112 REPORT—-1863. 
units as hitherto determined was well founded. It is certain that resistance- 
coils purporting to have been constructed from previous absolute determina- 
tions do not agree one with another within 7, 8, or even 12 per cent. 
Before further alluding to the results obtained by the Sub-Committee, it is 
desirable that the experiments themselves should be understood, and to this 
end the Committee have thought fit that a full explanation of the meaning of 
absolute measurement, and of the principles by which absolute electrical units 
are determined, should form part of the present Report, especially as the only 
information on the subject now extant is scattered in detached papers by 
Weber, Thomson, Helmholtz, and others, requiring considerable labour to 
collect and understand. In order to make this account as clear as possible, it 
has been thought best to disregard entirely the chronological order of the 
discoveries and writings on which the absolute system is founded, and this 
has rendered it very difficult to refer to the original source of each statement 
or conclusion. In the Appendix (C.) this want is, it is hoped, remedied. 
The word “ absolute” in the present sense is used as opposed to the word 
“relative,” and by no means implies that the measurement is accurately 
made, or that the unit employed is of perfect construction ; in other words, it 
does not mean that the measurements or units are absolutely correct, but only 
that the measurement, instead of being a simple comparison with an arbitrary 
quantity of the same kind as that measured, is made by reference to certain 
fundamental units of another kind treated as postulates. An example will 
make this clearer. When the power exerted by an engine is expressed as 
equal to the power of so many horses, the measurement is not what is called 
absolute ; it is simply the comparison of one power with another arbitrarily 
selected, without reference to units of space, mass, or time, although these 
ideas are necessarily involved in any idea of work. Nor would this measure- 
ment be at all more absolute if some particular horse could be found who was 
always in exactly the same condition and could do exactly the same quantity 
of work in an hour at all times. The foot-pound, on the other hand, is one 
derived unit of work, and the power of an engine when expressed in foot- 
pounds is measured in a kind of absolute measurement, 7. e. not by reference 
to another source of power, such as a horse or a man, but by reference to the 
units of weight and length simply—units which have been long in general 
use, and may be treated as fundamental. In this illustration, chosen for its 
simplicity, the unit of force is assumed as fundamental, and as equal to that 
exerted by gravitation on the unit mass; but this force is itself arbitrarily 
chosen, and is inconstant, depending on the latitude of the place of the 
experiment. 
In true absolute measurement the unit of force is defined as the force 
capable of producing the unit velocity in the unit of mass when it has acted 
on it for the unit of time. Hence this force acting through the unit of space 
performs the absolute unit of work. In these two definitions, time, mass, and 
space are alone involved, and the units in which these are measured, 7. e. the 
second, gramme, and metre, will alone,in what follows, be considered as funda- 
mental units. Still simpler examples of absolute and non-absolute measure- 
ments may be taken from the standards of capacity. The gallon is an arbi- 
trary or non-absolute unit. The cubic foot and the litre or cubic decimetre 
are absolute units. In fine, the word absolute is intended to convey the idea 
that the natural connexion between one kind of magnitude and another has been 
attended to, and that all the units form part of a coherent system. It appears 
probable that the name of “ derived units” would more readily convey the re- 
quired idea than the word “ absolute,” or the name of mechanical units might 
