’ 
Nov. 30, 1882 | 
NATURE © 
105 
There is a fine view down the valley from the top of the 
hill; it was mentioned by Sir J. Frankland, who has been 
through all this country. 
Fuly 24.—The Athabasca boats arrived last night, so 
we are off this morning. 
ON THE GRADUATION OF GALVANOMETERS 
FOR THE MEASUREMENT OF CURRENTS 
AND POTENTIALSIN ABSOLUTE MEASURE} 
Il. 
ie the preceding investigation nothing has been said as 
measured. 
to the units in which the quantities 72 and #H are 
It will be convenient, before proceeding 
further, to consider shortly the measurement of magnetic 
and electrical quantities in absolute units, and particu- 
larly the centimetre, gramme, second (c.g s.) system now 
generally adopted. 
According to what is called the electro-magnetic system, 
all magnetic and electrical quantities are measured by 
units which are derived from a magnetic pole chosen as 
the pole of unit strength. This pole might be defined in 
many ways; but in order to avoid the fluctuations to 
which most arbitrary standards would .be subject, and to 
give a convenient system in which work done in the dis- 
placements of magnets or conductors, relatively to mag- 
nets or to conductors carrying currents, may be estimated 
without the introduction of arbitrary and inconvenient 
numerical factors, it is connected by definition with the 
absolute unit of force. It is defined as ‘hat pole which, tf 
placed at unit distance from an equal and similar pole, 
would be repelled with unit force. The poles referred to 
in this definition are purely ideal, for we cannot separate 
one pole of a magnet from the opposite pole of the same 
magnet : but we can by proper arrangements obtain an 
approximate realisation of the definition. Suppose we have 
two long, thin, straight, steel bars, which are uniformly and 
longitudinally magnetised ; their poles may be taken as at 
their extremities ; in fact, the distribution of magnetism 
in them is such that the magnetic effect of either bar, at 
all points external to its own substance, wou!d be perfectly 
represented by a certain quantity of one kind of imagin- 
ary magnetic matter placed at one extremity of the bar, 
and an equal quantity of the opposite kind of matter 
placed at the other extremity. We may imagine, then, 
these two bars placed with their lengths in one line, and 
their blue poles turned towards one another, and at unit 
distance apart. If their lengths be very great compared 
with this unit distance, say 100 or 1000 times as great, 
their red poles will have no effect on the blue poles com- 
parable with the repulsive action of these on one 
another. But there will be an inductive action between 
the two blue poles which will tend to diminish their 
mutual repulsive force, and this we cannot in practice get 
rid of. The magnitude of this inductive effect is, how- 
ever, less for hard steel than for soft steel, and we 
may therefore imagine the steel of our magnets so hard 
that the action of one on the other does not appreciably 
affect the distribution of magnetism in either. If, then, 
the two blue poles repel one another with a unit of force, 
each according to the definition has unit strength. 
The magnitude of unit pole is by the above definition 
made to depend on unit force. Now unit force is defined, 
according to the system of measurement of forces founded 
on Newton’s Second Law of Motion, the most convenient 
system, as that force which, acting for unit of time on 
unit of mass, will give to that mass unit of velocity. 
Our unit pole is thus based on the three fundamental 
units of length, mass, and time. According to the recom- 
mendations of the B.A. Committee, and the resolutions 
of the Paris Congress, it has been resolved to adopt 
generally the three fundamental units already in very 
extended use for the expression of dynamical, electrical, 
* Continued from p. 35. 
and magnetic quantities, namely, the centimetre as unit 
of length, the gramme as unit of mass, and the second 
as unit of time. With these units, therefore, the unit 
force is that force which, acting for one second on a 
gramme of matter, generates a velocity of one centi- 
metre per second. This unit of force has been called a 
dyne. The unit magnetic pole, therefore, in the c.g-s. 
system of units is that pole which, placed at a distance 
of 1 centimetre from an equal and similar pole, is repelled 
with a force of 1 dyne. Each of the poles of the long thin 
magnets of our example above is therefore a pole of 
strength equal to one c.g.s. unit, if the mutual force 
between the poles is 1 dyne. 
The magnetic moment 7 of anyone of the deflecting 
magnets is equal to the strength of either pole multiplied 
into the distance between them, which for magnets of 
such great length in comparison with their thickness is 
nearly enough the actual length of the magnet. There- 
fore either pole has a strength of ee units. If y and /are 
2 
measured in centimetres, and W in grammes, the strengths 
of the magnetic poles deduced from equation (4) or (6) 
will be in c.g.s. units. 
A magnetic field is the space surrounding a magnet or 
a system of magnets, or a system of conductors carrying 
currents, at any point of which, if a magnetic pole were 
placed, it would be acted on by force. From the 
definition of unit magnetic pole we get at once the defini- 
tion of magnetic field of unit intensity. Uv? magnetic 
field ts that field in which unit magnetic pole ts acted 
on by unit force, and in the c.g.s. system, therefore, it 
is that field in which unit magnetic pole is acted on by 
a force of one dyne. In the theory of the determination 
of H, given above, the horizontal force on either pole of 
the needle due to the horizontal component of the earth’s 
field is taken as ope and again the horizontal force 
on either pole of the deflecting magnet as = neh als, 
Z 
therefore, the strength in units of magnetic field inten- 
sity of the horizontal component of the earth’s field. By 
formula (5) or (7), when v and / are taken in centimetres, 
and Win grammes, //is given in dynes; that is, it is 
the number of dynes with which a unit red pole would be 
pulled towards the north, and a unit blue pole towards 
the south if acted on only by the earth’s magnetic field. 
We can now go on to the measurement of currents. 
According to the theory of electro-magnetic action 
given by Ampére, every element of a conductor in which 
acurrent is flowing acts upon a magnetic pole with a 
force which varies inversely as the square of the length 
of the line joining the centre of the element with the 
pole, and directly as the strength of the current 
and as the length of the projection of the element on 
a plane at right angles to that line. The direction of 
this force is at right angles to a plane drawn through the 
pole and the element, and acts towards one side or the 
other of that plane, according as the current in the ele- 
ment is in one or the opposite direction, and according as 
the magnetism of the pole is red or blue. From this it is 
easy to obtain a definition of unit current in the electro- 
magnetic system. It is that current which, flowing in a 
wire of unit length bent into an arc of a circle of unit 
radius, acts on a unit magnetic pole placed at the centre 
of the circle with unit force. Thus the current of unit 
strength in the complete circle of unit radius would act 
on a unit pole at the centre with 27 units of force, in the 
c.g.s. system with 2m dynes. This force acts towards one 
side or the other of the plane of the circle, according to 
the nature of the pole and the direction of the current. 
If the current, considered as flowing from the copper 
plate to the zinc plate of a Daniell’s cell, were made to 
circulate round the face of a watch in the direction oppo- 
site to that in which the hands move, a red pole placed at 
