132 REPORT—1863. 
French system it is the gramme derived from the unit of length, by the 
use of water at a standard temperature as a standard of density. One cubic 
centimetre of water is a gramme=15'43235 grains= 00220462 Ibs. 
A table, showing the relative value of the standard and derived units in the 
British and metrical system, is given in § 55, 
The unit of force adopted in this treatise is that force which will produce 
a unit of velocity in a free unit mass, by acting on it during a unit of time. 
This unit of force is equal to the weight of the unit mass divided by g, 
where g is the accelerating force of gravity 
=32-088 (1+0-005133 sin* \) in British units at the level of the 
or =9-78024 (1+0-005133 sin?) in metrical units sea, 
\ being the latitude of the place of observation. A unit of force still very 
generally adopted is the weight of the standard mass. The value of the new 
unit is — times the old or gravitation unit. 
g 
The unit of work adopted in this treatise is the unit of force, defined as 
above, acting through the unit of space (vide § 55). 
4. Dimensions of Derived Units —Every measurement of which we have to 
speak involves as factors measurements of time, space, and mass only ; but 
these measurements enter sometimes at one power, and sometimes at another. 
In passing from one set of fundamental units to another, and for other pur- 
poses, it is useful to know at what power each of these fundamental measure- 
ments enters into the derived measure. 
Thus the value of a force is directly proportional to a length and a mass, 
but inversely proportional to the square of a time. This is expressed by 
saying that the dimensions of a force are = ; in other words, if we wish to 
pass from the English to the French system of measurements, the French 
- " ‘ 28 5.AS 
unit of force will be to the English as TAG KADES: 1, or as 50°6 to1; be- 
cause there are 3-28 feet in a metre, and 15-43 grains in a gramme. If the 
minute were chosen as the unit of time, the unit of force would, in either 
3 5 of that founded on the second as unit. 
A table of the dimensions of every unit adopted in the present treatise is 
given in § 55, 
system, be 
Part I1.—Tue Messvrement or Macnreric PHENOMENA. 
5. Magnets and Magnetic Poles—Certain natural bodies, as the iron ore 
called loadstone, the earth itself, and pieces of steel after being subjected to 
certain treatment, are found to possess the following properties, and are 
called magnets. 
If one of these bodies be free to turn in any direction, the presence of 
another will cause it to set itself in a position which is conveniently described 
or defined by reference to certain imaginary lines occupying a fixed position 
in the two bodies, and called their magnetic axes. One object of our magnetic 
measurements will be to determine the force which one magnet exerts upon 
another. It is found by experiment that the greatest manifestation of force 
exerted by one long thin magnet on another occurs very near the ends of the 
two bars, and that the two ends of any one long thin magnet possess opposite 
qualities, This peculiarity has caused the name of “poles” to be given to 
