1Q2 PHILOSOPHICAL TRANSACTIONS. [aNN0 1738. 



difference, as a measure, is i ; and y, y the two ordinates ; the magnitude of 

 the figure will be implied by the magnitudes of the two polygons, which are 

 made from the sum of the inscribing and circumscribing elements zy and zy , 

 though the figure itself is not to be resolved into any such primogenial rectan- 

 gular elements. 



And thus the symbol z, considered as a component part of the rectangle zy, 

 may bear a plain interpretation; viz. that it is the measure according to which the 

 quantity z is measured; nor can he see that any other interpretation need to be 

 put on a symbol, which, like a measure, is used only to make other things 

 known, but is of itself for nothing but a mark. 



And what is said of the elements of the first resolution, is easily applied to 

 those of a second or third, and so on ; the last may always be considered as 

 the measure of the former and indivisible, though, in respect of the following, 

 it be taken as the part according to which the measure was made, and therefore 

 divisible. 



A Description of a new Invention of Belloivs, called Water- Belloivs. By 

 Martin Triewald, F. R. S. Military Architect to his Swedish Majesty. 

 N°448, p. 231. 



The water-bellows now proposed by M. Triewald, as to their efl^ect, are no- 

 ways inferior to the wooden bellows, used in Sweden at all their iron forges, 

 and furnaces, &c. but far more advantageous, not only for iron furnaces, but 

 also for many other smelting-works requiring large bellows. 



It may seem at first a little strange, that water should be able to blow the 

 fire ; but whoever has read the Philos. Trans, and seen the invention there de- 

 Scribed, as used at Tivoli in Italy, and several other places, called Soffi d'Acqua, 

 and attentively considers the following description, will be convinced, that this 

 new invention of water-bellows, is built on the very self-same foundation, to 

 which leathern and wooden bellows owe their use and origin, and will in several 

 cases prove of more signal service. 



These water-bellows a, a, represented in fig. 8, pi. 6, are made of wood, not 

 unlike the shape of diving-bells, in the form of a truncated cone, and con- 

 sequently wider below than at top, where they are furnished with close heads b, 

 B, but at the lower ends e, e, quite open. At the heads b, b, are two valves v, 

 V, which open inwardly, and are made like the claps of other bellows, with their 

 hinges, and the valves themselves covered with hatters felt, and are shut by an 

 easy steel spring, till the air from above opens the same, which happens only 

 when these bellows receive their motion upwards ; but are shut by means of the 



