624 PHILOSOPHICAL TRANSACTIONS. [aNNO l/SO. 



being pressed out by the contraction of the large fragments of lava in cooling, 

 and which had bent downwards by their own weight. This curious substance 

 has the lightness of a pumice, and resembles it in every respect except being of a 

 darker colour. When the pores of the fresh solid lava were large, and filled 

 with pure vitrified matter, he found that matter sometimes blown into bubbles 

 on its surface, probably by the air which had been forced out at the time the lava 

 contracted itself in cooling: those bubbles, being thin, showed that this volcanic 

 glass has the kind of transparency of our common glass bottles, and is like them 

 of a dirty yellow colour. He detached with a hammer some pieces of this kind 

 of glass, as large as his fist, which adhered to, and was incorporated with, some 

 of the larger fragments of lava, and, though of the same kind, from their 

 thickness they appeared perfectly black, and were opaque. 



Another particularity was remarkable in the lava of this eruption: many 

 detached pieces of it were in the shape of a barleycorn or of a plumb stone, 

 small at each end, and thick in the middle. He picked up several, and saw 

 many more which were too heavy to carry off, weighing more than 6o pounds; 

 some of the smaller ones did not weigh an ounce. He supposed them to be 

 drops from the liquid fountain of fire of the 8th of August, which might very 

 naturally acquire such a form in their fall; but the peasants in the neighbourhood 

 of Vesuvius are well convinced that they are the thunder bolts that fell with the 

 volcanic lightning. He found many of the volcanic bombs, or properly speak- 

 ing, round balls of fresh lava, large and small; all of which had a nucleus com- 

 posed of a fragment of more ancient and solid lava. There were also some other 

 curious vitrifications, very different from any he had ever seen before, mixed with 

 the late fallen shower of huge scoriae and masses of lava. 



V. An Appendix to the Paper in the Philos. Trans, for \77B, entitled, " A 

 Method of exteruling Cardans Rule for resolving one Case of the Cubic EquO' 

 tion x^ — qx = r to the other Case of the same Equation, ivhich it is not natu- 

 rally fitted to solve, and ivhich is therefore called the Irreducible Case." By 

 Francis Maseres, Esq., F. R. S., &c. p. 85. 



In the above-mentioned paper in the Philos. Trans, the expression ^e x the 



^ss 205* 308*^ 



infinite series 2 + ^ — ^;^^ + g^jj^js — &c. is shown to be equal to the root 

 ' of the equation x^ — qx = r, whenever 

 '■'■ is less than |r, but greater than 4- of it, or than |-. This expression is wholly 

 transcendental, or composed of an infinite number of terms. But Mr. M. 

 thought that it might be convenient on some occasions to divide this expression, 

 if possible, into 2 others, whereof the one should be a mere algebraic expression, 

 or consist of a finite number of terms, and the other should be transcendental, 



