iq6 philosophical transactions. [anno 16C)7. 



in the foregoing corollary it is shown that yn = ■ . Therefore the centre 



of gravity of the space achd is in nw. And by these last two corollaries, the 

 centre of gravity is found, of any portion of a catena that does not reach to the 

 vertex a, or of any space of a catenaria, comprehended by any portion together 

 with right lines. 



Carol. 10. — Hence are measured the superficies and solids produced by the 

 rotation of a catenaria, or of any space comprehended by that and right lines, 

 revolving about a given axis. For the figure generated by rotation, as is com- 

 monly known, is equal to the evolving figure drawn into the periphery that is 

 described by the centre of gravity in the rotation ; which periphery is given, since 

 its radius is given, or the distance of the centre of gravity from the given axis. 

 Thus if the catenaria ad revolves about the axis ab, the periphery described by 



the centre of gravity o will be - X an, if- denotes the ratio of the periphery of 

 a circle to its semidiameter ; and therefore the superficies produced by the rota- 

 tion of the catena ad, will be - X an X ad = - X an X aij. That is, a cir- 



? f 



cle whose radius is equal in power to the double of the rectangle ean, will be 

 equal to the superficies produced by the rotation of the chain ad about the axis 

 ab. In like manner it may be shown, that a solid generated by the rotation of 

 the space achd about ac, is equal to a cylinder whose base is the aforesaid cir- 

 cle, and its height equal to ac. And so may the superficies and solids be mea- 

 sured, that are produced by the rotation of these figures about any other given 

 axis. For when the centres of gravity are known, the rest will easily follow. 



On the Production and Ejects of Hail, Thunder, and Lightning. By Dr. Wallis. 



N° 231, p. 653. 



Thunder and lightning are so very like the effects of fired gunpowder, that 

 we may reasonably judge them to proceed from like causes.* The violent ex- 

 plosion of gunpowder, attended with the noise and flash, is so like that of 

 thunder and lightning, as if they differed only as natural from artificial : as if 

 thunder and lightning were a kind of natural gunpowder, and this a kind of 

 artificial thunder and lightning. Now the principal ingredients in gunpowder 

 are, nitre and sulphur, the admixture of charcoal being chiefly to keep the parts 



* It is carious to observe the reasonings and conjectures of ingenious and learned men. These of 

 Dr. Wallis in the present instance, though very specious and plausible, and which were probably 

 satisfactory to the philosophers of his time, are now pretty generally known to be erroneous ; since 

 it has been found that lightning and electricity are the same or similar phxnomena. As will abun- 

 dantly appear in some future volumes of this work. 



