The apparatus depends fundamentally upon the perfect balancing of the
two sides of a differential electric circuit. A conventional diagram,
fig. 19, gives a schematic outline of the connections. The two
galvanometer coils, _fl_ and _fr_, are wound differentially and both
coils most carefully balanced so that the two windings have equal
temperature coefficients. This is done by inserting a small shunt _y_,
parallel with the coil _fl_, and thus the temperature coefficient of
_fl_ and _fr_ are made absolutely equal. The two thermometers are
indicated as T_{1} and T_{2} and are inserted in the ingoing and
outgoing water respectively. A slide-wire resistance is indicated by J,
and _r_ is the resistance for the zero adjustment. Ba, Z, and Z_{1} are
the battery and its variable series resistances. If T_{1} and T_{2} are
exactly of the same temperature, _i. e._, if the temperature difference
of the ingoing and outcoming water is zero, the sliding contact _q_
stands at 0 on the slide-wire and thus the resistance of the system from
0 through _fl_, _r_, and T_{1} back to the point C is exactly the same
as the resistance of the slide-wire J plus the coil _fr_ plus T_{2} back
to the point C. A rise in temperature of T_{2} gives an increase of
resistance in the circuit and the sliding contact _q_ moves along the
slide-wire toward J maximum until a balance is obtained.
[Illustration: FIG. 19.--Diagram of wiring of differential circuit with
its various shunts, used in connection with resistance thermometers on
water-circuit of bed calorimeter.]
Provision is made for automatically moving the contact _q_ by electrical
means and thus the complete balance of the two differential circuits is
maintained constant from second to second. As the contact _q_ is moved,
it carries with it a stylographic pen which travels in a straight line
over a regularly moving roll of coordinate paper, thus producing a
permanently recorded curve indicating the temperature differences. The
slide-wire J is calibrated so that any inequalities in the temperature
coefficient of the thermometer wires are equalized and also so that any
unit-length on the slide-wire taken at any point along the temperature
scale represents a resistance equal to the resistance change in the
thermometer for that particular change in temperature. With the varying
conditions to be met with in this apparatus, it is necessary that
varying values should be assigned at times to J and to _r_. This
necessitates the use of shunts, and the recording range of the
instrument can be easily varied by simple shunting, _i. e._, by changing
the resistance value of J and _r_, providing these resistances unshunted
have a value which takes care of the highest obtained temperature
variations.
Fig. 19 shows the differential circuit complete with all its shunts. S
is a fixed shunt to obtain a range on J; S' is a variable shunt to
permit very slight variations of J within the range to correct errors
due to changing of the initial temperatures of the thermometers; _y_ is
a permanent shunt across the galvanometer coil _fl_, to make the
temperature coefficients of _fl_ and _fr_ absolutely equal; Z is the
variable resistance in the battery-circuit to keep the current constant;
_r_ is a permanent resistance to fix the zero on varying ranges; S''
plus S_{1} constitutes a variable shunt to permit slight variations of
_r_ to finally adjust 0 after S' is fixed and _t_ is a permanent shunt
across the thermometer T_{1} to make the temperature coefficient of
T_{1} equal to that of T_{2}.
The apparatus can be used for measuring temperature differences from 0°
to 4° or from 0° to 8°. When on the 0° to 8° range, the shunt S is
open-circuited and the shunt S' alone used. The value of S, then, is
predetermined so as to affect the value of the wire J and thus halve its
influence in maintaining the balance. Similarly, when the lower range,
_i. e._, from 0° to 4°, is used, the resistance _r_ is employed, and
when the higher range is used another value to _r_ must be given by
using a plug resistance-box, in the use of which the resistance _r_ is
doubled.
The resistance S'' and S_{1} are combined in a slide-wire resistance-box
and are used to change the value of the whole apparatus when there are
marked changes in the position of the thermometric scale. Thus, if the
ingoing water is at 2° C. and the outcoming water at 5° C. in one
instance, and in another instance the ingoing water is 13° and the
outgoing water is 15°, a slight alteration in the value of S_{1}, and
also of S', is necessary in order to have the apparatus draw a curve to
represent truly the temperature differences. These slight alterations
are determined beforehand by careful tests and the exact value of the
resistances in S' and in S_{1} are permanently recorded for subsequent
use.