HOROLOGY. 
353 
to fet the balance in motion. Suppofe an impulfe to be 
given fufficient to carry it through the femi-arc O B, 
which is about 135 0 in Mr. Madge's conftruftion. The 
balance, during this motion, carries with" it the crank 
AX YD, and the affixed roils LM, ZW. When the ba¬ 
lance has defcribed 2^1 angle of about ~ the angle 
O C h, or OGi, the rod LM meets with the arm GH, 
and by turning the axis T R, and the pallet p, in the di¬ 
rection of the arc O/l releafes the tooth of the balance- 
wheel from the .projection at the extremity of the pallet p ; 
the balance-wheel immediately revolves, and, the lower 
tooth meeting with the pallet <7, winds up the auxiliary 
lpring v, and carries the arm IO with a circular motion 
through the angle Ol k, about 27°, jn which pofition the 
arm I O remains as long as the tooth of the balance-wheel 
is locked by the pallet q. While the lpring v is winding 
upthrough the arc O k, thebalance defcribes the remaining 
part of the femi-arc h B, and during this motion the rod 
LM carries round the arm G h, cauiing it to defcribe an an¬ 
gle h C B, or h G B, which is meafured by the arc h £ 108 0 . 
When the balance has arrived at the extremity of the femi- 
arc O 135 0 , the auxiliary fpring u will have been wound 
up through the fame angle of 130 0 , that is to fay, 27 0 by 
the force of the main-fpring afting. on the pallet p, and 
108 0 by the balance itfelf, carrying along with it the arm 
GO, or G^, while it defcribes the arc h B. The balance 
therefore returns through the arc BO, by the joint aCfion 
of the balance-fpring and the auxiliary lpring u ; the ac¬ 
celeration of both fprings ceafing the inftant the balance 
arrives at the quiefcent point O. When the balance has 
proceeded in its vibration about 27 0 beyond the point O, 
to the pofition C k, the rod ZW meets with the arm Ik, 
and by carrying it forward releafes the tooth of the ba¬ 
lance-wheel from the pallet q. The balance-wheel ac¬ 
cordingly revolves, and the upper tooth meeting with 
the pallet p winds up the auxiliary lpring u as before. 
The balance .with the crank, proceeding to defcribe the 
remaining femi-arc ^E, winds up the i'pringo through 
the further angle 4 CE“io 8 °, and returns through the 
femi-arc E O, by the joint action of the balance-lpring 
and the auxiliary fpring v, both of which ceale to acce¬ 
lerate the balance the inftant it has arrived at O. 
It may be remarked, in this curious fcapement, that 
the motion of the balance in its femi-vibration from the 
point of quiefcence is oppofed through an arc of no more 
than 108, but is accelerated in its return through the 
whole arc of 135 0 , and that the difference is what main¬ 
tains the vibration?; and moreover, that, the force from 
the wheel being exerted to wind up each auxiliary fpring 
during the time it is totally dilengaged from the balance, 
this laft organ cannot be affefted by its irregularities, ex¬ 
cept fo far they may render it more difficult to difengage 
the rim of the pallet from the tooth. The balance de- 
fcribes an arc of about 8° during this difengagement. 
Count Bruhl, in his pamphlet On the Inveftigation of 
Aftronomical Circles, after defcribing Mudge’s fcape- 
ment, proceeds thus: “By what has been faid, it is evi¬ 
dent, that whatever inequality there may be in the 
power derived from the main-fpring, (provided it be fuf¬ 
licient to wind up thole little paliet-fprings,) it can ne¬ 
ver interfere with the regularity of the balance’s motion 
but at the inftant of unlocking the pallets, which is fo 
inftantaneous an operation, and the refiftance fo exceed¬ 
ingly Irnrdl, that it cannot poffibly amount to any fenfi- 
ble error. The removal of this great obftacle was cer¬ 
tainly never fo effectually done by any other contrivance, 
and delerves the liighelt commendation, as a probable 
means to perfeft a portable machine that will meafure 
time correctly. But this is not the only, nor indeed the 
principal, advantage which this time-keeper will poffefs - 
over any other ; for, as it is impoffible to reduce friftion 
to fo fmall a quantity as not to affeft the motion of a ba¬ 
lance, the conlequence of which is, that it defcribes fome- 
times greater and lbmetimes fmaller arcs, it became necef- 
fary to think of fome method by which the balance might 
VOL. X. No, 6.66. 
be brought to defcribe thofe different arcs in the fame time. 
If a balance could be made to vibrate, without friftion or 
refiftance from the medium in which it moves, the me e 
expanding and contracting of the pendulum-fpring would 
probably produce the fo-much withed-for effect, as its 
force is fuppofed to be proportional to the arcs defcribed ; 
but, as there is no machine void of friction, and as, from 
that caul’e, the velocity of every balance decreafes more 
rapidly than the fpaces gene through decreafe, this ine¬ 
quality could only be Vemoved by a force,afting on the 
balance, which, a (Turning different ratios in its different 
llages, could counterbalance that inequality. This very 
material and important remedy, Mr. Mudge has eftefted 
by the conftruftion of his fcapement; for, his pallet- 
fprings having a force capable of being increafed almoft 
at pleafure at the commencement of every vibration, the 
proportion in their different degrees of tenfion may be al¬ 
tered tiil it anfwcrs the intended purpofe. This ffiows 
how effeftually Mr. Mudge’s fcapement removes the two 
greateft difficulties that have hitherto baffled the attempts 
of every other artift, namely, the inequalities of ih power 
derived from the main-fpring, and the irregularities ant¬ 
ing from friction, and the variable refiftance. of the me¬ 
dium in which the balance moves.” 
We have endeavoured to give fuch a reprefentation of 
the mechanifm of fcapement, together with the balance, 
&c. in one figure, as might exhibit to view all the pans 
of action. A few words more will fuffice. There are fix 
fprings employed in this time-keeper ; the main-fpring, 
the fpring of the going-fufee, the regulating or balance- 
fpring, the fpring of compenfation, and the two auxiliary 
fprings, u, v, on the two pallet-arbors. Thefe laft, which 
count Bruhl calls palletfpring's, from their fituaticn, are 
denominated auxiliary-fprings, becaufe they aid the two 
other fprings in the relpeftive returning parts of each vi¬ 
bration ; and in this point of view may be confidered alio 
as regulating fprings ; but, being only h of the ftrength 
of each of the others, are too weak of themfelves to per¬ 
form this office without the addition of the other more 
powerful ones, one of which has its effective length con- 
ftantly, though very flowly, changing by the fucceffive 
changes of atmofpheric temperature, which is the reafon 
why it has been called the compenfation fpring. The afting 
portions of the pallets are of flint, agate, ruby, or iapphire. 
It is of the utmoft importance that all the four fprings 
of the balance fhould be at their refpeftive points of qui¬ 
efcence when the balance is at reft, otherwife the law of 
their forces, which is affumed to be direftly as their ten- 
lions, will not be the fame in all, and fome may be acce¬ 
lerating while others are retarding, whereas they ought 
all, like one fpring, to accelerate and retard the balance 
conjointly in every part of the vibration, unlefs, indeed, 
the large fprings are found not to be ifochronal, and the 
fmall ones have their points of quiefcence fo placed as to 
effect a compenfation, which Mr. Atwood, in his ingeni¬ 
ous paper of Feb. 27, 1794, in the Philofophical Tranf- 
aftions, has fhown to be a feafibie adjuftment. For in- 
ftance, if the point of quiefcence of each of the auxiliary 
fprings, or even of one of them, be placed fomewhere in 
the firft femi-arc of vibration of the balance, the accele¬ 
ration effected thereby will be lefs in this than the retar¬ 
dation will be in the following femi-arc ; in confequence 
of which the time-keeper will go flower ; but, if the point 
of Quiefcence of the auxiliary fpring be in the latter lemi- 
arc of vibration, the contrary will be the cafe, that is, the 
.time-keeper will accelerate its rate. Nay, if the quantity 
of deviation from the exaft point of quiefcence be only 
one degree of a circle, the fame author has calculated, that, 
where the balance is of one inch radius, and of a corre- 
fponding given weight, the daily gain or lofs will be 
about 19!- 5 , and the quantity increases with the diminu¬ 
tion of the arc of vibration; fo that, if the arc of vibra¬ 
tion were to become 6o°, in one cafe the daily lots would 
be 44'33 s , and in the other the daily gain would be 43’6 S ; 
which coniideration ffiows the imperious nAeffity of hav~- 
4 X jng 
