ror WEIGHTS anno MEASURES. 329 
General and permanent immutability is to be found 
only in our abftract ideas; and none of thefe can define 
dimenfions but our ideas of geometrical diagrams ; there- 
fore, if we could difcover fuch relations or qualities in a 
geometrical figure, as aré peculiar to it, and as would dif- 
tinguifh it from all other fimilar figures, we fhould have 
a correct ftandard; but as every attempt to accomplith this 
has failed, we are obliged to refort to thefe general quali- 
ties of matter which are the moft durable and leaft variable. 
_ Of this clafs are cohefion, motion, gravity, &c. upon 
the laft of which the following theorem depends, and from 
which alfo Mr. Huygens has deduced the pendulum ftand- 
ard. 
But the pendalum is fubje& to many imperfeions; 
the principle of which are. 
1{t That the variation of the weight of the atmofphere 
aifects it. 
—adly.It is of different lengths at different diftances from 
the Equator. 
3dly. It requires a force in addition to its gravity to 
preferve it in motion a fufficient time, and as this may be 
greater or lefs, indifferent experiments, it may accelerate 
or retard the vibrations, and confequently render the 
length uncertain. 
4thly, Unlefs the pendulum move in a cycloidal arch, 
its ofcillations will not be perfetly ifochronous, and this 
has not been effected hitherto. 
sthly. Since the pendulum is a meafure of length only, 
the meafures of capacity and weight, if they be deduced 
from it will be erroneous in a triplicate proportion of the 
errors of the pendulum. 
The two firft of thefe faults are common to the fcheme 
here propofed alfo, and if the following theorem fhould be 
VOL, IIL Te thought 
