M. Van Swinden on the Invention (yf Pendulum-Clocks 
that, in order- completely to answer their end, they must be bent 
into Gycloidal arcs, a discovery which he communicates in the 
same letter : Quod igitur nunquam me inventurum speraveram, 
nunc denique reperi : veram nimirum figuram curvarum, quae 
efficiat ut osciUationes omnes accuratissime exaequentur. Earn 
ratlone geometrica determinavi — mihi quidem omnium fe- 
iicissima (inventio) videtur in quas unquam inciderim.” {Ley- 
den 
The decided advantages of the pendulum over the old ba^ 
lanpe$ to regulate the rate of clocks, were not however immediately 
perceived by all. In the first plape, it was thought by some, that as 
clocks furnished with balances moved faster, according as heavier 
weights impelled the wheels, the same might be the case with 
pendulum-clocks. In the next place, balance-clocks stood still 
on, being wound up, whereas Huygens, by his mode of suspend- 
ing the weights, made his move on during this operation. In 
the tliird place, the reciprocal actions of the pallets and crown- 
wheel appear not to have been thoroughly understood by many. 
Tliey imagined) that the irregularities in the motion of the 
wheels might perhaps in this manner communicate themselves 
to the pendulum, instead of being overruled and prevented by 
it Lastly, the inequalities in the lengths of the vibrations 
would alter the isochronism, an objection which Huygens was 
himself the first to make; but he shows at the same time that 
his manner of connecting the pendulum with the work, made 
these small anomalies imperceptible. {Horologium^ p. 12.) 
The attention of astronomers about this time was generally 
directed towards finding some means of rendering clocks more 
regular. Hevelius, who had already, it seems, devised some 
method by which the pendulum itself might indicate the num- 
ber of oscillations it had gone through during a certain time, 
* Abundant proofs of this occur in the letters of his correspondents, (£,e^dera MSS). 
The objection is stated in the most forcible manner by Jacquet, in a letter from 
Antwerp, 1658 ; “ Unus mihi scrupulus inhaerit, pendulum luum non tam suo, 
quam automati motu, cieri. Cum enim pendulum liberum neque vibrationum ar- 
cus sortiatur aequales, neque motum per se continuet, utrumque autem tui auto- 
mati beneficio consequatur, manifestum videtur illud agitari potius automati motu 
artificial! quam naturali suo. Manet dubium annon plus inaequalitalis de ma- 
china in motum penduli, quam aqualitaiis ex motu penduli in machina dcrive» 
;tur,” &c. 
