638 PHILOSOPHICAL TRANSACTIONS. [ANNO 1785. 



I took my departure from the mountain with great reluctance. Though I 

 encountered many difficulties to get up, yet it amply rewarded me for all my toil; 

 but I had not time to examine it with that attention I wished. When I got on 

 the peak from which I had my first view of it, and from which I could see its dif- 

 ferent parts, I could not help reviewing it several times. After imprinting its 

 structure on my mind, I took my final adieu of it, and returned down, and got 

 to Mr. Fraser's house about 7 at night, much fatigued. I am sorry I had no 

 instruments, to take the state of the air, or the exact dimensions of the dif- 

 ferent parts of the mountain; but I believe on measurement, they will be more 

 than I have mentioned. From the situation of these islands to each other, and 

 to the continent of South America, I imagine there are sub-marine communica- 

 tions between the burning mountains or volcanoes in each of them, and from 

 them to the volcanoes on the high mountains of America. The islands, which 

 are situated next the continent, seem to tend in the direction of those moun- 

 tains; and I have observed, that the crater in this island lies nearly in a line with 

 Soufriere in St. Lucia and Morne Pelee in Martinique, and I dare say from 

 Morne Pelee to a place of the same kind in Dominique, and from it to the 

 others; as it is certain there is something of this kind in each of these islands, 

 Barbadoes and Tobago excepted, which are quite out of the range of the rest. 

 There is no doubt but eruptions or different changes in some of them, though 

 at a great distance, may be communicated to and affect the others in various 

 manners. It is observed by the inhabitants round these burning mountains, that 

 shocks of earthquakes are frequent near them, and more sensibly felt than in 

 other parts of the island, and the shocks always go in the direction of them. 



IV. A Supplement to the Third Part of the Paper on the Summation of Infinite 

 Series, hi the Philos. Trans, for 1 782.* By the Rev. S. Vince, M. A. p. 32. 

 The reasoning in the 3d part of my paper on the Summation of infinite Series 

 having been misunderstood, says Mr. V., I have thought it proper to offer to the 

 r. s. the following explanation. When I proposed, for example, to sum the 

 series \ — $- + 4 — & c - sme fi ne 5 I wanted to find some quantity which, by its 

 expansion, would produce that series, and that quantity 1 called its sum; not, 

 as I conceived must have been evident to every one, in the common acceptation 

 of that word, that the more terms we take, the more nearly we should approach 

 to that quantity, and at last arrive nearer to it than by any assignable difference, 

 for there manifestly can be no such quantity ; but as being a quantity from which 

 the series must have been deduced by expansion, which quantity I found to be 

 — -l -f- h. l.2. If therefore, in the solution of any problem, the conclusion, 



* Page 309, of this volume. 



