22 SEC. 2. GEOMETRY. 



function of the other two. The original instrument was contrived for the use 

 of the Meteorological Office, where it is employed to derive the trace for 

 humidity from the traces of the dry and wet bulb thermometers. It consists 

 of a horizontal slab, whose upper surface has been shaped, as hereafter de- 

 scribed, in accordance with the numerical tables that have been calculated 

 from the desired function, the height of its surface at each point being the 

 tabular value corresponding to the two entries severally represented by the 

 distance of that point from the front and from one side of the slab. The 

 plate that carries the two traces is placed horizontally on a frame that travels 

 in front of the slab. Two slides move at right angles to this plate, and have 

 microscopes attached to them, that traverse the paper along ordinates having 

 the same abscissa. One of these slides is rigidly connected with a frame on 

 which the slab is able to move from front to back ; when this slide is pushed, 

 the frame and the slab together are pushed with it. When the other slide 

 is pushed, it also gives a sidelong movement to the slab on the frame by means 

 of a toothed wheel acting on a rack. Thus the particular point of the slab that 

 corresponds to the values of the two ordinates is brought vertically below a 

 descending rod, and this is caused to drop gently on the surface of the slab 

 by touching a treadle. The vertical space through which the rod descends 

 is consequently the function required. The rod carries a horizontal pricker, 

 with which it makes a dot on a plate held vertically in the same stage that 

 carries the plate on which the two traces are drawn. The slabs can readily 

 be fashioned Toy instrument-makers, who possess the necessary apparatus, 

 according to any required tables. They are drilled to the requisite depth at 

 various points, and are afterwards smoothed down. In the machine in use at 

 the Meteorological Office, there are many additional appliances not shown in 

 this rough model. 



76b. Rule; with joint, which serves to curve an elastic plate 

 into an arc of the circle, of any radius. 



Professor Tchebichejf, University of St. Petersburg. 



3O99. Intersecting Compasses (Arcograph). 



Geodetic Institute of the Royal Polytechnic School at 

 Munich, Prof. Dr. von Bauernfeind. 



The Arcograph serves to describe upon a given chord a circle the arc 

 of which contains a given angle. The exhibitor, by this invention, has 

 supplied the wants of the practical geometrician in solving, graphically, and 

 without construction Pothenot's problem and all the problems which are 

 described in geometry as " Kuckwartseinschneiden ". See Bauernfeind's 

 "Elemente der Vermessungskunde," 5th edition, Vol. II., pp. 167-173. 



III. MODELS OF FIGURES IN SPACE. 



COLLECTION OP MODELS OF RULED SURFACES, CONSTRUCTED 

 BY M. FABRE DE LAGRANGE, IN 1872, FOR THE SOUTH 

 KENSINGTON MUSEUM. 



This collection illustrates the principal types of the class of surfaces which 

 can be traced out m space by the motion of a straight line. 



These surfaces, on account of the facility with which they can be con- 

 structed and represented, and of the ease with which their intersections can 

 termmed, are of more consequence than any others in the geometry of 



