VOL. XLII.] PHILOSOPHICAL TRANSACTIONS. 571 



sion, to see the astonishment and general confusion that prevailed ; every body 

 looked pale as death, without knowing what he did or said. 



Before the earthquake on the IQth, the waters swelled, and then fell again ; 

 soon after they swelled half a yard higher than ever they were used to do. The 

 same night and the following, there was a strong smell of sulphur in the streets. 

 This smell was likewise found in the water of some wells. The sea was seen in 

 sundry situations, now high, and then presently very low again ; sometimes 

 strongly agitated, and at others on a sudden calm. On the 27th, the waters 

 were observed to rise as high or something higher than the igth. 



It is said here, that the sea roared with such violence and smartness, that its 

 noise was like the firing of large cannon, A fisherman, a Frenchman by nation, 

 being then in his boat, found it of a sudden raised up a prodigious height, and 

 then it fell down so low, that he thought it had touched the bottom of the sea, 

 and concluded himself lost. During this uncommon motion he affirms to have 

 heard one of these noises resembling the firing a cannon, and afterwards felt 

 no storm. 



j4 Demonstration of Newton s Method of raising a Binomial to any Power. By 

 J. Castilion, Profes. of Philos. in the Academy at Lausanne, and F.R.S. 



N°464, p. gi. 



Every index is either an integer or fraction, and these either positive or ne- 

 gative. 1 . When it is a positive integer ; then to raise the binomial to any 

 power of the index m, is nothing more than to write down the given binomial 

 as often as there are units in m, and to draw or multiply all these binomials into 

 one another. 



2. When the index is a positive fraction, as — ; then to raise the binomial 

 to this power, is to raise the given binomial to the r power, and, this power 

 being given, to find the quantity which raised to the n power, equals the ;• 

 power of the given binomial. 



3. But when the index is negative, either an integer or a fraction ; then to 

 raise the power, we must first proceed as in Art. 1 or 1, and then divide a unit 

 by the power so found. 



M. Castilion then assumes p -\- q ior any given binomial, to be raised to any 

 power m. He remarks that p" and q'" will be the extreme terms of the power, 

 and the intermediate terms will be the m — 1 intermediate terms between those, 

 without the co-efficients, but as to the finding of these co-efficients, in which 

 consists the chief difficulty, his process is so illogical and embarrassed, and so 



4D 2 



