3 10 IT O II O 
alfo carries an index, which by the. vibrations of the pen¬ 
dulum pafles over the degrees of an arc of a circle which 
is applied below or behind it. By this arrangement (which 
we lhall farther illuftratfe in the next figure) the number 
of degrees defcribed by the pendulum is fhown, and the 
quality or inequality of the vibrations is afcertaiped. 
It is eafy now to underftand the aftion and effect of 
this pendulum. Suppofing heat to adt upon it, it is evi¬ 
dent that the frame ABCD becomes longer, i.e. its lower 
part defcends, or recedes from the point of fufpenfion m. 
As the brafs rods P P, P P, lengthen alfo, their upper parts 
rife, and, by the excefs of their dilatation, (which we have 
before noticed is about as 5 to 3,) they lift up the inner 
frame EFGH by means of the Ihoulders _EF. EFGH 
lengthens all'o by the heat, which caufes the part GH to 
del'cend; biit the other two brafs rods RR, RR, length¬ 
ening alfo, by their excefs of dilatation raife up the middle 
fteel rod K L ; l’o that the bob T will remain at the fame 
diftance from the point of fufpenfion m. On the other 
hand, when cold afts upon the pendulum, the frame 
ABCD Ihortens, and the part CD comes a little nearer 
to the point of fufpenfion m ; but, as the brafs rods P P, 
%P P, Ihorien ovneontraft in like manner, but in a greater 
degree, they pulh downwards the inner frame EFGH j 
which,contracfingalfo,raifes the brafs barsR R, R R : thefe, 
in their contraction draw down the rod -KL, which car¬ 
ries the bob : and, if we fuppofe the bob T to be hereby 
pullied down as much as the frame ABCD by its con¬ 
tracting had caufed it to rife, it is evident that the com- 
penfation is complete. 
Calculation will determine the length of the frames and 
bars, fo as to form a juft compenfation. We have already 
noted the proportions ; but repeated experiments with a 
pyrometer muft be reforted to, before the work can be 
laid to be complete. Thefe experiments take up a confi- 
derable time ; but great exaftnefs is mot to be attained 
without much labour. M. Berthoud gives the following 
dimenlions (in lines or twelfths of an inch), for the pen¬ 
dulum above defcribed : 
Length of A C, BD, fromthe point of fufpenfion 
to the bottom of the frame - - 474 lines. 
EG, FH, from beneath the Ihoulders to the 
bottom of that frame - - - - 417 
KI, from underneath the Ihoulders - - 396 
Length of P P and P P - 438 
Length of R R and RR - - - 355 
M. Berthoud farther obferves, that the thicknefs of the 
frames and bars muft bear a certain proportion to the 
weight of the bob of the pendulum. He found that a 
compenfation-pendulum, which had a ball or bob of 6slbs. 
did indeed dilate with heat; but that afterwards the con- 
denfation by cold did not take place in the fame propor¬ 
tion. A pendulum fuch as we have defcribed may carry 
a bob of 24lbs. without danger of {training the compen- 
fation-bars, provided they are made of the following thick- 
nefles : AC, BD, EG, and F H, each 34 lines ; P P, R R, 
and K L, each 44 lines; or perhaps it might be well to 
make KL fomewhat thicker, efpecially if a bob of 24lbs. 
be appended. It is neceffary that the bars or rods Ihould 
be exactly parallel, that their motions upward and down¬ 
ward may be .as free as polftble: they fnould be polifhed, 
to lelfen the friction. The pieces marked SS Ihould be 
made large enough, fo as not to, confine the bars, nor 
luffer them to be too loofe. Mr. Gumming obferves, that 
round bars or wires are much preferable to Iquare bars, 
in conftructing gridirons, as there is a more equal and 
free admilfion of air to each wire, to promote which the 
wires Ihould never ftand dole together; for gridirons 
compofed of fquare bars clofely fitted to each other, par¬ 
take in fonae degree of the inconvenience of immoveable 
thermometers, though not to fuch a degree as where hol¬ 
low cylinders are ufed. 
Arnold's Gridiron Pendulum. This pendulum confifts of 
only five bars, three of fteel and two of zink. As the 
dilatation of zink is very confiderabie, (double that of 
L O G y. 
Heel,) thefe two rods will be fufficient for the purpofe 
but, as.zink is'not fo llrong as copper, the rods or bars 
muft be made fo thick as not to be acted, upon by the 
weight of the bob. This pendulum is lhown Ihortened 
at fig. 34. AAa is a cylindrical rod of fteel, to which 
the ball or bob is fuipended; only part of this rod can be 
feen in the engraving; this rod mpves freely in the crofs- 
piece L; its lower extremity .enters a hole pierced in the 
piece KK, and is fattened to it by a pin a. The two 
zink rods BBi, BBi, are alfo fattened .at their lower ex¬ 
tremity to KK by the pins bb ; and their upper ends are 
let into the piece L, to which they are fecurely fixed by 
the pins gg. The two rods CCc, CCc, are of fteel, fixed 
at top to the piece L by the pins dd, and below to F by 
the pins c, c. The crofs-piece H is fixed to the two outer 
rods by the pins e, <?; and the three inner rods have a free 
motion in this piece. The bob E is alfo free to rife and 
fall; being fuftained and fixed to the compenfation-rods 
by the 1 ’crew D, which works in the piece F. This {"crew 
has a cylindrical head G, divided in the manner lhowir 
in the figure: thefe divifions fhow, by means of the upper 
index A, how much the bob is raifed or let down. The 
graduated flat lcale M fhows the extent of the arcs of vi¬ 
bration, having over it the lower index in. 
The aCtion of the compenfation-rods is upon the fame 
principle as that of the other gridiron-pendulum. Heat 
caufes A A a to lengthen; but, being fuipended above, it 
lengthens downwards, and makes the piece KK defeend 
a little. The rods BBd, BB£, lengthen more than A Ac; 
and, being alfo fattened to KK, their dilatation a£ts up¬ 
wards, againft the crofs-piece L, to which they are alfo 
faftened, and raites it a little. 1 The outer rods, being in 
like manner faftened to L, rife at the fame time, notwith- 
ftanding their dilatation, juft enough to keep the piece F 
Hill at the fame diftance from the point of fufpenfion. That 
the compenfation may be exaft, the fum of the dilatations 
of AAa, CCc, and the ferew F G, muft be exactly equal 
to the dilatation of BEL To attain, this, Mr. Arnold 
made the different parts of this pendulum of the follow¬ 
ing dimenlions: 
AAa from the point of fufpenfion to the lower in. li. 
extremity - - - - - - - 383 
The zink rods B B b, each - - - --172. 
The fteel rods C C c, each - - - -1710 
Diameter of the ball - - -71 
The zink rods Ihould be-nearly twice the diameter of the 
fteel ones, to avoid ftraining. Mr. Arnold fufpends his 
pendulums by a gold fpring: it is likely that a knife-edge 
fufpenfion would anfwer the purpofe better. Upon the 
whole, the fimplicityof this ingenious contrivance is much 
in its favour; and the difficulty of adjuftment is not fo great 
as in tire common gridiron pendulum with nine bars. The 
principal objections to this mode of compenfation are, ilt. 
The difficulty of exactly adjufting the lengths of the rods, 
2dly. Of proportioning their thicknefs, fo that they thall 
all begin to expand or contract at the fame inftant. sdly. 
The connecting bars of a pendulum thus conftruCted are 
apt to move by ftarts. 4thly. This kind of pendulum is 
more expofed to the air’s reiiftance than a Ample pendulum. 
In Voigt’s Magazinfuer den nevejicn Zufande de Naturkunde, 
vol. iv. are defcribed the gridiron-pendulums of Mr. Ben- 
zenberg, which are compofed of lead and iron. Mr. B. 
was induced to employ lead on account of its great dila- 
tability, which is to iron as 2-57 to 1, fo that i6’j inches 
of lead compenfate 1-3 of iron; and he chofe iron in pre¬ 
ference to fteel, becaufe eafier to work. The coinpenfa- 
tion was made by a fingle rod in tire centre, 161 inches 
long, French meafure, apd half an inch thick. It was 
Amply pinned into gorges in the crofs-piece of copper; 
but the other parts of the gridiron were riveted in the 
ufual way. The iron rods were made of the belt thick 
iron wire. The materials of this pendulum are cheap, and 
it may be made in a couple of days. As the prelfure takes 
place in a vertical direction,' there is no danger, according 
to Mr. B. of rods of thele dimenlions bending.. To cor- 
