Feb. 8, 1883] 
for the last five years in Brazil, and who by my request has 
given especial attention to the matter, is the immediate occasion 
of my inquiry. Protective mimicry is a fact too well establiched 
to admit of its supporters feeling the question a delicate one, 
Admission into your paper will speedily settle the question. 
Liverpool, Eebruary 2 Henry H. HIGGIns 
ON THE GRADUATION OF GALVANOMETERS 
FOR THE MEASUREMENT OF CURRENTS 
AND POTENTIALS IN ABSOLUTE MEASURE 
IV. 
WE shall now consider, very briefly, the graduation of 
instruments for measuring volts and amperes in 
practical work, and we shall take as our example Sir Wil- 
liam Thomson’s graded galvanometers. The graduation 
of these instruments is effected by a comparison of their 
indications with those of a standard galvanometer such 
as that described above. We shall consider first the 
graduation of a potential galvanometer, or galvanometer 
the resistance of which is so high, that the attachment of 
its terminals to two points in a conductor carrying a 
current does not perceptibly change the difference of 
potentials formerly existing between these points. Of 
course any galvanometer which measures currents also 
measures potentials, for, if its resistance is known, the 
difference of potentials between its terminals can be 
calculated from Ohm’s law ; but the convenience of a 
galvanometer specially made with a high resistance coil 
is that the difference of potentials, thus calculated as 
existing between the two points at which its terminals 
are applied while they are in contact, may be taken as 
the actual difference of potentials which exists between 
those two points when nothing but the ordinary con- 
ductor connects them. For, let Y be this actual difference 
of potentials in volts, let » ohms be the resistance of the 
conductor, and “& ohms the resistance of the galvano- 
meter. Then bythe application of A, V is diminished in 
the ratio of & to R + 7, and therefore the difference of 
potentials between the ends of the coil is now Va 2: 
Hence by Ohm’s law we have for the current through 
the galvanometer the value a = ne or Ls, If x 
RR+r R(i+ 4) 
R 
be only a small fraction of 2, = is inappreciable, and the 
difference of potentials calculated from the equation 
C= z will be nearly enough the true value. 
The instrument to be graduated is first tested as to 
the adjustment of its coil, needle, &c. The standard 
galvanometer and it are then properly set up with 
their needles pointing to zero, in positions near which 
there is no iron, and at which the values of H have been 
determined. The high resistance coil of the standard 
galvanometer and the coil of the potential instrument 
are joined in series with a constant battery of as many 
Daniell’s cells as gives a deflection of about 45° on the 
standard galvanometer, and the magnetometer is adjusted 
with its index at zero, in such a position on its platform 
that a deflection ofits needle also of nearly 45° is produced. 
The current actually flowing in the circuit is calculated 
by equation (11) or (12) from the reading obtained on the 
standard, and reduced to amperes by multiplying the 
result by 10. The difference of potentials between the 
two ends of the coil of the potential galvanometer is 
found in volts by multiplying the number of amperes 
thus found by the resistance of the coil in ohms. We 
can then obtain, by an obvious calculation, the number 
of divisions of deflection which corresponds to one volt 
between the two ends of the coil, and thence from the 
* Continued from p. 321. 
NATURE 
339 
value of 7 the number of divisions which would corres- 
.pond to one volt if the intensity of the field were one 
c.g.s. unit. This would be the number which would be 
marked at that position on the platform of the instru- 
ment; but, except for the position of the magnetometer 
nearest to the coil, positions the corresponding numbers 
of which are multiples and submultiples of 2 are alone 
marked. The numbers corresponding to the two of these 
positions adjacent on the two sides of the position of the 
magnetometer in our experiment, may be readily found 
by keeping the same difference of potential on the coil, 
and moving the magnetometer nearer to or further from 
the coil until the deflection is increased or diminished in 
the proper ratio. For example, let the deflection be 40 
divisions for 20 volts, and let the value of # at the instru- 
ment which is being graduated be 17. The number of 
divisions of deflection which would correspond to one volt 
for that position, ifthe field were of unit intensity, would be 
4° x 17 =°34. Hence the marked positions nearest to 
this in the two sides of it, are to be those for which the 
corresponding numbers are 4 and 3. Therefore the 
magnetometer must be moved further from the coil for 
the latter until the deflection produced by 20 volts be- 
comes 294. This is the position at which the number + 
is to be marked. To find the position at which 4 should 
be marked a smaller difference of potentials must be 
used, as the deflection with the same battery as before 
would be beyond the limits of the scale. Suppose that 
when its number of cells is diminished to one half; we 
get a deflection for our first position of 20. While the 
potential difference in the coil remains constant, the 
magnetometer is pushed in until the deflection again 
becomes 29°4- At this position the number 4 is to be 
marked. From this it is easy to see how the position for 
the number 1 can be found, and in the same way those 
for the other numbers of the series, 2, 4, &c. The 
number corresponding to the position of the magneto- 
meter nearest to the coil, although not one of the terms 
of this series, is determined in the same way, and marked 
at that position on the platform. This is the method 
adopted in practice in the graduation of these instru- 
ments. 
Another method sometimes convenient is as follows. 
The standard instrument, a few good Daniell’s cells, and 
a resistance which gives a deflection of about 45° on the 
standard are joined in series, and the galvanometer to be 
graduated is applied at two points in the circuit which 
include between them such a portion of the resistance as 
gives a deflection of about the same amount, Let R 
ohms be the portion of the resistance included between 
the terminals of the galvanometer, and let G ohms be 
the resistance of the galvanometer coil. Let the current 
calculated from the deflection on the standard be C 
amperes, then if V be the potential difference in volts 
between the terminals of the potential instrument, we 
have by Ohm’s law— 
c=¥, 
where 4” is the resistance equivalent to the divided 
RG 
circuit of Rand G. But A’ = ae and therefore 
c= VRE 
KG 
Hence, 
sa RE 
RAG 
This last equation gives the number of volts indicated 
by the deflection on the potential instrument, for the 
position at which its magnetometer is placed; and from 
this in precisely the same manner as described above, 
the series of positions of the magnetometer on its plat- 
form are determined and numbered. 
