no 



MECHANICAL PHILOSOPHY. HYDROSTATICS. 



[nRAMAIl's 



I..- UK 



without entering into minute detail* of its constnio- 



r communicates 

 with tro cylinders of metal, 

 as in the figure : one of 

 these cylinder! U of con- 

 siderably larger section 

 than the other. Water- 

 tight piston* A, B being 

 fitted to both, any force or 

 pressure applied don n ward* 

 to the smaller A, acU up- 

 ward* upon the larger B 

 with an intensity a* many 

 time* the applied pressure 

 a* the area of it i* con- 

 tained in the area of B ; 

 BO that by diminishing the 

 diameter "of A, or by in- 

 creaiing the diameter of 

 B, we may make the upward pressure upon B a* 

 many times the downward pressure upon A as wo 

 please. Suppose, for instance, the diameter of the cy- 

 linder A is half an inch, and that of the cylinder B one 

 foot ; then as the areas of circles are proportional to 

 the squares of their diameters, we shall have 



(J) 1 : 12* : : applied pressure : : resulting pressure 576 

 times the applied pressure ; 



so that a pressure of 1 cwt. applied to the piston A, will 

 produce a pressure of 576 cwt., or nearly 29 tons upon 

 the piston B. It is plain that, by means of a lever, ap- 

 plied to the piston-rod A, the downward pressure may be 

 increased to any required amount ; and, in fact, by in- 

 creasing the disparity in the diameters of the cylinders, 

 and using only a moderate leverage on A, the transmit- 

 ted pressure may be made as great as the metal cylinders 

 can sustain. Something of this kind, no doubt, takes 

 place in nature : water limls its way down the chinks and 

 crevices of rocks and mountains, settling in whatever 

 cavity within there may be to receive it. This cavity in 

 time becomes filled, and a number of slender and irregular 

 columns of water reaching from the reservoir to the sur- 

 face, the upward and lateral pressure of the reservoir 

 becomes at length greater than the rocky receptacle can 

 sustain, a rupture takes place at the weakest part, and 

 devastation is spread around. On a small scale, this 

 effect is actually produced artificially in mining ; where 

 water-pressure is sometimes thus introduced for the pur- 

 pose of blasting rocks. 



It may not be altogether UK worthy of notice here, that 

 the Creator has provided a remarkable preventive for 

 these destructive effects of fluid-pressure when exerted 

 through a high column. The sap of trees, extending 

 from the roots to the height of 80 or 100 feet, if it gravi- 

 tated like the column of wafer in a Bramah's press, would 

 rupture the trunks of the largest trees ; but when fluid 

 U introduced into very narrow tubes, an upward force, 

 called capillary attraction, acts on the fluid in opposition 

 to its downward pressure ; and it is this force which sus- 

 tains the sap in trees, and neutralises the downward 

 pressure of the fluid. 



EXPLANATION OF TERMS. In the treatise on 

 Dynamics (page 742), the meaning of the term mats was 

 explained, and the distinction shown between it and 

 weight. The weight or pressure produced by a mass M 

 under the influence of gravity, mar be denoted thus ; 

 namely, W-Mj. Bui in applying this notation, care 

 should be taken to preserve consistency of moaning be- 

 tween the two member* of the equation. M should be 

 regarded as to many units of mass, just as, in Dynamics, t 

 is regarded as so many units of time : the unit of mass 

 may be arbitrarily chosen ; and whatever it be, 



one unit of mass X weight of the unit ; 

 so that here a is not to be regarded as the symbol for the 

 accelerating force of gravity, but for the tcriyhf-forr,- 

 the force which gives to the miss M its weight or pres- 

 inire ; and employing M as an abstract number, namely, 

 the number f units <if mass, we have 

 1 X JT weight of the unit of 



that is, in the present inquiry, y stands for the following 

 effect namely, the weight impressed by gravity on the 

 unit of mass. This is a definite and perfectly intelligible 

 measure of the effect of gravity as a statical force ; with 

 the acceleration produced by it we have here no concern ; 

 and when, as in the current works on this subject, it is 

 said, "let M represent mass, and g the accelerating force 

 of gravity, and we shall have W=M;/," the language is 

 calculated to mislead the student into the supposition, 

 that the mass of a body is the 92nd part of its weight, 

 which is of course an absurdity. The term " accelerating 

 force" should never be employed in any statical inquiry, 

 as it is unintelligible without reference to motion : the- 

 effect of the influence so called is, in statics, continued 

 but stationary pressure or weight, and nothing else. 



In order to estimate the mass or quantity of matter in 

 any body, it is necessary as in all other cases of mea- 

 surement- to have reference to. some conventional stan- 

 dard, as the unit of measure : accordingly, by general 

 consent, the mass-unit is the quantity of matter con- 

 tained in the volume unit (a cubic foot, or cubic inch) of 

 distilled water at a certain temperature. Consequently, 

 ;/ stands for the weight of a cubic foot or inch, as may be 

 agreed upon, of distilled water : as the cubic foot weighs 

 just 1000 ounces, this is the unit to be preferred ; so that 

 the expression W=M<; implies, that if we take the num- 

 ber of cubic feet in a body of distilled water containing 

 the same quantity of matter as (and therefore of the 

 weight of) W, then 1000 oz. multiplied by that inimlHT 

 will give W, the multiplying number being all that is 

 represented by M. 



If a body contain D times as much matter as a body 

 of distilled water of equal volume, the former is said to 

 have D times the density of water ; so that the density of 

 water being taken = 1, that is, beim; taken for the unit 

 of density, D will denote the density of the body : hence, 

 if V be the volume, or rather the number of cubic feet in 

 the body, DV will be the numlxir of cubic feet in its 

 equivalent, as to quantity of matter, of water ; and 

 therefore 



.... (1) 



Also if a body weigh S times as much as a body of dis- 

 tilled water of equal volume, the specific gravity of the 

 former is said to be 8. By the specific gravity, there- 

 fore, of any substance, is simply meant the ratio of the 

 weight of any volume of it, to the weight of an equal 

 volume of distilled water. 



Both the density and specific gravity of any substance 

 are expressed by the same abstract number : thus the 

 density of mercury, as compared with distilled water, is 

 14 ; its specific gravity also is 14 ; but the density refers 

 entirely to the mass, the specific gravity to the weight. 

 As there is 14 times as much matter in a cubic foot of 

 mercury as in a cubic foot of distilled water, the density 

 of the former is 14 times that of the latter ; and since, as 

 a consequence of this superior density, a cubic foot of 

 mercury is 14 times as heavy as a cubic foot of distilled 

 water, the specific gravity of mercury is 14 also. 



Hence, \\ and V denoting weight and volume as be- 

 fore, we have 

 W S Vg (g = one thousand ounces) .... (2) 



INTERPRETATION OF SYMBOLS. From the 

 explanations now given, it will be perceived that the 

 .i\ ml nils to be hereafter employed have the following 

 significations ; namely : 



M the number of cubic feet in a body of water con- 

 taining the same quantity of matter (and there- 

 fore of the same weight) as the body proposed. 



V the number of cubic feet in the body proposed. 



D the numlirr by which a volume of water must be 

 multiplied, to give the same quantity of matter 

 as is contained in an equal volume of the pro- 

 posed body. 



8 = the number by which a volume of water must be 

 multiplied to give the same weight as an tqiial 

 volume of the proposed body. Hence, D and S 



