Volume 183001

Mechanics / By Henry Kater and Dionysius Lardner.

  • Kater, Henry, 1777-1835
Date:
1830
Catalogue details

Licence: Public Domain Mark

Credit: Mechanics / By Henry Kater and Dionysius Lardner. Source: Wellcome Collection.

    390/408 (page 332)
    substance. In like manner, if we multiply the linear ex- pansion by 2, we shall have the superficial expansion. If we want the apparent expansion of mercury, the absolute or cubical expansion of the glass vessel must be deducted from the absolute expansion of the mer- cury, which will leave its excess or apparent expansion. In like manner, deducting the superficial expansion of glass from the absolute expansion of mercury, we shall have its relative vertical expansion. Now, taking the rate of expansion of glass to be ‘(000004:79, and multi- plying it by 2, the relative vertical expansion of the mercury in the glass cylinder will be ‘00010010 — ‘00000958 = -000090582. The expansion of a steel rod, according to our table, is ‘0000003596; which, divided by -00009052, gives ‘0708 for the length of a column of mercury, the expan- sion of which is equal to that of a steel rod whose length is unity. We have now to multiply 42 inches by ‘0703, which gives 2:95 inches; and this, deducted from 42, leaves 39:1 inches ; so that the length of rod we have chosen is sufficiently near the truth. Now, double 2°95 inches, and add one tenth of its product, and we shall have 6:49 - inches for the length of the mercurial column forming the requisite compensation. Mr. Baily’s more accurate calculation gives 6°31 inches. A mercurial compensation pendulum may be formed, having a cylinder of steel or iron, with its top con- structed in the same manner as the top of the stirrup, so as to receive the screw of the rod. To find the length of the mercurial column necessary in a pendulum of this description (that is, with a cylinder made of steel), we must double the linear expansion of steel, and take it from the absolute expansion of mercury to obtain the relative vertical expansion of the mercury. This will be ‘00010010 — :00001272 = :00008738 ; and, *0000063596 700008738 ~- 07279. Let the length of the steel rod be, as before, 42 inches. proceeding as before, we have