3i8 
H O R O 
fcrews; there is alfo a fcrew palling through the ftem, to 
t'erve to regulate to mean time. Another metallic bar, 
equal and ftmilar, and furnifhed like the other, but re- 
verl'ed in pofition, is placed parallel to it. 
“ When the whole balance is heated, the metallic rods 
will pufh forward the fhort ends of the levers, and which 
quantity will be juft equal to the difference of the expan- 
fion of the two metals. Suppofe the fhort ends of the 
two levers to be each equal to i, and the long ends of the 
levers to be each equal to zo, then it is evident that the 
motion of each globe will be twenty times the excefs of 
fche'fteel bar and metallic rods nearer to the centre of the 
axis of the balance than before the expanfion took place ; 
and, what is a very grand and neceflary property in the 
motion of the two globes, they will always move direftly 
to the axis of the balance; that is, their aftion will be 
conftantly in a plane pafling through the axis of the globes 
and axis of the balance. To increafe or diminifh the ex¬ 
panfion of the balance, will be only to Aide or fcrew up 
or down the globes upon their ftems, until the balance 
produces the defired effe< 5 t; and, however we increafe or 
diminifh the expanfion of the balance, or whatever may 
be the degree of temperature, it ftill retains this admirable 
property, namely, that the two fpherical weights move 
not only in the fame plane in a ftriff mathematical fenfe, 
but alfo in the fame right line in a phyfical one. This 
quality, united with the direfl motion of the brafs bars, 
renders the motion of the globes Ample and uniform, and 
therefore the effeft (depending on fuch fimple and direft 
«aufes) is regular and certain. 
“The common compenfation-balance, when in motion, 
caufes the weights to fly off or recede from the axis of the 
balance, and this flying off will increafe and diminifh 
with the arc of vibration in the balance : for, as there is 
nothing to brace the rim at the extremity of which the 
weight is fufpended; as the arc of vibration increafes, the 
weight and rim are thrown outward as much as the cen¬ 
trifugal force of the weight exceeds that of the elafticity 
of the rim. And as the arc of vibration diminifhes, and 
vonlequently the centrifugal force, the weight is thrown 
inward by the elafticity of the rim. My weights or 
fpheres are firmly braced in every degree of temperature, 
mid confequently not influenced in the fmalleft degree by 
any change in their centrifugal forces ; therefore, in every 
yefpeift, this balance may be confidered as permanent. 
“ The great difficulty in conftruiting a balance, and in 
applying the direct expanfion of metals, is to contrive it 
fo as that it fliall prelerve its equilibrium in every degree 
of temperature, and alfo admit of having all its parts made 
perfectly equal and fimilar by mechanical means. Both 
thefe important problems I have folved,by theintroduction 
and application of a different principle from any yet ufed 
in the conftruCtion of the balance of a time-keeper; and 
I am fully fatisfied, from a variety of experiments which 
I have made, that by this total change of fyftem, I have 
made a higher ftep towards the perfection of time-keepers, 
than has been effected by any other means that have come 
within my knowledge.” 
This balance is fhown at fig. 46. A A are two globes 
which Hide on the cylindrical Items of two upright levers, 
and are fattened by fcrews, by which the effect of the ex¬ 
panfion is increafed or diminifhed. CC, two equal and 
fimilar fcrews,‘by which the watch is adjufted to mean 
time. DD, the verge or axis of the balance. EE, SS, 
the combination of the fteel bar with the brafs bars. In 
the model prefented to the Society, the following are the 
proportions of the compenfation-bars : The length of the 
fteei bar is r6 inch; breadth, C232; thicknefs, o - o3a. 
The two brafs bars, in length each, 1-47 inch; breadth, 
C078 ; thicknefs, C32. Length of the two fprings 
formed out of the fteel bar, 0-03. 
The above invention has in its favour the teftimony of 
Mr. Nicholfon, and of that veteran artift Mr. Gumming' 
Of the form of the Balance fpring .—In common watches 
the balance-fpring lies flat, the coils of the Ipiral being in 
LOGY. 
the fame plane, as Ihown at fig, 47. But to longitude 
time-pieces, the fpiral is ufually thrown into the cylindri¬ 
cal form, as delineated at fig. 48. The latter has this ad¬ 
vantage, that the coils cannot touch each other in the 
largelt vibrations, even in thole of two turns and more, 
which may be eafily proved by trial. Their motion is alfo 
more concentric to the pivot of the balance, which leflens 
friction. Suppofing the balance always to lie horizontally, 
as is moltly the cafe with marine watches and all box 
time-keepers as they are called, we can, by means of a 
cylindrical fpring, diminilh the friction on the lower end 
of the pivot which bears the whole weight of the balance, 
by comprefling the fpring according to its height; the 
coils then approach each other, and tend to raile the ba¬ 
lance, fo that the pivot will have lefs preflure. But in 
this cafe the fpring mult be high enough, and the coils 
or turns fulficiently dittant, fo that in the comprefled ftate 
they may not touch each other. 
We have feen the fimple mode by which ifochronifm is 
obtained in the pendulum. To render the vibrations of 
a balance ifochronous is not fo eafy. F. Berthoud has 
proved that this regularity is to be obtained by means of 
the ipiral, regard being had to its lhape and its length. 
A very Ihort fpring makes the large vibrations quicker 
than the fmall ones ; a very long fpring, but of the fame 
power in other refpefts as the Ihort one, makes the large 
arcs flower than the fmall ones. It is therefore evident, 
that between thefe extremes a medium-length is to be- 
fought in which the greateft and leaft vibrations will be 
performed in equal times. If the large arcs are flower 
than the Ihort ones, the fpring mult be fliortened; and 
the contrary. 
Mr. Berthoud farther informs us, that a fpring confift- 
ing of many turns or coils pretty dole together is more 
favourable to ifochronifm than one of the fame length 
with fewer and wider coils ; and this becaufe the attend¬ 
ing force during the vibrations afts by the inflections of 
the fpring upon levers more equal to each other. Hence 
it follows, that cylindrical fprings are more favourable to 
ifochronifm than flat fprings; for we know that the coils 
of the cylindrical fpring are equally dittant from the cen¬ 
tre of the balance ; confequently the motion of the coils 
atts by levers evidently equal to each other. Added to 
this and the other advantages of the cylindrical fpring, 
before mentioned, we may obferve, that fprings of this 
form are more eafily made by the workmen, and may 
even be tempered after they are bent, a thing extremely 
difficult with common balance-fprings. 
Another mode of obtaining more eafily the ifochronifm 
of vibrations of unequal lengths, confilts in making the 
balance itfelf to delcribe very large arcs. From Mr. Ber- 
thoud’s experiments it appears, that the difference of a 
certain number of degrees in the extent of large arcs of 
vibrations caufes lefs variation in the going of a watch 
than the fame difference aiding upon linailer arcs ; and 
this indeed is moft confonant to reafon. With fome de¬ 
tached fcapements it is practicable to make the balance 
defcribe 360 degrees,or a complete circle; by which means 
a great quantity of motion is produced, and the balance 
thereby better calculated to refill the external agitations 
of the whole machine. 
According to the theory and experiments of Mr. Ber¬ 
thoud, the fpring when once rendered ifochronous, will 
continue fo, although the weight of the balance fhould be 
increafed or diminifhed, or even though the centre of of- 
cillation fhould be fhifted. It is unnecefl'ary therefore to 
regulate the watch till the ifochronifm of the balance- 
fpring is effected ; and the regulating weights may be 
moved to or from the centre of the compenfation-balance, 
without fear of difturbing the ifochronifm of the fpring. 
But for a full explanation of the principles upon which 
the ifochronifm of the balance-fpring is founded, we mutt 
refer the reader to Mr. Berthoud’s valuable work before 
quoted, Traite des Horloges marines, and the Supple¬ 
ment to the fame 3 and for three new methods of produc- 
3 
