VOL. XXVI.j PHILOSOPHICAL TKANSACTIONS. 471 



capable of dilation. I then took that water I had purged of all its air. (as near 

 as I could) and gave it a degree of heat not exceeding luke-warm ; and on 

 weighing the bottle in it, I found that although the heat it had received was 

 very inconsiderable, yet the bulk of the water in that state, equal to that of 

 the bottle, was now diminished 2 grains: which plainly shows, that although 

 the water contained no air that I could discover, yet there seems a matter latent 

 in it, capable of intumescence. 



Of the Nature and Properties of Sound. By S. Guido Grandi^* F. R. S. 

 N° 319, p. 270- Translated from the Latin. 

 The archbishop of Armagh (^in N° 156, Philos. Trans.) compares hearing 

 with vision; and as the latter is divided into direct, reflected, and refracted 

 vision, so in like manner he divides the former into three parts, and considers 

 not only direct and reflected sounds, which have been long known, but also 

 refracted ones: for, as he observed that former ages had, in a great measure 

 perfected the doctrine of vision, by optic, catoptric, and dioptric inventions, 

 so likewise he did not doubt, but that the doctrine of sounds, both with respect 

 to the object, and the medium or organ, might be brought to perfection by 

 acoustic, catacoustic and diacoustic, or (as he denominates them both ways) by 

 phonic, cataphonic, and diaphonic instruments. And for that end he lays 



* Guido Grandi, a learned mathematician of Italy, was born at Cremona in 1671, named pro- 

 fessor of mathematics at Pisa in 1714, and died in 1742. In l699> this author published, in 4to. 

 the demonstration of Viviani's wonderful or quadrable dome, under the title of Geometrica Divinatio 

 Vivianeorum Problematum: a work which contains more than its title would lead Us to expect, and 

 in which the author remarks many other curiosities in geometry of the same kind, and among 

 others, a portion of the surface of a right cone, which is perfectly quadrable, and to which he 

 gives the name of Velum Camaldulense, he being a friar of the order of the Camaldules; from 

 which it seems he did not know that the same thing, in a more general form, had before been given 

 by John Bernoulli, in the Ijeipzic Acts. In 170I he published his demonstration of Huygens's 

 theorems on the Logistic Curve, which that author had simply announced without demonstration; 

 being an excellent specimen of the ancient geometrica] method j in which piece also, as well as in 

 his letter to the Jesuit Ceva, which follows it, are found several other curious and novel particulars. 

 Another paper of Grandi's is also inserted in the 33d volume of the Philos. Transactions, called a 

 Handful or a Bouquet of Geometrical Roses, being a dissertation on certain curves geometrically de- 

 scribed in a circle. This he afterwards enlarged in another treatise, published in 1728, entitled 

 Flores Geometric! ex Rhodonearum, &c. He was also author of several other miscellaneoas pieces 

 on the ancient and modern szeometry; as, his Quadrature of the Circle and Hyperbola by Infinite 

 Parabolas, in 1703 and 1710 j his Dissertation on Infinites of Infinites, &c. in I7IO; an Italian 

 edition ofEuclid's Elements ; and a posthumous treatise on Conic Sections, also in the Italian lan- 

 guage, in 1744. Grandi it seems was of a turbulent and quarrelsome disposition, being almost 

 always engaged in disputes on various subjects, geometrical, theological, metaphysical, or. phi- 

 lological. 



