Feb. 1, 1883] 
NATURE 221 
o 
change-ratio for rate of change of velocity or acceleration 
is 7 ; and the change-ratio of any other physical quan- 
tity may be found by determining from its definition the 
manner in which its unit involves the fundamental units 
of mass, length and time. Now the theory of the change- 
ratios of electrical and magnetic quantities, in the electro- 
magnetic system of units, shows that the change-ratio 
for resistance is the same as that for velocity ; that in 
fact a resistance in-electro-magnetic measure is expres- 
sible as a velocity; and hence we may with propriety 
speak of a resistance of one ohm as a velocity of 10° 
centimetres per second, 
It is obvious from equation (14) that if V and 2, each 
initially one unit, be increased in the same ratio, C will 
remain one unit of current; but that of VY be, for ex- 
ample, 10° c.g.s. units of potential, or one volt, and & be 
a resistance of 10° cms. per second, or one ohm, C will 
be one:tenth of one c.g.s. unit of current. A current of 
this strength—that is, the current flowing in a wire of 
resistance one ohm, between the two ends of which a 
difference of potentials of one volt is maintained,—has 
been adopted as the practical unit of current and called 
one ampere. Hence it is to be remembered one ampere 
is one-tenth of one c.g.s. unit of current. 
The amount of electricity conveyed in one second by 
a current of one ampere is called one cow/omb. This 
unit although not quite so frequently required as the 
others, is very useful, as, for instance, for expressing the 
quantities of electricity which a secondary cell is capable 
of yielding in various circumstances. For example, in 
comparing different cells with one another their capacities, 
or the total quantities of electricity they are capable of 
yielding when fully charged, are very conveniently 
reckoned in coulombs per square centimetre of the area 
across which the electolytic action in each takes place. 
The magneto-electric machine we have imagined gives 
us avery simple proof of the relation between the work 
done in maintaining a current, the strength of the current, 
and the electromotive force producing it. By the defini- 
tions given above of a magnetic pole and a magnetic 
field, a unit pole must produce at unit distance from 
itself a magnetic field of unit intensity. Again, unit 
current is defined as that current which flowing in a wire 
of unit length, bent into an are of a circle of unit radius, 
acts on a unit magnetic pole at the centre of the circle 
with unit force. Hence, as the reaction of the pole on 
the current must be equal to the action of the current on 
the pole, this wire carrying the current is acted on by unit 
force tending to move it in the opposite direction to that 
in which the pole is moved, and it plainly does not matter 
which we suppose held fixed and which moved. Therefore 
a conductor in a magnetic field, and carrying a unit cur- 
rent which flows at right angles to the lines of force, is 
acted on by a force tending to move it in a direction at 
right angles to its length, and the magnitude of this force 
for unit length of conductor, and unit field, is by the defini- 
tion of unit current equal to unity. 
Applying this to our slider in which we may suppose a 
current of strength C to be kept flowing, say, from a 
battery in the circuit, let Z be the length of the slider, 
v its velocity, and / the intensity of the field; we have 
for the force on the moving conductor the value 7ZC, 
Hence the rate at which work is done by the electro- 
magnetic action between the current and the field is 
TL on or 7Z Cv, and this must be equal to the rate at 
which work is done in generating by motion of the slider 
a current of strength C. But as we have seen above 
{Lv is the electromotive force produced by the motion of 
the slider. Calling this now /:, the symbol usually em- 
ployed to denote electromotive force, we have / C as the 
rate of working, that is, the rate at which electrical energy 
is given out in the circuit. 
By Ohm’s law this value for the rate of working may 
‘2 
‘ F E 
be put into either of the two other forms, namely: =, or 
R 
C*R. In the latter of these forms the law was discovered 
by Joule, who measured the amount of heat generated 
in wires of different resistances by currents flowing 
through them. This law holds for every electric circuit 
whether of dynamo, battery, or thermoelectric arrange- 
ment. 
We have, in what has gone before, supposed the slider 
to have no resistance comparable with the whole resistance 
in the circuit. If it has a resistance 7, and & be the 
remainder of the resistance in circuit, the actual difference 
of potentials between its two ends will not be /Zv or Z, 
but Ext, The rate per unit of time at which work is 
given out in the circuit is however still &C, of which 
Bee a 
the part / Cr+ = 
R 
R+7 
In short, if 7 be the actual difference of potentials, as 
measured by an electrometer, between two points in a 
metallic wire connecting the terminals of a battery or 
dynamo, and C be the current flowing in the wire, the rate 
at which energy is given out is /C, or if & be the re- 
sistance of the wire between the two points, C*”. 
One of the great advantages of the system of units of 
which I have given this brief sketch, is that it gives 
the value of the rate at which work is given out in the 
circuit, without its being necessary to introduce any co- 
efficient such as would have been necessary if the units 
had been arbitrarily chosen. When the quantities are 
measured in c.g.s. units, the value of 2 Cis given in terms 
of the centimeter-dyne or evg, the recognized dynamical 
unit of work. Results thus expressed may be reduced to 
horse-power by dividing by the number 7°46 X 10°; or if # 
is measured in volts, and C in amperes, & C may be 
reduced to horse-power by dividing by 746. Thus, if 90 
volts be maintained between the terminals of a pair of 
incandescent lamps joined in series, anda current of 1°3 
ampere flows through these lamps, the rate at which 
energy is given out in the lamps is approximately °157 
horse-power. ANDREW GRAY 
is given out in the slider, and the 
remainder, “ C in the remainder of the circuit. 
(To be continued.) 
NATURAL SCIENCE IN THE OPEN COMPE- 
TITIVE EXAMINATIONS FOR CLERKSHIPS 
(CLASS I.) IN THE CIVIL SERVICE 
HE Civil Service Commissioners have done much to 
encourage the thorough study of natural science in 
our Universities by the weight which they have assigned 
to it in the competitive examinations for first-class clerk- 
ships in the Government service. These posts are of 
sufficient value to attract young men of one or two-and- 
twenty, fresh from the University. It will be seen from 
the list of marks assigned to subjects, which we print 
below, that 1000 marks may be made in two branches of 
natural science, for instance, Zoology and Geology ; 
whilst Greek and Roman language, literature, and history 
only stand for 1500. Hence a candidate who makes 
science his strong side and can do something in either 
English, classical, or foreign literary subjects, is by no 
means at a disadvantage. 
We take this opportunity of prominently drawing atten- 
tion to the encouragement thus given to the pursuit of 
natural science as a branch of culture. t 
The schoolboy who is excused from verse-composition 
and sent into the chemical laboratory, is distinctly recog- 
nised, and has a fair chance given to him by the Com- 
missioners. So too the Oxford undergraduate who breaks 
with the wearisome iteration of Greek play and Latin 
