54 DISPLACEMENT INTERFEROMETRY. 



B and B', alternately dense and rare. Hence two bolometers, B and B', 

 within the pipe PP' can now be joined to form a Wheatstone bridge, as indi- 

 cated in the figure, where E is the battery and T the telephone or vibrator. 



This, therefore, corresponds to the usual bolometric adjustment and may 

 be pushed to much greater sensitiveness, particularly if the nearly equal resist- 

 ance in B and B' are unavoidably small. 



37. Equations. If - denotes absolute temperature, p pressure, r resistance, 

 and i electric current, we should have in succession 



dr k c dp dp 



7 = 1T7 =0 - 2 V 



where k and c are the specific heats of air; 



dr dr dp 



(2) = = O.2Q 



r r p 



if the electrical temperature coefficient of the wire is the same as the coeffi- 

 cient of expansion of a gas. Thus finally, by Ohm's law for large non-inductive 



resistances, di dr dr dp 



= -- = =0.20 

 i r r p 



or dp di 



(3) 7 =3 - 5 T 



This assumes that all the resistance is in the bolometer. As this is not the 

 case, let R be the other resistances (telephone). Then 



(A) & r , r dp 



= v-r-dr/r = 0.29-5- -- f- 

 i R+r R+r p 



or dp R+rdi 



(5) 7 =3 ' 5 ~7-7 



Thus if di= io~ 7 ampere can still be heard in the telephone and the total cur- 

 rent is i = o.i ampere, and if (R-\-r}/r=2 



so that dp=io 6 XjX io~ 6 = 7 dyne per square centimeter. This is the virtual 

 pressure increment, the maximum being V '2 larger. At all events, as the 

 actual acoustic dp is much below this, it would imply a virtual acoustic energy 

 of less than 7 ergs per cubic centimeter at the node. 



Lord Rayleigh* finds 42.1 ergs/sec, issuing from a tuning-fork just audible. 

 This is equivalent to an energy residence of 42. 1/3 3,100=1. 3X10^ erg per 

 cubic centimeter. Again, according to Rayleigh's later estimate, the dp/p = 

 6X io- 9 is at the beginning of audibility. Hence the above excessive superior 

 limit would be over 1,000 times larger. 



Two reasons thus suggest themselves for the failure of the present experi- 

 ments. Either the note at the node is not loud enough to produce an impres- 

 sion sufficient to actuate the telephone, or the alternations of pressure (130 

 per second) are too rapid to enter the wire or foil appreciably as a heat current, 

 even when this wire or foil is the thinnest available. _ 



* Rayleigh, Phil. Mag., 1894, xxxvm, p. 369. 



