258 On the reciprocal Action of Pendulums. 



than that of Boida. It is remarkable that in applying tlie pre'*' 

 ceding correction to the rpsults of two measurements, their dif- 

 ference should l)e reduced to less than a half a hundredth of a mil- 

 limetre ; a fact which proves at once the accuracy of the experi- 

 ments made, and precision of the apparatus invented, by Borda, 

 a precision wiiich it would be very difficult to surpass. 



If the edge of tlie knife were to slip upon the plane which 

 supports it, the correction would depend on the law of resistance 

 of friction, and it would become almost impossible to determine 

 it. It is of use, therefore, to allow a few slight as))erities to sub- 

 sist upon the plane to prevent the knife from slipping. It is 

 better also not to suffer the oscillation to be so strong as that 

 the part of the edge of the knife that is in contact with the pl'.ne 

 can overcome the friction which it experiences. 



On the reciprocal Action of Pendidums. 



The previous remarks on the measure of the seconds pendu- 

 lum by Borda, have led me to examine particularly the different 

 circiunstances wliich may have an influence on this class of ex- 

 periments, and the precautions to be taken to ensure the utmost 

 exactitude of result — -precautions which ouglit to be extreme, 

 when it is sought to determine the length of the pendulum to a 

 .hundredth nearly of a millimetre. The most important of these 

 consists in fixing the instrument in as solid a manner as possible, 

 by attaching it to some very massive body, such as a thick wall, 

 the particles of which are not themselves suscej;tii)le of extended 

 vibrations, Daniel Bernoulli reported, in the Memoirs of Peters- 

 burg for the year 1777, an observation of Ferdinand Berthoud, 

 who, having fixed an excellent astronomical pendulum very 

 firmly, which before was rather loosely fixed, found that by this 

 change alone it lost five minutes in one day — a fact which 

 Bernoulli explains in a very ingenious and sound manner. Se- 

 veral time-pieces fixed upon the same bar impress it with ix 

 slight motion, which causes their particles to vibrate, and by the 

 co-operation of tiiese causes the time-pieces act one upon the 

 other, and reciprocally modify their oscillations. Huvgens in 

 his work De Horologiu Oscillalorio reports, that having thus 

 fixed two time-pieces which went exactly alike, he saw them 

 with surprise o.'.cillate ([uite differently; the oscillations of the 

 one always commencing at the same instant when the oscil- 

 lations of the other terminated. It is still more remarkable that 

 this should be the case even when there exists a sligiit diiference 

 in the going of two time-pieces placed apart from each other. 

 Ellicot has made upon this subject some curious experiments, 

 which he has recorded in the Philosophical Transactions of the 

 year 1/41; and M. Breguet has obtained similar results from 



two 



