112 ee 
which represents the time-constant T of the gauge. Expressing T in thousandths of 
a second and M in ounces— 
T= °16,/M . (2) 
The gauge therefore has a time-constant which depends on the inertia of the moving 
parts, but is independent, of the extent to which the copper is crushed. 
It is desirable to examine to what extent the time-constant is affected by the fact 
that the pressure in the water falls off instead of remaining constant, as assumed 
above. Suppose that the pressure decays linearly from its initial intensity, falling 
to P (1 — j) during the nominal period T of the gauge. Then-— 
_ dts it 
Mae tt + ke = PA (I — aos 
The solution is— 
s = a+ bsinct — acos ct — bet 
where— 
DA Te Ay, 3 kk 
ea rmes Vae raid Vt 
a 
The movement ceases when— 
cos ct + - Scheele 
This moment is always earlier than the nominal period—- 
7 
? 
c 
the difference being determined by the factor— 
pie RAs 
Di i. PAR 
The ratio of the actual period T’ to the nominal period T for different values of this 
factor is as follows— 
eRe = Se atio: # Gs, 
a= 1 °935 875. 
For example, if the pressure falls 21 per cent. in the nominal period of the gauge, so 
that— 
B= 45, 
] 4 
and if the initial pressure is PA = 1,200 lbs. = 3 r, (which implies that 4 = about 
20 x 107% inch) the actual period of the gauge is 64 per cent. less than the nominal 
period. To take a second case, if the pressure falls 314 per cent. in time T, so that— 
7 — 10, 
J 
and if PA = 800 lbs. = 2 r, (which implies that A = about 10 x 10~° inch) the 
difference between the nominal and actual periods is 12$ per cent. Roughly 
speaking, therefore, it may be said that a gauge of this type will have an actual 
period falling short of its nominal period by not more than about 10 per cent., provided 
the period is such that the pressure does not fall more than about 30 per cent. during 
the operation of the gauge, and provided the copper is crushed -not less than 
10 x 10-* inch. 
The form in which this type of gauge was finally embodied is shown in Fig. 37 
(type GF). There are two plates in each gauge, and each plate is clamped by a 
central screw against a tripod of coppers. The mass of each plate is “96 ounce and 
of each copper °20 ounce, so that the total effective mass associated with each copper 
is M =-°39 ounce. The time-constant of the gauge is therefore, by formula (2), 
T = 10-*second. The pressure registered by each tripod of coppers is found by 
means of formula (1), E being the sum of the energies recorded by the three coppers, 
A the average shortening of the three coppers, and A the area of the plate not covered 
by the screw-head. At the same time a parallel form of gauge (type GH) was used, 
