube must be firmly fixed in its place. Let C be the cistern which should be 
cylindrical near the surface of the mercury, suspended by the frame F' from the cylin- 
drical pillar or stem S of a hydrometer H, which floats in a vessel 4 cylindrical near- 
its upper part, firmly fixed in its place, and filled to a proper height with mercury, oil, 
water, or any other proper fluid ; it is now obvious, that if the barometer should fall, 
mercury would descend from B into C, add to the weight of C, and cause it to sink 
until the stem S should have displaced as much additional fluid as would be equal in 
weight to the weight added to C’; on the contrary, if the barometer should rise, mer- 
cury would ascend from C into B, and the hydrometer would rise as far as was 
necessary for re-establishing the equilibrium by the emerging of part of S.A scale, 
it is also obvious, may be placed beside an index attached to any moveable part of 
instrument, which scale shall bear a certain proportion to the scale of the common ba- 
rometer. Let us now endeavour to discover what that proportion is. 
Let h denote the height of the common barometer at any instant (say when it 
stands at 30 inches). 
Let sh denote a change in that height caused by a change of atmospheric pressure, 
Let 8h’ denote the vertical alteration of level of the surface of the mercury in the 
tube B, caused by that change. 
Let dh” denote the vertical descent or ascent of the cistern and hydrometer in con- 
sequence of that change; it is then obvious that eh” is the part of the scale of the 
new barometer which corresponds with éh upon the scale of the common barometer. 
Let sh’ denote the rise or fall of the surface of the mercury in the cistern. 
Let 8° denote the rise or fall of the surface of the mercury in the vessel 4, in 
consequence of the sinking or rising of the stem of the hydrometer. 
Let s denote the internal cross section of the tube B at its upper part; s’ the 
external cross section of B where it dips into the cistern ; s” the excess of the cross 
section of the cistern, at the surface of the mercury, above s’ ; s’” the cross section of 
