ACOUSTICS AND GRAVITATION. 117 



effect of a slow influx of air into the apparatus, when exhausted to different 

 pressures. The conditions of influx were throughout about the same, being 

 about 7 cm. of mercury per 30 minutes at the highest vacua. The phenomenon 

 is thus very nearly isothermal, and yet the results of the heating produced are 

 phenomenally marked. The individual readings are given in figure 142, where 

 the numbers show the exhaustion. Figure 149 contains the mean results 

 Ay at the different vacuum-pressures p. The irregularity of results is to be 

 ascribed to the change of Ay, even for the plenum, and to the difficulty of 

 controlling the influx; but apart from this the excursions Ay rapidly diminish, 

 nearly proportionally to p, throughout the large part of the curve, while at 

 very low pressures the effect is possibly even accelerated. It often appears as 

 if for p = there would be no excursion. 



These results are so striking that one may well ask whether temperature is 

 here only in question. The effect of influx (10 to 15 cm. per hour) is to heat 

 the interior relatively to the ball M, without. Hence the region between the 

 shot m and ball M is relatively cool as compared with the other side of the 

 needle, and the result would be a repulsion on the cold side counteracting grav- 

 itational attraction. So far the reduced results are consistent with the experi- 

 ments of figures 144 to 148, though the graph figure 149 is incorrect as to 

 slope. Again, the earlier data demand an inversion of the effect at about (say) 

 50 cm. of exhaustion; *'. e., an attraction. The present data here show no inver- 

 sion, but rather an accentuated repulsion. True, the inversion in figures 147 

 and 148 is not marked. It is present, however, while in figure 149 Ay in a 

 vacuum of 50 cm. is but one-half of the value for a plenum. 



The work done by this influx, so nearly isothermal, would be Rmr log p/p f , 

 where m is the mass of gas, p and p' are the initial and final pressures, and m 

 varies as the mean pressure, nearly. Thus 



Pressures 43 -36 cm. 33-25 23-16 11-3 7-2 



Work done oc 31 35 31 40 28 



Log P'/P = -8 0.12 o. 16 0.56 0.54 



A0 = 14 23 30 108 104 



The work done is therefore not so different in the various cases, but as the 

 mass is inversely as the pressure, the rise A0 of temperature would vary as 

 log p'/p and would thus be greatly in excess at the higher vacua. In this respect 

 the results of figure 149 may in a general way be interpreted, if the radiometer 

 effect is ignored. It would have to be nil in a perfectly symmetrical needle, but 

 what is curious is the persistence of the plenum effect. There is a persistent 

 pressure on the colder side of the needle at all exhaustions. 



The total amount of heat produced and its temperature effect may be com- 

 puted. If T is absolute temperature, m the mass of gas, the work done is in 

 the usual notation for a pressure increment of dp, 



dW = RmT(dp/p) 



If dd is the corresponding rise of temperature without loss by radiation, 



= Jkmdd 



