468 FHI1J9SOPHICAL TRANSACTIONS. [anNO 16Q1. 



Now with regard to the first inquiry, it is a known experiment of two unison 

 strings, that striking one of them, the other moves ; which probably proceeds 

 from hence, that the impulses of the air which are made by one string, do 

 more easily set another in motion which lies in a disposition to have its vibration 

 synchronous to them, than a third whose motion would be cross. We may 

 improve this a little, by observing that a string will move not only on the strik- 

 ing.of a unison but an 8th or 12th, though after a different manner. If a 

 unison be struck, it makes one entire vibration in the whole string, as in fig. J 3, 

 and the motion is most sensible in the middle at m, for there the vibrations take 

 the greatest scope. If an 8th be struck, it makes two vibrations, as in fig. 14, 

 and then the point m is in a manner quiescent, and the most sensible motion 

 at n, n. If a 12th be struck, then it makes three vibrations, as in fig. 15, and 

 the greatest motion at q, m, q, and hardly to be perceived at p, p. All which 

 may be plainly experimented by putting a little piece of paper upon the several 

 parts of the string, to make the motion more conspicuous. So that, in short, 

 this experiment holds, when any note is struck, which is a unison to some 

 aliquot part of the string ; as in the former examples, an 8th is unison to half 

 the string, and a 12th to a third part of it. 



In this case, the vibrations of the equal parts of a string being synchronous, 

 there is no contrariety in their motion to hinder each other ; whereas it is other- 

 wise if a note is unison to s, in the fig. l6, which does not divide the string into 

 equal parts ; for then the vibrations of the remainder r not suiting with those of 

 the other parts, immediately make a confusion in the whole. 



Now in the trumpet marine, you do not stop close as in other instruments, 

 but touch the string gently with the thumb, by which there is a mutual con- 

 currence of the upper and lower parts of the string to produce the sound ; 

 which is sufficiently evident from this, that if any thing touch the string below 

 the stop, the sound will be as effectually spoiled as if it were laid upon that part 

 which is immediately struck with the bow. From hence therefore we may col- 

 lect, that the trumpet-marine yields no musical sound, but when the stop makes 

 the upper part of the string an aliquot part of the remainder, and consequently 

 of the whole, otherwise, as before remarked, the vibrations of the parts will 

 cross one another, and make a sound suitable to their motion, altogether con- 

 fused. 



Now, that these aliquot parts are the very stops, which produce the trumpet 

 notes, will be plainly shown in treating of the second inquiry, viz. what is the 

 reason that the 7 th, llth, 13th, and 14th notes, are out of tune, and the rest 

 exactly in tune ? 



