574 Prof. C. V. Raman on the Partial 



bridge, the partials having a node at snch point cannot be 

 excited by the bow, and must thus be absent in the motion 

 maintained by it. The graphs representing the relation 

 between the amplitude of the partials and the position of the 

 bowed " point " cannot thus be of the simple hyperbolic form 

 mentioned above but must deviate from it, especially in the 

 neighbourhood of the nodes of the respective partials. What, 

 then, are the actual forms of these graphs? Then, again, in 

 the simple Helmholtzian type, the phases of the partial 

 vibrations are such that at two epochs in each vibration the 

 displacements are everywhere zero. To what extent are 

 these phase-relations modi tied in actual practice ? It is 

 proposed in the present paper to furnish an answer to these 

 two queries. 



2. Kinematics of Motion under the Action of the Boic. 



It is not intended here to enter into any detailed discussion 

 of the mechanical theory of the action of the bow and of the 

 manner in which the pressure and speed of bowing influence 

 the character of the motion. For this, I would refer the 

 reader to my monograph. It is sufficient for our present 

 purpose to remark that, in general, when the pressure of the 

 bow is sufficiently large in relation to its speed, the speed of 

 the bowed " point " in the forward motion attains equality 

 with that of the bow. But in the backward motion, the 

 speed of the bowed point is generally non-uniform. In 

 certain special cases, however, that is when the bow is applied 

 with sufficient pressure exactly at one of the nodes distant 

 1/5 or 1/6 or 1/7 &c. of the length of the string from one 

 end, the speed in the backward motion closely approaches 

 or attains uniformity, the partials having a node at such 

 point completely dropping out. It is obvious that the bow 

 has to be removed to some distance from a node, before the 

 corresponding partials can be fully restored in the motion 

 maintained by the bow, and in the intermediate cases the 

 character of the motion at the bowed point becomes slightly 

 modified. The speed in the forward motion remains equal 

 to that of the bow, but the speed in the return motion is 

 non-uniform. The kinematics of these intermediate or 

 "transitional modes w of vibration have been fully discussed 

 by graphical methods in my monograph. My object here is 

 to show how the harmonic analysis of these transitional 

 modes enables us to trace the variation in the amplitudes and 

 the phases of the partial vibrations with the position of the 

 bowed point. 



In the cases of musical interest, we are only concerned 



