Having obtained C, we put the instrument in the direction A B C. Then each point of C F describes a circumference of the same center o. 16. If the distance of the points A and B were too great, then it would be easy to determine a series of points belonging to the arc of circumference sought (Fig. 4). Being given C, the direction C I, and C I = R, on C I I lay off C E = d, draw A E B perpendicularly, and calculate C A or A E. I shall have ___ d = (R - d) = AE²; [TEX: d = (R - d) = \overline{AE^2};] or, as absolute value, __________ / A E = \ / d (R - d) . (10) \/ [TEX: AE = \sqrt{d (R-d)}] The instrument being arranged according to A C B, I prolong C B and take B C' = B C, when C' will be one of the points sought. It will be readily understood how, by repeating the above operations, but by varying the value of d, we obtain the other intermediate points, and how we may continue the operation to the right of C' with the process pointed out. 17. If the three rulers were three arcs of a large circle of a sphere, the instrument might serve for drawing the meridians on such sphere. 18. If we imagine, instead of three axes placed in one plane and converging at one point, a system of four axes also converging in one point, but situated in any manner whatever in space, and if we rest three of them against three fixed points, we shall be able to solve in space problems analogous to those that have just been solved in a plane. If we had, for example, to draw a spherical vault whose center was inaccessible, we might adopt the same method.--_Le Génie Civil_. * * * * * FEED-WATER HEATER AND PURIFIER. [Footnote: A paper read before the Franklin Institute.] By GEORGE S. STRONG. In order to properly understand the requirements of an effective feed-water purifier, it will be necessary to understand something of the character of the impurities of natural waters used for feeding boilers, and of the manner in which they become troublesome in causing incrustation or scale, as it is commonly called, in steam boilers. All natural waters are known to contain more or less mineral matter, partly held in solution and partly in mechanical suspension. These mineral impurities are derived by contact of the water with the earth's surface, and by percolation through its soil and rocks. The substances taken up in solution by this process consist chiefly of the carbonates and sulphates of lime and magnesia, and the chloride of sodium. The materials carried in mechanical suspension are clay, sand, and vegetable matter. There are many other saline ingredients in various natural waters, but they exist in such minute quantities, and are generally so very soluble, that their presence may safely be ignored in treating of the utility of boiler waters. Of the above named salts, the carbonates of lime and magnesia are soluble only when the water contains free carbonic acid.