( ‘ 4 * ) 
concife Lincammon Method for calculating Briggs's 
Canon of Logarithms ; together with Rules for finding 
intermediate Logarithms and Numbers, even beyond 
the Limits of the Canon. In the* 3d Propofition he 
conflrudis any Syftem of Meafiires by'a Canon of Lo- 
garithms; not only when the Meafiire of fome one 
Ratio is gijven, but alfo without that T>atum^ by feeking 
the Modulus of the Syftem by the Rule abovemen- 
tioned. In the 4th, 5th, and 6th Propofitions he 
fquares the HyferboLa^ defcribes the Logiftic Line and 
iEquiangular Spiral by a Canon of Logarithms, and 
fiiews fome curious Ufes of thefe Propofitions in their 
Scholia. Take an eafy Example of the Logometrical 
Method, in the common Problem for finding the Den- 
fity of the Atmoiphsere. Suppofing Gravity uniform, 
every one knows, that if Altitudes are taken in any A- 
rithmetical Progreftion, the Denfities of the Air in 
thofe Altitudes will be in a Geometrical Progreftion ; 
tiiat is, the Altitudes are the Me*afiires of the Ratio’s 
of the Denfities below and in thole Altirudes,' and lb 
the difterence of any two Altitudes is the'Mealure of 
the Ratio of the Denfities in thofe Altitudes. Now 
to determine the abfolute or real Magnitude of thefe 
Mealiires, the Author lliews, a^riori^ that the Mo- 
dulus of the Syftem is the Altitude of the Atmo- 
IphserejWhen reduced every where to the fame Denfity ‘ 
as below. The Modulus is given (as bear- 
ing the lame Proportion to the Altitude of the Mer- 
cury in the Barometer, as the Ipecific Gravity of Mer- 
cury does to the fpecifick Gravity of Air) and conle- 
quently the whole Syftem is given. For fince in all 
Syftems the Mealiires of the lame Ratio’s are analo- 
gous among themfelves ; the Logarithm of the Ratio 
of the Air’s Denfity in any two Altitudes will be to the 
Modulus of the Canon, (that is, to the Logarithm of 
A a the 
