32 M« G. Kirchhoff on the Relation of the Lateral Contraction 



partly by the screws 7, 7. In order to ascertain whether the 

 desired parallelism exists, 1 have adopted the following method : — 

 In two points of the f axis of the scale arc fastened the threads 

 /, /, which terminate below in two loops. In these loops a rod 

 g, of similar dimensions to those of the rod d, is placed. The 

 length of the threads is so chosen that both rods are of about 

 the same height, one behind the other. On the rod g is sus- 

 pended a strip of mirror by means of hooks, which are like the 

 hooks of a level, fig. 4, Plate I. ; upon this mirror is directed 

 a telescope, in front of whose object-glass a plummet is so sus- 

 pended that the image of the plummet is covered by the vertical 

 cross-hair of the telescope. Thereupon the same strip of mirror 

 is suspended to the rod d } and this is so arranged that, when the 

 position of the telescope remains unchanged, the image is covered 

 as before. 



On the ends of the rod d are screwed the supports of two 

 silver mirrors h, h } the centres of which must be almost in the 

 lines of vision of the two telescopes. To judge whether this is 

 the case, there are two leads suspended to the intersection of the 

 threads, which, as already mentioned, are underneath each of the 

 two object-glasses. Each mirror can be moved within narrow 

 limits towards its support by means of three pairs of small 

 screws, and so arranged that suitable points of the scale are in 

 the field of vision of the corresponding telescope. 



Fig. 5 represents one of the two cross-rods. It is made 

 of steel plate : in its middle is a hollow, the sides of which 

 are knife-edges ; when this is placed on the rod d, these edges 

 fit into fine incisions made with the file on the bar d, and 

 are soldered here by a small quantity of tin. On the ends of 

 the cross bar, which are somewhat thickened, steel points b } b are 

 screwed ; they serve to support the rings c, c } on which fine wires 

 are attached, terminating in hooks : on these are suspended the 

 weights which are to bend and twist the. bar d. 



If it be allowable to consider the angle under which the rays 

 reaching the telescope are reflected to be infinitely small, we 

 may directly take as measures for the flexions and torsions of the 

 two halves of the rods the changes of the coordinates of the 

 points of the scales, the images of which are covered by the 

 intersections of the two cross-hairs. But in the present experi- 

 ments the finite magnitude of these angles must be allowed for. 

 This correction renders some closer considerations necessary. 



I establish a triaxial rectangular system of coordinates, two of 

 whose axes shall be the f axis and the 77 axis of the scale : of these 

 the first has the direction of the line A' A", fig. 1, Plate I. ; 

 the second the direction of the line A'D'; the third, which I will 

 call the faxis, shall be turned vertically backwards. The rod to 



