304 H O R O 
of an affixed piece of cork, l'o that, as the cork and its 
bar rofe in the veflel, the teeth of the bar turned a fmall 
wheel, fixed to the upper part of the frame by a cock, on 
the arbor of which wheel a hand was put, which revolved 
and indicated the hours on a fixed dial-plate. This ad¬ 
dition, however, did not render the inftrument a more 
accurate meafure of time, but only indicated the hours, 
fuch as they were, in an improved manner. It may be 
worthy of remark here, that water was at once the regu¬ 
lator and the maintaining power of the inftrument before 
us; the interval between two lucceflive drops was to the 
clepfydra what one vibration of the pendulum is to a 
clock, or one ofcillation of the balance is to a watch ; and 
the floating of the indented bar was in place of a weight 
or fpring to move the wheel to which the hand was at¬ 
tached; confequently it might be faid to be an horologi- 
cal machine of the fimplelt conftruftion poffible. The ad- 
juflment of the two cones-Avas-regulated by the latitude 
. of the place, owing to the manner in which the hours 
were divided ; at Alexandria, for inflance, the greateft 
and leaft velocity of the drops were required to be to each 
other as 70 to 50, the longefl and fliorteft hours in that 
latitude being respectively i h 10“ and 50™ of equable time; 
and in higher latitudes the difparity. is ftill greater. 
The next attempt to improve the clepfydra was by 
conflructing it l'o that its aperture was variable, being ad- 
jufled, as the year advanced, by the putting of an index 
to the fun’s place in an ecliptic circle; which attempt, of 
courfe, rendered the inftrument more complex. Perrault 
conceives the parts to have been thus adapted, according 
to the defcription given of it by M. Vitruvius Poilio, in 
his book De Architcftura, cap. ix. lib. ix. But this clep¬ 
fydra, like the preceding one, compofed of two cones, 
requires two manual adjuftments, one in the morning 
and the other in the evening, and makes no allowance 
for the (fuppofed) variation of fluidity occafioned by the 
different Hates of the weather; and the variation in the 
breadth of the groove or flit, it is prefumed, was more 
plaufible in theory than feafible in practice. The con¬ 
trivance, however, was ingenious, and befpoke the in¬ 
ventor’s acquaintance with aftronoiny. 
The cleplydra, in one of its earlier forms, was ufed as 
an aftronomical inftrument, by the help of which the 
equator was divided into twelve equal parts, before the 
mathematical diviflon of a circle was underftood ; it 
was deemed of more value than a fun-dial, on account of 
its dividing the hours of the night as well as of the day, 
Pliny flays, (lib. xxxvii.) that Pompey brought a valua¬ 
ble one among his flpoils from the Eaftern nations : and 
Casfar is faid to have met with an inftrument of this kind 
in England, by the help of which he obferved that the 
flummer nights of'this climate are fhorter than they are in 
Italy. The ufe which Pompey made of his inftrument 
was to limit the lpeeches of the Roman orators ; which 
Cicero alludes to when he fays latrare ad clepfydram. 
Beiides the ancient clepfydrse, above defcribed, F. 
Berthoud mentions another (Hiftoire de la Mefure du 
Temps, tom. i. p. 20.) which was called the anaphoric , on 
the dial-plate of which were projected the circles of the 
fphere, including the parallels of the fun’s altitude, with 
the femi-diurnal and femi-no< 5 turnal arcs, to which an 
adjuftable bead, as the fun’s reprefentative, pointed as an 
index to fhow the hours, parallels, &c. as the dial-plate 
revolved daily by means of wheel-work, which was im¬ 
pelled by water. It does not leem certain at what period 
this inftrument was invented and ufed; but Berthoud 
thinks that tables of the fun’s motion mull have exifted 
previoufly to its invention, and alfo a knowledge of pro- 
jeftions of the fphere on a plane lurface, whence he-fixes 
the date pofterior to the time of Hipparchus, who, ac¬ 
cording to Pliny, died about 125 years B. C. The name 
anaphoric is evidently derived from anaphora , which was 
the fecond houfe in the heavens, according to the doctrine 
pf aftrology, which prevailed abouffthe time here fpecified. 
The modern method of dividing the natural day into 
LOGY. 
24 folar hours of equal length, has rendered the preced¬ 
ing conftructions of the clepfydra ufelefs for fome centu¬ 
ries back ; and, notwithftanding the fcience of hydrofta- 
tics is much better underftood by the modern than it was 
by the ancient philofopher, fio that a fcale of altitudes cor- 
refponding to the variable velocities of the efflux of a 
fluid out of a given aperture can be afeertained by calcu¬ 
lation for a containing veflel of any capacity or figure, 
yet, fince the happy inventions of the balance and pen¬ 
dulum, as regulators of watches and clocks, horological 
machines, actuated by the motion of water, have become 
l’o rare, as to be confldered objefts only of curiofity. 
The fimpleft form of the modem cleplydra derives its 
origin from that law in hydroftatics by which the efflux 
of water out of an orifice is influenced under different 
preflures, or, which is the fame thing, at different depths 
from the lurface, the velocity being direflly as the fquare 
root of the height of the furface from the aperture. If a 
glafs veflel, like that in Plate VI. fig. 2 5, therefore be 
taken, out of which all the water wili flow in exaftly 12 
hours, from a iinall aperture in its lower extremity, the 
whole height muft be divided, or fuppofed to be divided, 
into the fquare of 12 or 144 equal parts, of which parts 
11 X 11, or 121 meafured from the bottom, or 23 mea- 
fured from the top, will give the diviflon for the hour ii, 
10 x 10 or 100 from the bottom will give the line for 
10, 81 for 9, 64 for 8, and lo on down to the bottom, as 
reprefented in the figure; which fcale is in the inverted 
proportion of that according to which heavy bodies fall 
in free fpace by the foie force of gravity. 
If, inftead of the veflel itfelf being divided by hour¬ 
lines as above direfted, the ftem of a floating piece like 
an hydrometer were to have a fimilar fcale kept in a per¬ 
pendicular direction, by palling through the central hole 
of a cap or cover of the veflel, the indication of time 
would be made on the ftem at the lurface of the cap, 
which conftruftion would admit of the veflel being of 
wood or metal. 
But fuch a figure might be given to the containing vefl- 
fel as would require the dividing marks to be equi-diftant, 
which Dr. Hutton, in his recent edition of Ozanam’s Re¬ 
creations, has afferted to be a paraboloid, or veflel, formed 
by the circumvolution of a parabola of the fourth degree, 
the method of aeferibing which, he has given thus: Let 
A B S, fig. 26, be a common parabola, the axis of which 
is P S, and the fummit S. Draw, in any manner, the line 
RbT parallel to that axis, and then draw any ordinate 
of the parabola A P, interfering R T in R ; make P Q a 
mean proportional between PR and PA, and let p q be s 
mean proportional alfo between pr and pa;, and lo on. 
The curve pafling through all the points Qq, See. will be 
the one required, which,Joeing made the mould foravef- 
fel to be call by, will produce an inftrument, which, when 
perforated at the apex, will have the Angular property of 
equalizing the fcale, fo as to correfpond to equal times 
while'the water is running out. Mr. Varignon has given 
a geometrical and general method of determining the fcale 
for a clepfydra, whatever may be the lhape and magnitude 
of the veflel. See Memoires de^ l’Academie Royale des 
Sciences, p. 78, 1699. 
Another method of making a water-clock w’ith equi- 
diftant hour-iines in any regular veflel, is effefted more 
Amply than in the preceding one, founded on the pro¬ 
perty of the fyphon, (which property will be more parti¬ 
cularly elucidated under the article Hydrostatics.) 
Provide a fyphon ABC, (fig. 27,) and affix to the Shorter 
branch AB a piece of cork, capable of keeping the whole 
lyphon in a vertical Situation, as flee’n in the figure. When 
this apparatus is made to play, and the water begins to 
flow off through the longer branch, it will continue to 
efcape with the fame velocity, whatever may be the height 
of the water : for, in this machine, the efflux takes place 
in conl'equence of the inequality of the force with which 
the atir.cfphere preffes on the furface of the liquid, and 
on the orifice of the longer branch; fince the fyphon then 
flaks 
