VOL. XXIV.] PHILOSOPHICAL TRANSACTIONS. 121 



the depth of the surface of the water in the tube, below the surface of the outer 

 water, is = ^ + ^ i therefore the pressure on that inner surface is as the altitude 

 of the atmosphere above it =/+ ^+1 +a = p+ a, putting p =/+ b -{- \. 

 Then, since the spaces into which the air is contracted, are reciprocal to their 

 respective pressures; and that while the instrument is out of the water, the 



fc 

 pressure /"answers to the space c, therefore p -f a: f '.'. c: = space which 



fc 

 the air takes up in the instrument under water ; therefore, -^, — — rf = that 



part of the tube which is possessed by air = an, supposing the tube's area 



2 = n : therefore/c — wd — ad = van + aan ; and hence aa -^ (v -\ — ) X 



a = — ^^^^. Put p H — = Is:, then aa + 2s:a = "^^^ — ; therefore a = 



Then suppose the atmosphere's gravity so much less as to sink the mercury 

 ^ inch =1.4 of water; therefore putting (p = p — 1.4, and in the last equa- 

 tion a instead of a, and y instead of ^, we have a = ^'.- -{• yy '• — y- 



Thus I find a = 2.72, and x = 2.94, therefore « — gj = .22 ; which .22 X n 

 gives .44 cubic inches, and (supposing a cubic inch = 253 grains) .44 X 253 

 = 111 grains-weight of water, that was raised up into the tube in the first case 

 more than in the second, and therefore the baroscope requires an addition of 

 J 1 1 grains on its top to sink it to the level of the water in the second case more 

 than in the first, and this upon the sinking of the mercury in the common baro- 

 scope only tV of an inch ; now 1 grain in this new baroscope, is nearly as dis- 

 cernible as -rV inch in the common, and therefore this new baroscope is 111 

 times more exact than the common one. 



Put/ =247, c = 172, d = 163, w= 2 as above, only changer, putting it 

 = 437.3, that is, suppose the body sunk in water 4 inches lower; in this case 

 £t = 208, therefore a — a := .64, which multiplied into (pn = 1 .28 cubic inches, 

 which X 253, gives 324 grains ; and so much (the body's top xm being sunk 4 

 inches under water) the body becomes heavier than while xm was at the surface 

 of the water. Therefore this 1.28 divided by the aforesaid depth 4, gives .32, 

 the area of the top pipe, such as would balance or buoy up the body at any 

 depth. Strictly speaking, the pipe should be gradually wider upward, in order 

 to sustain the instrument at any depth, but as to sense it is cylindrical, and its 

 circumference = 2.005. But as the least alteration of the air would make the 

 body's top xm in that case pass through the 4 inches, which 4 inches I suppose 

 all the variety of depth that the instrument has room given it in the bucket to 



VOL. V. R 



