J. H. Gore — Decimal System of Seventeenth Century. 25 



"In making use of the following and similar experiments, a 

 very exact knowledge is required of the time that has elapsed. 

 In order to obtain this knowledge more readily we must have 

 recourse to the clocks of Christian Huygens, which are con- 

 structed with hanging weights. This Huygens was a remark- 

 able man, of great learning, and one to whom posterity will 

 always be largely indebted for his great assistance in mathe- 

 matics. His clocks excel all others and correspond so nearly 

 to the daily revolution of the sun that nothing more accurate 

 can be hoped for. The fewer the wheels that are required in 

 their construction, the more regular is their motion, but it is 

 necessary for them to show the seconds as well as the minutes 

 and hours, or if they fail to do this, we must count the single 

 vibrations of a pendulum which will take place in a certain 

 specified time. The motion of the pendulum, or the defi- 

 nite number of vibrations in a given time, when all outside 

 resistance has been excluded, depends entirely upon its length, 

 and if this varies very little, it must necessarily either increase 

 or diminish the number of vibrations, and we prove by a com- 

 mon experiment that the squares of the numbers of vibrations 

 of two pendulums that are equal in all respects except that 

 of length, and vibrating the same length of time, are to each 

 other in a reciprocal ratio as the lengths of the pendulums ; 

 and conversely the lengths of the pendulums are to each other 

 in a reciprocal ratio, as the squares of the vibrations. I made 

 a pendulum with a hemp string and an iron ball I divided 

 the length — which may be anything — of the pendulum into 

 6772 equal parts, by means of an arbitrary division, for any 

 number will do for the purpose, and nothing else is necessary 

 except that the parts be very small. The length of the pendu- 

 lum is the distance from the center of the sphere to the end of 

 the thread. In this case the diameter of the ball was 160 of 

 these parts, and the thickness of the thread almost 2 of the 

 same. Having compared the aforesaid pendulum with the 

 virga, the length of the virga was found to consist of 5397 of 

 these parts. This being duly determined, I began counting 

 the single vibrations of the pendulum, using two clocks with 

 very fine weights, indicating seconds as well as minutes and 

 hours. On the 8th of March, 1665, I counted different num- 

 bers of vibrations, corresponding to different periods of time, 

 and repeated the operation about ten times. Upon' the agree- 

 ment of all these, the number of single vibrations in the space 

 of half an hour was found to be 1117f, which, applying the 

 proportion already given, would show that a pendulum, the 

 length of which is equal to a virga, makes 1251*8 single vibra- 

 tions in half an hour." Subsequent observations gave for this 

 quantity 1252, 1252*1, 1252*1, using pendulums of different 



