i68 
Mr. Atwood’s Investigations , &c. 
the time of a semi vibration is 
the same as is deduced from the more general 
8 If 
’Zonary to to solution in page . 4 6.-If .he point, of quiescence of ,he auxd, £ 
springs are in the latter semiarcs of vibration, and the vibratron commences from he 
point N (fig. 50 . i" this case i = b. or c = a d, andby the solution rn page ,46, the 
rime of a semivibration becomes v/—== X an arc of which the sine is 
/ d' x 7 T^ or an arc of 9 o° -L: wherefore the time of a semivibration = 
d l XI + 271 
ZEE. We observe, therefore, that whether the points of quiescence of 
the auxiliary 1 springs are situated in the first or latter semiarcs of vibration, if the sem,- 
arc of vibration should be = to the distance of the said points from the point o qui- 
eTcence of the balance spring, the times of vibration will be the same whatever be 
tlie magnitude of that semiarc* # c ______ 
Vouto page 164,— -Supposing, as in the former examples, the points of 
-f the auxiliary springs to be at the distance of 1° from the point of quiescence of t 
balance spring, the variations of rate from mean time, when the semiarcs of vibra ion 
are 135 0 , iz5°> 60°. and 10° severally, will be as expressed underneath. 
Points of quiescence In the first semiarcs of vibration. 
Variation of the daily rate 
from mean time. 
- * 9 " * 4 ° 
_ 20**92 
- 44"-33 
- 4.24". 24 
Points of quiescence in the latter semiarcs of vibration. 
+ i9"-38 
* _ + 2o".gi 
+ 43 "- 6 ° 
+ 4'. 23". 60 
suppose the balan , of (he forcc of the balance spring, or per- 
lZ ITgle aTxihary spring proportionally stronger, will. Inmost cases, be sufficient 
to compensate for the want of isochromsm in the balance spring. 
Semiarcs of vibration. 
J 3 S° 
125° 
6o° 
io c 
135 ° 
125 0 
:6o° 
io c 
