The principle on which the instrument I am about to describe is constructed, is,
that the volume of a given quantity of air under a constant temperature, is inversely as the pressure to which it is subjected
; and the means I employ to estimate the change of volume which that quantity of air undergoes, by being subjected to differences of pressure caused by a change of elevation, are the determination of the difference of weight which a floating body is capable of sustaining in both situations. Thus, if a vessel containing a quantity of air and water be floated in water, and there be a communication between the water in the floating body and that in which it floats, it will follow, that when such an apparatus is subjected to diminished pressure, the air within the float will dilate, and cause a volume of water equal in amount to the dilatation of the air to be driven from the float; and the difference of weight which the floating body will sustain, will be the exact weight of the water expelled : if such an apparatus is subjected to an increased pressure, the air within it will contract, and consequently a quantity of water, from that in which it floats, will enter the float, and the diminished weight it is capable of sustaining will be the weight of the water which has entered the float, in consequence of the diminution of the volume of the air. It is by such means, with the instrument immediately to be described, and by the help of a very simple calculation, that I propose to determine the difference of level between any two places. Plate X. fig. 1. represents the floating part, made of thin sheet brass, the body of which (
a
), in form the frustum of a cone, is nine inches long, two inches in diameter at one end, and one inch at the other, and capable of containing about fourteen cubic inches. In the centre of the widest end, a small stud of brass (
b
) is hard soldered, into which a brass wire (
c
) is screwed, an inch and three-eighths long, and about one twenty-fifth or one thirtieth of an inch in diameter : the other end of the wire is screwed into a brass stud in the middle of the convex side of a shallow cup (
d
), made also of brass, and as light as possible, so that it will retain its shape, and be capable of sustaining a weight of about eight hundred or one thousand grains.