388 



THE POPULAR EDUCATOR. 



of which candidates must be so familiar as to be able to trans- 

 late French or German prose or poetry into English at sight ; 

 and to answer questions in Grammar. 



Candidates must, in order to pass, satisfy the examiners in 

 each of the above subjects of examination, those who are suc- 

 cessful being arranged in two divisions, each in alphabetical 

 order, and being entitled to a certificate signed by the registrar. 



Those who have passed may, as we hope many of our readers 

 will, present themselves for a further examination in honours 

 in any one or more of the following subjects : 



1. Mathematics, including Algebra, Theory of Equations, 

 Plane and Spherical Trigonometry, Pure and Co-ordinate Geo- 

 metry of two dimensions, up to and including the properties of 

 the conic sections ; Differential Calculus, Integral Calculus, 

 Statics, Kinetics, and Hydrostatics. 



2. Latin, in which the examination consists of extracts for 

 translation from the " Miles gloriosus " and " Menaechmei" of 

 Plautus; tho " Phormio " and " Hautontimorumenos " of Ter- 

 ence ; the First and Second Books of Lucretius ; Virgil ; Horace ; 

 the Third, Fourth, Tenth, and Eleventh Satires of Juvenal ; 

 Cicero, " De Natura Deorum," " Orator," " Pro Pnblio 

 Sestio," " Pro Plancio," " Ad Atticum," XIV. to XVI. ; Lucan, 

 I. and II. ; the Fifth, Sixth, and Seventh Books of Livy; and 

 Tacitus, Annals XL to XVI. 



The examination also includes the analysis of any of the 

 selected subjects, original composition upon questions arising 

 out of the selected classical authors, prose composition in Latin 

 and English, and questions in grammar, history, and geography. 



3. English. The subjects of examination in this branch are 

 defined from time to time ; the papers include original composi- 

 tion upon questions arising out of the authors selected. 



4. French. 5. German. Some proficiency in conversation 

 is essential to first-class honours in French and German, and 

 the papers usually contain questions upon a limited portion of 

 the history of the literature of France and Germany. 



The examination for honours in Mathematics and Latin con- 

 tinue during three days, for those in English during two days, 

 and for honours in French and German, during one day. Suc- 

 cessful candidates are arranged in three classes, according to 

 their proficiency. 



HYDROSTATICS. II. 



PRINCIPLE OF EQUALITY OF PRESSURE HYDROSTATIC PRESS. 



THE apparatus known as the hydrostatic bellows, and repre- 

 sented in Fig. 1, is an interesting illustration of the principle of 

 equality of pressure. Two circular boards, A B, are connected 

 together by flexible sides, so as to form a circular pair of bellows. 

 A long tube opened out at the upper end into the shape of a 

 funnel is made to open into this. The whole arrangement is 

 then partly filled with water, not, however, so much so as to 

 fully expand the bellows. If now several heavy weights be 

 placed upon the upper board, and water be poured down the 

 tube, the weights will be raised. A man may even stand on the 

 board, and, if the tube be long enough, be raised by pouring in 

 a jug of water. Let us suppose that the area of the tube be 

 half a square inch, and that of the board 1 foot, and that a 

 pound of water be poured into the tube. The. pressure ,on the 

 bottom of the tube is, of course, 1 pound ; and a similar pressure 

 is exerted on every half a square inch in the inner surface of 

 the bellows. Now the surface of the board is 144 square 

 inches, the pressure produced on it by the pound of water is 

 therefore 288 pounds. On account of the great apparent gain 

 this is sometimes called the Hydrostatic Paradox, but on con- 

 sideration it is seen to be no more paradoxical than the gain 

 effected by any other mechanical power; as, always, what is 

 gained in power is lost in time. 



In a similar way, if a cask be filled with liquid, and a long 

 tube be inserted tightly into the top and filled also, the weight 

 of water in this tube, though trifling in itself, will exert such a 

 pressure as to burst open the cask. If the diameter of the 

 pipe be rather over one-third of an inch, its area will be about 

 one-tenth of a square inch, and 2 pounds of water poured into 

 it will fill it to a height of about 46 feet. This will cause a 

 pressure of 20 pounds per square inch; and as the surface may 

 have an area of about 2,000 square inches, the total pressure 

 produced by the 2 pounds of water will be about 40,000 pounds, 



Fig. 3. 



Fig. 1. 



a pressure sufficient to burst almost any cask. For this 

 reason, when the parts of a town lie at different levels, and 

 the water is supplied from a reservoir situated in an elevated 

 part, the pipes have to be made very strong, as they have to 

 sustain the pressure produced by a column of water as high 

 as the most elevated part is above them. 



Perhaps the most important application of this principle is 

 seen in the hydrostatic press, an 

 instrument which is largely used 

 in the manufactures where a very 

 powerful pressure is required. The 

 general principle on which it acts 

 is simply this : by means of a 

 piston or plunger, of small dia- 

 meter, water is forced into a cylin- 

 der in which a largo piston works. 

 The latter is forced out with a 

 pressure as much greater than 

 that exerted on the plunger, as 

 its area is larger. If the large 

 piston have 20 times the diameter 

 of the small one its area will be 400 

 times as large; therefore a pressure 

 of 1 pound will exert a force of 400. 



The annexed figure (Fig. 2) will 

 give a good idea of the general 

 construction of the machine. It 

 varies, however, greatly in shape 

 and minor details according to 

 tho power required or the special i 

 purpose to which it is to be applied. 

 A B represents a lever hinged at 

 B to an upright, and working a 

 solid plunger, D, which is so arranged as only to move in a ver- 

 tical direction. This plunger, which is of small dimensions, 

 works water-tight in a small cylinder, c. When it is raised by 

 means of the handle, A, water rises from the reservoir, G, into 

 tho cylinder through the valve, E, which then closes and prevents 

 tho water passing back again. The piston is now forced down, and 

 drives the water through the pipe into the largo cylinder, L, and 

 thus communicates the pressure it receives from D. A second 

 valve is placed at F, so as to keep the water from flowing back 

 when D is raised again. The making of the large cylinder, L, 

 requires tho greatest care, on account of the immense pressure 

 it has to withstand. When the Great Eastern steamer had to 

 bo launched, some presses were used in which the cylinder was. 

 made of iron 7 or 8 inches thick, and yet they were split open 

 by the immense strain exerted on them. The piston, K, is made- 

 of as large dimensions as practicable, as on this mainly depends 

 the power of the machine. It works water-tight through a 

 collar at I, and it was here that the greatest practical difficulty 

 was found, for the water oozed through, and thus the power of 

 tho machine was greatly diminished. The difficulty was at last 

 met by making a collar of stout leather, and so that its section 

 was of the shape of the letter U inverted. This ring is placed 

 in a groove prepared for it, and it is easily seen that when the- 

 water presses on it, it tends to open the bend, and thus causes 

 the collar to press more firmly against the piston. The books 

 or other articles to be compressed are laid upon the flattened 

 top of the piston, and pressed against a strong iron framework 

 constructed for the purpose. 



The advantage gained by the machine depends upon two- 

 things : first, the comparative sizes of the pistons ; and second, 

 the proportion between the distances A B and H B. Suppose, 

 for example, that the diameter of K is 15 inches, and that of r> 

 half an inch ; also that the length of A B is 3 feet and B H 

 2 inches, what power will a man pressing at A with a force of 

 50 pounds exert ? Since the diameters are in the proportion of 

 1 to 30, their areas are in the proportion of 1 to 900, and there- 

 fore whatever pressure is exerted on D, K sustains 900 times 

 the amount. But A B is a simple lever of the second kind, and 

 the gain produced by its use is 3 2 6 , or 18. The pressure of 

 50 pounds at A produces, therefore, one of 900 on D ; and thus 

 the total force with which the books at M are compressed is 

 900 x 900 = 810,000 pounds, or upwards of 360 tons. As we 

 can increase the length of the lever or diminish the diameter of 

 the small piston greatly, the only practical limit to the power 

 of the machine is the strength of th large cylinder. An addi- 



