( 165 ) 
ti ty, tas ta, which parts do not correspond exactly with those of the 
former calculation. Let (cf. Plate II, Conn. N° 69) U, be the volume 
of the small piezometer reservoir with « cm. of glass capillary, U 
that of the remaining glass capillary, U; = V3 again that of the steel 
capillary with the joints gg and gs to a mark on b;, U, the remaining 
volume from this to the mean mercury meniscus. 
The volumes are all calculated to 17° C. and so with sufficient 
accuracy we may put the volumes U’, U,', U;', Uy’, of these parts 
at the temperatures tj, to, ts, t, under the pressure p as 
Uy! = UV, tw + wy’, Uy = Ug, Uz! = Us, Us = Uy + wy + wy! (4) 
w, = k(t4—17) Uj, wy =k (t4—17) Uy w') = 2) p Uj, wa = By p Ui 
where (6, and (4, are the coefficients for the elastic deformation of 
the glass walls calculated after the formulae of CLeBscH and Lami 
which agreed satisfactorily with some direct determinations. 
If we call Vy, the normal volume of the gas in the piezometer 
volume Ui’ and Vy, that of the gas in Us, Us, U4 together then is 
Vm = Vv Var = VN — (Ug daptg + U3 dapts + Us dapty) « « (5) 
where dsp etc. are the densities at p and tz etc. in terms of the 
normal density. 
If further we call zz etc. the difference t,—t, of the temperatures 
t, etc. from a given temperature ¢, not far removed from them at 
which the values of d,,, are known. 
Let U,", U;", Us" be such quantities that Ug!" day = Ug! dang, etc. 
and put 
Pie Ugh An thy eten dake eerie de eee 
If then we replace d,, by (pva), where the volume va of the 
gas is expressed in terms of the normal volume, we have with (5) 
pu,’ 
Pa ae se 
Vn we e U,’ + Us a Us’ | ) 
(pv A)te ( \ 
The quantities uz etc. in (6) are calculated by 
Ug = pe Ug Tg, Ug = Mpa Uz T3, Us — Gp Uy ty. « (8) 
where owing to the small difference of f4 from tf , either at 15.°6 C. 
or 20:°0" C. ee | 
ae ol Sale ORE oa 
as ts lies between 15.°6 and 20° C. we put 
1 dva Ik: 
— RR TEN e ° r . ° 10 
a as ( dt jj 15.6 we) 
assuming the same mean expansion coefficient for all cases, but 
VA) = 
(pv An an 
