OF NATURAL PHILOSOPHY. 126 



mates of time, velocity, and all other matters of 

 quantity ; they are absolutely vague, and inadequate 

 to form a foundation for any exact conclusion. 



(118.) In this emergency we are obliged to have 

 recourse to instrumental aids, that is, to contrivances 

 which shall substitute for the vague impressions 

 of sense the precise one of number, and reduce all 

 measurement to counting. As a first preliminary 

 towards effecting this, we fix on convenient standards 

 of weight, dimension, time, &c., and invent contriv- 

 ances for readily and correctly repeating them as 

 often as we please, and counting how often such a 

 standard unit is contained in the thing, be it weight, 

 space, time, or angle, we wish to measure ; and if 

 there be a fractional part over, we measure this 

 as a new quantity by aliquot parts of the former 

 standard. 



(119.) If every scientific enquirer observed only 

 for his own satisfaction, and reasoned only on his 

 own observations, it would be of little importance 

 what standards he used, or what contrivances (if 

 only just ones) he employed for this purpose ; but if 

 it be intended (as it is most important they should) 

 that observations once made should remain as records 

 to all mankind, and to all posterity, it is evidently of 

 the highest consequence that all enquirers should 

 agree on the use of a common standard, and that 

 this should be one not liable to change by lapse 

 of time. The selection and verification of such 

 standards, however, will easily be understood to be 

 a matter of extreme difficulty, if only from the mere 

 circumstance that, to verify the permanence of one 

 standard, we must compare it witls others, which it 



