122 PHILOSOPHICAL TRANSACTIONS. [aNNO 1704. 



ascend or descend, therefore the pipe is made a small matter larger, viz. its 

 circumference is 2.14, by which the pipe, according as the body sinks more, 

 gives more resistance to the descending body. The pipe's area is .3643 ; there- 

 fore the capacity of the pipe in 4 inches altitude is = 1.457. But as abovesaid 

 to give justly no resistance, its capacity should be 1.28. Therefore this 1.28 

 taken from 1.457, leaves .177 the actual resistance in 4 inches depth, viz. .177 

 X 253 = 44 grains. 



But this resistance will not be the same in all weathers. In order therefore 

 to calculate what it will be, when the mercury of the common baroscope is very 

 low; for example, only 28 inches high = 392 of water, y must be supposed = 

 392, therefore p=/+^-|-1= 398.3, and the rest as before; viz. d = l63, 

 fc = 67424, Yd = 649229. Thence by the aforesaid equation a = 2.59, 

 a = 2.84 ; therefore » — a = .25, which X n, gives .50 cubic inches, which 

 X 253 =126 grains. So that this baroscope, when the mercury is lowest, is 

 126 times more, exact than the common one, supposing the body immersed 

 afresh when the mercury is so low. 



Next, while the mercury is so very low, suppose the top of the body depressed 

 4 inches under water : therefore 9 = p + 4 = 402.3 ; the rest are as before, viz. 

 fc =^ 67424; then a will be 1.9; but before, while the top of the body was at 

 the surface, a was 2.59; therefore the difference .69 X tube's area 2, gives 1.38 

 cubic inches, which X 253 gives 349 grains; and so much the baroscope is 

 heavier when the top xm is 4 inches under water ; or, which comes to the same, 

 supposing that mercury at 28, and xm at the surface, this baroscope by the 

 mercury's ascending -^ inch, will become 349 grains heavier. The pipe's capa- 

 city in 4 inches altitude, was 1.457, from which take the aforesaid 1.38, the 

 residue = .077, which X 253, gives I9 grains in 4 inches; so that the pipe will 

 sustain the baroscope, and also 44, when the mercury is 304- high, and only I9 

 grains when the mercury is 28 high. The fewer grains difference there are in 

 its sinking through 4 inches, the more nice the baroscope will be. 



Where the thread cuts the surface of the water, there is formed a bubble ; 

 therefore, while the instrument sinks in water 4 inches, which is all the room 

 that I give it, the bubble moves on the two diagonal threads 20 inches ; it fol- 

 lows therefore, that 1 20 grains difference would make the bubble pass over 120 

 inches, if the threads were so long ; but, as it has been above calculated, about 

 120 grains difference of weight of the instrument, is produced by so much of 

 the alteration of the air, as would make the mercury of the common baroscope 

 -ji^-inch; therefore when the mercury ascends ^V inch, the bubble of this new 

 baroscope ascends 420 inches : therefore this new baroscope is about 1200 times 

 more exact than the common one^ 



