318 
MR. WHEATSTONE ON NEW INSTRUMENTS AND PROCESSES FOR 
§ 12 . 
The resistance or reduced length of a rheomotor may be ascertained by either of 
the following processes : — 
First Method . — Place the galvanometer and the rheostat in the circuit, and adjust 
the latter until the needle of the galvanometer stands at a determined point. Then 
divide the current which passes through the wire of the galvanometer, by placing an 
equal resistance by its side ; the needle will recede. The reduced length, measured 
by the number of turns of the rheostat, required to be taken out of the circuit in 
order to make the needle stand at its former point, will be equal to half the total re- 
sistance of the undivided portion of the original circuit. The resistance of the gal- 
vanometer and connecting wires, and of the coils of the rheostat in the circuit before 
the experiment, having previously been determined, that of the rheomotor is easily 
obtained by subtracting the former from the total resistance measured. 
Let E be the electro-motive force, g the resistance of the galvanometer wire, and 
R all the other resistances in the circuit. The force of the current acting upon the 
needle will be F = 
E 
R + <L 
adding by the side of the galvanometer wire another wire 
having the same resistance, is equivalent to substituting for it a wire of double sec- 
q 
tion, and the expression for the resistance of the circuit becomes R + -z ; but since, 
in consequence of the division of the current, only one-half its force acts upon the 
IE 
needle, this action may be represented by R + L ~ . To render this expression equi- 
valent to the first, the resistance R must be reduced one-half, for p ■ — = r~ u i ; 
2 + 2 y 
the resistance taken out of the circuit to effect this reduction is obviously equal to 
half the resistance of the undivided portion of the original circuit ; 
E jE _ R 
01 R + # R + £ g — a ' ' A 2* 
Second Method . — Bring the needle of the galvanometer, by means of the rheostat, 
to a determined point which we will call h. Ascertain the resistance r requisite to 
reduce the needle to a lower point a. Restore it to h ; then place a wire to divide 
the current with the galvanometer, and alter this wire until the needle again stands 
E 
at, a. When the needle stands at b, F = ^ ; when it stands at a in the first, case 
R + g 
F' = 
E 
R + (j + r- 
in the second case F' = 
E r 1 
R {g + r') + g r r 
Equating these two expressions, 
E E r' „ rr' 
R + g + r R {g + r') + g r 1 ' ' g ’ 
and as these factors are known, R may be readily determined. The resistance of the 
rheomotor may be obtained from this as before. 
