C 215 ] 
the angle of the lever was 165“, the counterpoife 
1.46057 ounces, the fcale 1,19543 or AS = 
0,378024, therefore his machine did not admit of a 
maximum higher than between 26 and 27 fkains to 
the -pound. 
Fig. 3. 7 ^® one example of finding the incli- 
nation of the index, let it be required to find 
the angle for a Ikain of 32 to the pound, whofe 
weight IS o. 5 ounce; whence Cl- 1.18, CA = j 
GI-CA;or 2,*i8 : o, i 8 : : Tang! 
A C K = 84* : 03'. Tang. E C P = 38° : 23^'. ^ 
This rule for the inclination of the index, fuggefis 
an eafy way of finding the alterations in it, occafion’d 
by any fmall variation in the angle of the lever; othdr 
things remaining the fame. 
For the change in the Logarithmic Tangent of 
EC P, the fourth term in the proportion, is equal to 
that made in the Logarithmic Tangent of A CK, the 
third term ; the other two terms being the fame. 
Take therefore the difference of tfie Logarithmic 
Tangents of the two femi-angles, and divide it by 
the natural numbers i, 2, 3, 4, &c. fucceffively, and 
their quotients among the differences of the Logarith- 
mic Tangents, in Tables for each minute, will point 
out the quantity of the angle E C P, when the alter- 
ation in it is I, 2, 3, 4, 6cc. minutes fucceffively ; by 
which means a table may be eafily formed for the 
corredion of that firft computed. Suppofe, for in- 
fiance, the femi-angle of the lever to be only 84*^ : 
inftead of 84 : 03“^, for which a table has been made, 
it is required to corred this table, fo as to fuit it to 
this femi-angle 84". ^ The difference of the Log. 
Tangents of thefe femi-angles is 36,608 ; divide this 
by 
