35K LORD RAYLEIGH ON THE COMPRESSIBILITY OF GASKS 



action of the thermometers is elimiuated in the actual results, which depend only 

 upon a comparison between operations with and without the large bulbs. For 

 example, suppose that there is an error in the rather ill-defined temperature of the 

 space V 3 . The conditions are the same whether the large bulbs are in use or not ; 

 and thus whatever error occurs in the one case may be expected to repeat itself in 

 the other. So far as this repetition is complete, the error disappears in the 

 comparison. Again, it might happen that one of the large bulbs tended to be 

 warmer than the other or than the thermometer. But this, so far as it is constant, 

 could lead to no error, the effect when the bulb is used alone being compensated by 

 the effect when it forms one of the pair. Purely accidental errors are, in any case, 

 eliminated when the mean is taken of a number of observations. 



The Large Reservoirs. 



The tubes forming the principal parts are of glass, 25 centims. in length, 41 millims. 

 in internal diameter, and about 2^ millims. thickness in the walls. There are 

 prolongations above and below of narrow bore, upon which are placed the marks 

 defining the volumes. 



As has been explained, the accurate comparison of these volumes is unnecessary. 

 As it happens, the actual volumes between the marks are so nearly equal that it is 

 difficult to say which is the larger. The total volume V 1; required only to be roughly 

 known for the sake of the subsidiary terms, is 632'6 cub. centims. 



But there is another question to be considered. The single bulbs are used under 

 an internal pressure of an atmosphere. Under the same pressure the combined 

 volume of both bulbs would of course be exactly double the mean of those of the 

 bulbs used separately. But when the bulbs are in combination, the internal pressure 

 is reduced to half an atmosphere, and the bulbs contract. A correction is thus 

 necessary which runs similarly through all the results calculated on the supposition 

 that the ratio of volumes is exactly 2:1. 



The amount of the correction has been determined in two ways. Direct observa- 

 tion of the change of level of water filling the bulb and standing in the small upper 

 prolongation, when the internal pressure was changed from one atmosphere to half 

 atmosphere, gave a total relative alteration of 4'4X10~ 5 per half atmosphere, of 

 which 2'3X10~ 5 would be due to the contraction of the water. The difference, 

 viz., 2'1X10~ 5 , represents the relative contraction or expansion of the volume per 

 half atmosphere of pressure. 



A calculation founded upon the measured dimensions of the tubes, including the 

 thickness of the walls, combined with estimates of the elasticity of the glass, gave 

 2'0x 10~ 5 per half atmosphere, in better agreement than could have been expected. 



The real ratio of volumes with which we are concerned in these experiments is 



thus not 2 exactly, but 



2(1 -000021). 



