( >4° ) 
as various kinds of Quantities are made life of, fiich as 
Numbers, Time, Velocity, and the like ; or accord- 
ing as the Meafures of any one Syftem may be all iii- 
crcafcd or diminillied in any given proportion ; in fiich 
Variety much Confufion may polfibly arife as to the 
Kind and abfolute Magnitudes of particuiar Meafures, 
which happen to fall under Confideration. Our Au- 
thor very happily removes this Difficulty ; by ffievv- 
ing that the Nature of the Subjed: points out th^Mea- 
fiire of a certain immutable Ratio for a Modulus in all 
Syftems, whereby to determine the Kind and abfolute 
Magnitudes of all other Meafures in each Syftem. 
The firfl; Propofition is to find the Meafure of any 
propofed Ratio. This he confidersin a way fb fimple 
and general, as naturally leads to the Notion and De- 
finition of a Modulus -^ namely, that it is an invariable 
Qiiantity in each Syflem, which bears the fame Pro- 
portion to the Increment of the Meafiire of any pro- 
pofed Ratio, as the increafing Term of the Ratio bears 
to its own Increment. He then ffiews, that the Mca- 
flire of any given Ratio is as the Modulus of the Sy- 
ftem, from whence it is taken : and that the Moduhs 
in every Syftem is always equal to the Meafiire of a 
certain determinate and immutable Ratio, which he 
therefore calls the Ratio Modular 'ts . He ffiews that 
this Ratio is expreffed by thefe Numbers 2,7181818 
^c. to I, or by i to 0,-3678794 So that in 
Briggs'^s Canon the Logarithm of this Ratio is the 
Modulus of that Syftem ; In the Logiftic Line the 
given Subtangent is the Modulus of that Syftem : In 
the Hyperbola the given Parallelogram, contained by 
an Ordinate to the Afymptote and the Abfeifs from 
the Center, is the Modulus of that Syftem : and in 
other Syftems the Modulus is generally fbme remark- 
able Quantity. In the fecond Propofition he gives a 
2 concife 
