64 PHILOSOPHICAL TRANSACTIONS. [aNNO l673. 



in China, desiring them to spare no pains in procuring it : to promote which a 

 sum of money had been sent thither, for a reward to the translators. 



The contemptibleness of the modern music to him is such, that he says there 

 is hardly so much as the shadow of the pristine majesty of it remaining; wonder- 

 ing that those, who in this and the former age have written of music, have writ- 

 ten nothing of the rhyme, or have done it so that they seem to have been 

 altogether ignorant of what it is; regarding nothing but to please the ear; 

 whereas to affect the mind, it is necessary the sound should signify what may be 

 understood by the mind, without which there can be raised no true pleasure, 

 nor any strong affection. He adverts to the excellence of the Chinese music, 

 though that people complain of the loss of their ancient way of singing, which 

 if they do justly, our author scruples not to affirm, that their music must have 

 been divine, seeing the present state of it is so excellent, that they may easily 

 silence all the music of Europe. The rare contrivance for rendering even and 

 strong sounds, of the old Roman hydraulic organ, described by Hero and Vitru- 

 vius, and explained by our author, and by him declared to excel our organs, 

 yielding an unequal and weak blast. The art of the ancients in making such 

 tibias or pipes of so many different forms and figure as there are kinds of affec- 

 tions ; concerning which he affirms, that there is none to be found at this day, 

 that even know how to make such pipes as are able to produce such m.otions; 

 since our modern artificers, in his opinion, fail not only in the matter of which 

 those instruments are to be made, but also in the proportion which is to be ob- 

 served in their form. 



Demonstration of the Synchronism of the Vibrations in a Cycloid, By a Person 

 of Quality * N° 94, p. 6032. Translated from the Latin. 



Let ab, be, cd, de, ef, &c. (fig. 1 . pi. 2), be mutually equal; and b 1, c2, d3, 

 64, f5, &c. increase equally as the numbers 1, 3, 5, 7 , 9, &c. I say, that any 

 heavy body, falling from any point of this line, will arrive at the lowest point in 

 the same space of time, in which it would arrive at it, if the body should fall 

 from any other point of the line. For if you put a = ab = be = cd, &c, and 

 Zj = bl, also jr for any number of the others: then, putting xa for af, xxb 

 must represent f J", and then the time of descent must necessarily be —- — or — ; 



^ -^ XX aa aa 



and the same holds in all cases. Therefore, &c. 



I say farther, that this curve is the cycloid : which is easily demonstrated from 

 the construction, and from what was just now hinted; viz. that this curve 



* Lord Viscount Brouncker. See the Paper^ more fully demonstrated in Birch's Hist, of the 

 Royal Society, Vol. I, p. 70. 



