500 PHILOSOPHICAL TRANSACTIONS. [aNNO 1755. 



//, Investigation of a General Rule for the Resolution of Isoperimetrical Pro- 

 blems of all Orders. By Mr. Thomas Simpson, F.R.S. p. 4. 



The different species of problems comprehended under the name of Isoperi- 

 metrical ones, are of much greater extent than the name imports; since, not 

 only the determination of the greatest areas and solids, under equal perimeters 

 or bounds, whence the name is derived, but whatever relates to the maxima and 

 minima of quantities depending on a line, space, or body, of which the figure 

 is unknown, is by mathematicians included under that denomination. But not- 

 withstanding the usefulness and great extent of this subject, nothing had been 

 done in it further than the resolution of certain particular cases (such as finding 

 the line of the swiftest descent, and the solid of the least resistance), till the ce- 

 lebrated mathematician Mac Laurin, in his treatise effluxions, gave the investi- 

 gation of an elegant and very easy method, by which the principal problems 

 belonging to the first order may be resolved. 



The paper Mr. S. now lays before the Society contains further improvements 

 on this subject ; as it is by far more general than any thing yet offered, and is 

 drawn up with a view to obviate the difficulties attending the resolution of a very 

 intricate kind of problems, and thus to open an easy way to some very interest- 

 ing inquiries in natural philosophy. But instead of reprinting the calculations, 

 it will be better to refer to p. 98, &c. of the author's Miscellaneous Tracts in 

 4to, published 1757» where the same paper is given in a more extended and im- 

 proved state. 



///. On the Effects of Lightning at Plymouth. By John Huxham, M.D., 



F. R. S. p. 16. 



Sunday, December 15, 1754, 25 minutes after one p.m. a vast body of light- 

 ning fell on the great hulk at Plymouth-dock, which serves to hoist in and fix 

 the masts of the men of war. It burst out about a mile or two to the westward 

 of the hulk, and rushed with incredible velocity towards it. The piece of the 

 Derrick cut out was at least 1 8 inches diameter, and about 15 or 1 6 feet long : 

 this particular piece was in 3 or 4 places begirt with iron hoops about 2 inches 

 broad, and half an inch thick, which were completely cut in two by the light- 

 ning, as if done by the nicest hand and instrument. The lightning was imme- 

 diately succeeded by a dreadful peal of thunder, and that by the most violent 

 snower of hail, which fell only in and about this town, for a mile or two : there 

 was very little of it at the dock, though only 1 miles distant. The hail-stones 

 were as large as small nutmegs, all very nearly of the same size and shape. They 

 measured, immediately after they fell, near 2 inches round. 



