Self-Registering Barometer. ATS 
mt 
Then by substituting in D the respective values for dh,’ éh'’ and éh* found in 
(3) (4) and (5) we obtain 
dh (s'—s')s + 8h’. 8".s — 8h". (8 +8'—s8) + 0h.s.9 + Oh'.8.8' —Oh'.s'.s 
8+s"—s' Pape re 
fei tn td EES, f 
w 
wo 
s¥—gl 
Hence concinnating both sides, we have 
h.s'.s+ 0h" .s" (s—s’) Ons 8” wl 
s+s"—s! sv¥—s" w 
Hence we deduce the general equation 
3h = 8h" pelaese) eae tty 
ss (s’—s") w s (E) 
In which equation it is obvious that the multiplier of 64” 1s a constant quantity ; 
and since that multiplier is capable of receiving any value by altering the dimensions 
of the cross sections, of the upper and lower part of the tube B, of the cistern, of the 
pillar of the hydrometer, and of the vessel A, we have it in our power to establish any 
relation we may desire between oh and o/” that is between the scale of the common 
barometer and of this new barometer. 
When the fluid used in the vessel A is mercury, which for many reasons is to be 
preferred, w'=w and equation / becomes 
3°.8""(s+s"—s') s—s’ 
sha sh" rary -— (G) 
Equation (#) is more general; but when (G) is used, a much less ball will be re- 
quired for the hydrometer, the other dimensions being the same. In these equations 
the effects of diversified atmospheric pressure alone, is considered; no account being 
as yet taken of a variation of temperature. 
In the modification of this instrument, which I described popularly to the subsec- 
tion of useful arts of the British Association, I supposed the cross sections of the 
cistern and of the vessel 4 to be so large as that the level of the surfaces of the mer- 
cury in them was not materially altered by the oscillations of the instrument; also, 
in order to diminish or remove its oscillations, I supposed the cross section of the part 
_of the tube B which dips into the cistern, to be very small. Now, if in the equation 
( G) we suppose s” and s” to be very large and s’ to be very small, it assumes the form 
aaah" (=) 
in which case if s’” the cross section of the stem of the hydrometer, were equal to s the 
cross section of the upper part of the tube B, the multiplier of 8h” would be cipher and 
ch” would be infinite for any finite 8h, or the new instrument would require an infi- 
VOL. XVII. é‘ 4p 
