150 



SCIENCE 



[N. S. Vol. XXVI. No. 657 



When two coincident vectors, have not the 

 same origin, both the but and barb of one 

 vector must be stepped over, as in Fig. 2. 

 Each letter refers to the whole vector between 

 the next but and the nest barb in order, on 

 either side of it. Thus in Fig. 2, r" and r 

 coincide in r'. 



When one collinear vector begins where 

 another ends the case is still definite, if the 



shows the following qualities without am- 

 bi^ity. 



The axes of coordinates, x, y, z. 



The axes of elasticity a, h, and c, each with 

 its three directions. 



The two wave normals or velocities Wj and 

 w, and their direction cosines, Z, m, n. 



The two wave fronts, wf^ and wfj. 



The two vectors of the wave surface, or the 



barb and step-over be on the same side of the 

 specification, as stated. Thus in Fig. 3, 

 /' ^ r ■+ '''• Complications, however, should 

 be avoided. 



As an example of this method. Fig. 4 shows 

 the case of the Fresnellian wave surface with 

 two nappes, together with the reciprocal wave 

 surface also with two nappes. The figure 



rays r^ and r„, and their direction cosines, ?/, 

 m/, n/, and Z/, m/, n/. 



The two intersection curves of the wave 

 surfaces ws-^ and ivs„ 



The two displacem_ent vectors p^ and Pj and 

 their directions, which are the projections of 

 j'j and r, on the respective wave fronts wf^ 

 and wfj. 



