478 Professor STEVELLY 07 a new ~ 
Let 8m, denote the variation of cubic unit of mercury for a change of tempe- 
ot cast iron rature of 1° Fahrenheit. 
dt = the total change of temperature from 60°, 
dh = the sinking of the index of the instrument caused by that change, 
dh’ = the elevation of the surface of the fluid in the cistern, so caused. 
dii' = the elevation of the surface of the fluid in vessel A. 
Then will ¢ (8m—8i) dé = the column of mercury which descends from B. 
c” (8m—é) dt = change of volume of mercury in cistern. 
ce & dt = change of bulk of the part of B immersed in cistern. 
dh'—dh = total alteration of immersion of B in fluid in cistern. 
Then by considering the causes of alteration of level of surface in the cistern, it 
will be seen that 
a! at fon 98 ae 
(ahi —ah) * ¢ ae e c sal ot) dt i ce (8m 3 8) dt mona) male 
ane (c+c") (8m— SHS +c di dt—s' dh : nd 
+s 
dki=+dk) = (c+c") (8m—&) di+c' di dt—s" dh ; pipee 
s'—s 
c+e’) (d8m—s2) dt+c!' di dt—s'' dh : weight virtually added to the cistern, in conse- 
asia M Sela dia heros » SwW= je of change of part of tube B immersed in 
SoHE 
Ss 8 cistern. 
30 dt __ § weight lost by cistern in consequence of the decrease of specific gravity of fluid dis- 
EPL UR ON at laced by part of B immersed in cistern. 
P YP 
c(sm—v)di.w = { weight of mercury which descends from tube B into the cistern. 
(cs! +0’s') (8m bi) dt-+e's (8m + di) dt~c's" dm dt—s's' dh 
ee eee 
v w= $ tot weight gained by the cistern. 
—s' 
rising of surface in vessel A, in consequence of total sinking of the pillar 
: sll! 
Again, (dh + dh’) i= sai the hydrometer. 
(cc) (dm—er) dt _ § rising of surface in vessel A, in consequence of change of volume of mercury, 
vessel A, and hydrometer. 
s’ 
hence, 
Th+dh’)s" OF — oi) de 
ch” = Seen’ te 2) Gm Bat , from whence we deduce 
Py Ww pv om 
an Soh ee ; and from hence 
n _ S*dh+(c"—c" —6i) dt Apes : 
dh +dh’ = ALES Ra Gide) ee sinking of pillar of hydrometer ; from 
sv —sg 
whence we infer 
(2 dh+ (c"~c") (om—di) dt ea = cat of buoyant force caused by the sinking of the 
" g¥—eg" P hydrometer. 
