Theory of Mr. B. Hamilton's String-Organ. 99 



papers before the Physical Society, the Ashmolean Society of 

 Oxford, and the Musical Association ; and in view of the interest 

 generally expressed about it, I have thought that an account of 

 the theory, as far as it goes, may be acceptable to the readers of 

 the Philosophical Magazine, The two sets of observations 

 given towards the close of these remarks were made by me at 

 Mr. Hamilton's laboratory in November 1874. 



It is not my purpose to describe the instrument here ; it will 

 be sufficient to point out that it produces continuous tones by 

 means of combinations of strings and harmonium-reeds. There 

 is a separate string to each note, and to some point on each string 

 the extremity of a harmonium-reed is attached. The reed is 

 then set in vibration by wind ; and the problem is to determine 

 the forms of vibration of the combination. 



The method of the following investigation is substantially that 

 employed at p. 139 of Donkin's ' Acoustics/ with the extensions 

 necessary for the purposes of the problem. 



The instrument may be regarded as a string loaded at the 

 point of attachment to the reed, subject also at the same point 

 to a force tending towards the position of rest, and varying 

 directly as the displacement of the point from that position ; 

 this force represents the elasticity of the reed. 

 Let jju be the load at the point of attachment, 



T the tension of the string, 



p mass of unit of length of string, 



a elastic force of reed per unit of displacement, 



y the displacement, 



I the length of the string, 



b distance of point of attachment from one end, 



oo distance of any point from the same end, 

 T 



P 



Then the equation of motion of the point of attachment is 



and for the rest of the string 



ff=^ (2) 



dt 2 dx 2 v ; 



Assume (see Donkin's ' Acoustics/ pp. 119, 139) 



y= sin m(l— b) sin mx(A cos«w/ + B sin amt) . . (3) 

 from x=0 to x = 5, and 



?/= sin m6sinm(/— a?) (A cos amt + B sin amt) . . (4) 

 from x—b to x=I. 



H2 



