[ 97 ] 
therefore I fhall not take up your time in ufelefs re- 
petitions, but only fhew, on what principles the di- 
vifions of the logarithmic fines, tangents, and verfed 
fines, are ufually protradted. 
The line of numbers on thefefcales confifts of two 
equal lengths, commonly called two radii ; the firfl 
containing the logarithms of numbers from io to 
ioo ; and in the fecond are inferted thofe between 
100 and 1000, or fuch of them, as can conveniently 
be introduced. 
Thefe divifions are taken from a fcale of equal 
parts ; fuch, that ioo make the length of one radius; 
and from this fcale, the divifions for the fines, tan- 
gents, and verfed fines, are alfo taken. Now, from, 
this conftrudtion of the line of numbers, it is plain, 
that, as the numbers in one radius exceed thofe in 
the other, by one place in the fcale of numeration ; 
therefore the difference of their indices muff alfo be 
unity : fo that fuch numbers only, whole index dif- 
fers by i, can be effimated in a length of two radii: 
but, in a length of three radii, numbers, whofe in- 
dices differ by 2, may be read; and a difference of 
3 may be reckon’d in a length of 4 radii, &c. The 
tables of logarithmic fines, tangents, fecants, and verfed 
fines, are generally computed for a circle, whofe ra- 
dius is 10,000,000: therefore, 
In the fines, the index 9 be- £ , (/ a , „ 
longs to all between po o o and f 44 36 
The index 8 y 44 3 6 and 0 34 2 3 
The index 7 to all between o 34 23 and o 32 7 
6 0327 and o 021 
&c. 
N 
In 
