the principle of specific gravity. This latter mode, which has the very great advantage of not losing power, consists in so proportioning the thickness of tube or size of cup in the cistern to the quantity of mercury added to the column by atmospheric pressure, that the tube can be moved by a small increase of column to any length required. In the case of a tube of uniform bore throughout (where no additional weight of mercury is added by moving the tube downwards), it is obvious that the thinner the lower end of the tube is, a proportionally greater length of it must dip into the mercury in the cistern, before a volume of mercury is displaced equal to what has entered the tube. But, in the case of the tube with expanded bore at top, it is evident that after atmospheric pressure has produced its full effect in increasing the weight of the mercurial column, further weight is added merely by the continued depression of the tube—because this depression magnifies, according to the length of if, an equal extent of the small area of narrow portion of the mercurial column to the large area of expanded top. This will appear evident on referring to Mr. Taylor's second diagram, in which if c c represented the bottom of the expanded portion before the tube be moved down, the upper portion of the narrow column d will after the tube descends be magnified to c c.
With respect to the expanded tube, therefore, when it is wished to magnify the indications, the increased weight of mercury occasioned by a given atmospherical pressure, must be added to the weight occasioned by the descent of the tube to the extent of the enlarged indication wanted, and the area of the float made of such size as the product of it into the length of the enlarged indication will equal the sum of the bulks of the two weights of mercury just named. Suppose it is desired to magnify the indications five times—expanded upper portion of tube being two inches square, small bore of tube one-tenth of an inch square. Here, for 110 of an inch of rise of mercurial column, the tube must descend ½ inch; taking the cubic inch of mercury to weigh 3434,
Then one cubic inch (=½ of 2 cubic inches) = 3434
From which deduct weight of mercury already in bore = 210 inch area ½ inch long. 17.17
Weight of mercury added by x inch depression of tube. = 3416.83
210 of one cubic inch (= 110 of two cubic inches) added by atmospheric pressure. 686.8
Sum of weight of mercury added by pressure and depression = 4103.63 grains.
Then
½ cub. inch mer. 1717
4103.63
area sq inch 1
4103.63/1717
= 2.39 square
inches the area of the float. A correction is of course required for the thickness and specific gravity of the substance of the cup float. In an
