ORIGINATING THE CONSTRUCTION OF A HYDROSTATIC QUADRANT. 181 



level, that large towns and cities are supplied with water from a 

 distance; the city of Edinburgh, in Scotland, is supplied in this way; 

 but the successful execution of all such complicated and elaborate 

 undertakings, requires an immense outlay of capital, directed by the 

 skill and judgment of the most eminent engineers.* 



191. The principle which we have demonstrated in the foregoing 

 proposition, with respect, to two fluids of different specific gravities, 

 may in like manner, be shown to obtain with any number of fluids 

 whatever ; a separate demonstration, however, would here be out of 

 place, we shall therefore content ourselves with the general enuncia- 

 tion ; but the reader may, for his own satisfaction and improvement, 

 supply the demonstration ; the enunciation is as follows. 



If any number of fluids of different specific gravities, communicate 

 with one another through the arms of a bent tube, and remain in 

 equilibrio : 



The sums of the products of their perpendicular heights and 

 specific gravities, in each branch of the communicating tube, 

 shall be equal to one another. 



Various interesting and important problems might be proposed, on 

 the principle of fluids of different densities, communicating with one 

 another in the opposite branches of a bent tube ; but our limits will 

 only admit of the following, which on account of its elegance, is 

 worthy of a place in our present inquiry. 



PROBLEM XXX. 



192. The ratio of the specific gravities of two fluids being 

 given, if equal quantities of the fluids be poured into a circular 

 tube of uniform diameter : 



It is required to determine their position when in a state of 

 equilibrium. 



* Baths and aqueducts contributed largely, in the Roman empire, to the wealth 

 and comfort of the meanest citizen, whether in the solitudes of Asia and Africa, or 

 the well watered provinces of the west. The splendour, the wealth, even the 

 existence of those numerous and populous cities which are now no more, was 

 derived from such artificial supplies of a perennial stream of fresh water. The 

 boldness of the enterprise and the solidity of the workmanship may be judged of by 

 those of Spoleto, Metz, Segovia, &c. The aqueduct of Troas, constructed partly at 

 the expense of the generous Atticus, is but a solitary instance of the spirit of 

 those PATRICIANS who were not afraid of displaying to the world that they had the 

 wisdom to conceive and wealth to accomplish the noblest undertakings. See 

 Gibbon's Decline and Fall, vol. i. chap. II. 



