HORO 
fcribed ; and, fince the fpace defcribed by the pivots of 
the large balance is lefs than that defcribed by the liriall 
one, we may conclude, that, “ Of two balances of equal 
weights, but of different diameters, the balance with a 
large diameter has the lefs friftion.” 
We have l'een that a due proportion between the weight, 
the velocity, and the fize, of the balance, contributes 
greatly to annihilate, or at leaft to lellen, friftion. Let 
us now confider the means of leffening' friftion in the pi¬ 
vots themlelves. Experiment has proved, that large pi¬ 
vots occafion more friftion than fmall ones, and this in 
proportion to their diameters. We know alfo, that the 
length of the pivots does not fenfibly increafe friftion ; 
that linooth and well-poli(hed bodies produce lefs fric¬ 
tion than thofe with uneven furfaces ; that hard bodies 
'are rnofr capable of receiving - fuch polilh ; alfo that fric¬ 
tion is diminilhed when the'bodies in contaft are made 
of different materials, (this rule is not without excep¬ 
tions,) and if oil be introduced between them. Hence 
we have the following Rules : 
i. That pivots of a fmall diameter occafion the leaft 
friction ; and that we fhouid make the pivots as fmall in 
diameter as the material and a proper degree of Strength 
will admit.-—Remark. A pivot of fmall diameter wears 
away the pivot-hole fooner; but this may be remedied 
by making the pivot and the hole longer ; for we know 
that the length of the pivot does not fenfibly increafe 
friction, and a long pivot fullers lefs preffure of its dif¬ 
ferent parts in proportion to its length, and confequently 
preffes lefs againft the different parts of the hole. 
a. That the pivots and pivot-holes lhould be polifhed 
as highly as poilible; as not only friction is thereby 1 e 11'- 
cned, but the parts are longer in wearing out. 
3. That friction is diminilhed by making the pivots of 
a different material from the holes; e. g. the pivpts tem¬ 
pered fteel, and the holes of brafs, or of gold well harden¬ 
ed, or (ftill better) of diamonds. There is another very 
ingenious method of leffening friction at the pivots of the 
balance, which is by means of rollers, of which H. Sully, 
an Englifhman, is laid to be the inventor. It has been 
uled by Monf. Berfhoud and Mr. Mudg'e with much fuc- 
cefs ; but has been laid afide fince the adoption of per¬ 
forated jewels for pivot-holes, which is a fimple and ele¬ 
gant method. 
4. To keep the different parts from corroding, and to 
promote a free motion of the pivots in their holes, oil is 
ufed, which ought to be the cleared and pureft olive-oil. 
5. As the balance-fpring might greatly increafe fric¬ 
tion ir it prelfed the pivots with too much force againft 
the fides, of the holes, to avoid that inconvenience, the 
centre of the fpring and that of the balance, or the pivot, 
mu ft be abfolutely united in one and the fame point. 
It remains only to fpeak of the refiftance of the air. 
This, we have l'een, is not a matter of indifference in the 
conftruciion of a pendulum ; nor can it be fo in the for¬ 
mation of a balance. But in this latter cafe we have l'ome 
difficulties to furmouht which did not occur in the former. 
We. cannot reduce the refiftance of the air to a very fmall 
quantity without increaftng friftion, the effefts of which 
are infinitely more injurious to the regularity of the mo¬ 
tions of the balance than the refiftance of the air. The 
refiftance of the air increafes. with the refilling furfaces ; 
yet we have Ihown that it is advifeable to make the balance 
of a large diameter in order to lelfen friftiqri. Taking 
therefore into confideration that we mult not attempt to 
lefl'en the refiftance of the air by making fhorter vibrations 
and a fmaller balance, it only remains for us to make the 
balance prefent a Surface as fmall as may be. To this end 
the balance lhould be made of a metal of the greateft l'pe- 
cific weight pofllble : the newly-difcovered metal called 
platina is the moil advantageous ; next to platina, gold ; 
next to gold, brafs: but our balances are ulually made of 
Heel. There are other metals of a greater fpecific weight 
than brafs, but they fail in the needful quality of conflu¬ 
ence. As to the lliape of the balance, that is to be pre- 
LOGY, 313 
ferred which contains the mod matter, or largeft mafs, in 
the fmalleft fpace : this, no doubt, is the circular form. 
The three bars which go from the centre to the ring 
lhould be fharp-edged, in order to prefent a fmall refift¬ 
ance to the air. 
That the balances of watches, when manufaftmred of 
fteel, as they generally are, might be in a fmall degree 
magnetic, and that this property might have-lome influence 
in difturbing their vibrations, fome have fufpefted, and 
others have denied; but Mr. Varley has lately (fee Phil. 
Mag. vol. i. p. 18.) pointed out a lource of error which 
has been hitherto little, if at all, apprehended ; and this 
is the polarity of the balance, or tendency of a particular 
point to the north ; and of an oppofite point to the fouth, 
fo ftrong as to be fufficient materially to alter the rate of 
going of the machine, when put in different politions. 
If this caule of error had been known, the life of fteel 
balances would have been laid afide long ago, particularly 
where accurate performance is indifpenfable, as in time¬ 
pieces for aftronornical and nautical purpofes. Mr. Var- 
ley, having afeertained the fa ft, and knowing the pofition 
of the poles, proceeded to examine the effefts produced 
by this caule upon the watch’s rate of going. Having- 
put on the fpring, and replaced the balance in the watch, 
he laid the watch with the dial upwards, that is, with the. 
plane of the balance horizontally, and in fuch a pofition 
that the balance when at its place of reft lhould have its 
marked fide towards the north; in this fituation it gained 
5' 35" in 24 hours. He then changed its pofition, fo that 
the marked fide of the balance when at reft lhould he to¬ 
wards the fouth, and in 24 hours it loft 6 ' 48''; produc¬ 
ing, by its change of pofition only, a difference of 12' 
23" in its rate. This difference mult be ftill further aug¬ 
mented or diminilhed as the wearer might happen to carry 
in his waiftcoat pocket, a key, a knife, or any other article, - 
made of fteel. Subftituting, in the room of the fteel-ba- 
lance, one made of gold, he found that the watch’s rate 
of going was as uniform as that of any watch on the like-, 
conftruftion. 
When we have reduced friftion and the refiftance of 
the air to the leaft poilible quantity, beiides having em¬ 
ployed the means proper for annihilating, as nearly, as- 
pofllble, the influence of exterior motion, the balance has 
acquired a great degree of precision as a meafurer of time. 
When greater precilion is required, it behoves us to con¬ 
fider the influence of temperature upon the balance, and 
to feek for methods of producing a compenjation for the ef- 
feft of heat and of cold upon the duration and extent of. 
the vibrations. 
The oppofition of two natural effefts, produced by an- 
aitificial arrangement of the afting parts, is very properly 
called the compenjation, which has been effefted in various 
ways. The molt fimple compensation that has been pro¬ 
duced in a machine for meafuring time, is that which de¬ 
pends upon the variable fluidity of the oil applied to the 
pivot-holes of the balance-arbor, and of the other arbors 
cf a watch : oil, it is well known, however good, is more, 
fluid in hot weather than in.cold, and therefore diminilhes 
the friftion at the pivots more in fummer than in winter, 
the conlequence of which variation in the friftion of a 
watch with the ordinary crown-wheel efcapement, would 
have its rate accelerated" in the former feafon, and retarded 
in the latter, by this Ample caufe, if there were no com- 
penfating property in the ftrufture of fome part of the 
mechanilm ; but this property naturally exifts in the ba¬ 
lance and balance-fpring, both which are fubjeft to have 
their dimenfions enlarged by heat, and contracted by cold; 
and thefe changes alternately occafion retardations and 
accelerations in the rate of going; but in fuch a way, 
that, when the watch is difpofed to have its rate accele-, 
rated by the molt fluid ftate of the oil, it is alio dilpofed 
to have the fame retarded by the contemporary enlarge¬ 
ment of the balance and balance-fpring ; hence the quan¬ 
tity that one of thefe difpofltions prevails over the other 
in any watch, when regulated to- mean time at a mean 
temperature-, 
