Complete Radiation at a given Temperature. 461 



In conformity with this Michelson supposes that 



p = l, /(^)=K^^ 

 so that (2) assumes the more special form 



i^=^^dh~'^'\-\ . / . . . (3) 



If, as appears to be preferable, Ave take n as independent 

 variable, F(«) dn is of the form 



Ae-"'"'7iVn, (4) 



A, a being functions of 6, but independent of n. 



Weber's formula, so far as it here concerns us, is of a still 

 simpler character. Expressed in terms of n, it differs from 

 (4) merely by the omission of the factor n*, thus correspond- 

 ing to ^ = — 1 in (2) ; so that 



F(n)c?n=A^-«'«'^w (5) 



The agreement between (5) and the measurements by Langley 

 of the radiation at 178° C. is considered by Weber to be 

 sufficiently good. 



In contemplating such a formula as (5), it is impossible to 

 refrain from asking in what sense we must interpret it in 

 accordance with the principles of the Undulatory Theory, 

 and whether w^e can form any distinct conception of the cha- 

 racter of the vibration indicated by it. My object in the 

 present paper is to offer some tentative suggestions towards 

 the elucidation of these questions. 



The first remark that I would make is that the formula 

 must not be taken too literally. If there is one thing more 

 certain than another, it is that a definite wave-frequency 

 implies an infinite and unbroken succession of waves*. A 

 good illustration is afforded by intermittent vibrations, as 

 when a sound itself constituting a pure tone is heard through 

 a channel which is periodically opened and closed. Such an 

 intermittent vibration may be represented byt 



2(1 + cos 27rmi) cos ^irnt, (6) 



where n is the frequency of the original vibration, and m the 

 frequency of intermittence. By ordinary trigonometrical 

 transformation (6) may be written 



2 cos 27rni+ cos 27r(?z + 772)^-1- cos 27r(?i—m)^ ; . (7) 



* "The pitch of a sonorous body yibrating freely cannot be defined 

 with any gieater closeness than corresponds with the total number of 

 vibrations which it is capable of executing." (Proc. Mus. Assoc. Dec. 1878, 

 p. 25.) 



t "Acoustical Observations," III., Phil. Mag. April 1880. 



Fidl. May. IS. 5. Vol. 27. No. 169. June 1889. 2 I 



