ACOUSTICS AND GRAVITATION. 89 



Hence, if the vessel C is placed on a vertical micrometer-screw, so that C 

 may be raised and lowered with precision, the pressure needed to just float 

 the diver may be applied at C, and its value accurately read off at D. This 

 obviates the need of a special barometer reading. The vessels B and C must 

 be large enough to admit of the expansion of the air a.t a and at c. The en- 

 deavor should also be made to eliminate the water-head h" '. With divers about 

 an inch or more in diameter and two or more inches long the apparatus need 

 not be cumbersome. The height of the stand-glass need not exceed a foot. 

 Pressures of about 60 cm. at D and 16 cm. at C, B are convenient. There i? 

 the outstanding objection, however, that the air-bubble is stored under pres- 

 sure. This will be treated below. 



76. Equations. If M is the mass of the diver, m that of the air contained at 

 the absolute temperature T and pressure h+(H ir)p m /pv,, in centimeters of 

 water (h being the incidental water-head, figure no, H the residual mercury- 

 head, and TT the vapor-pressure in centimeters of mercury, p m ,p*,p s , the densi- 

 ties of mercury, water, and glass, all read off at T), we may write for the gravi- 

 tational acceleration, g: 



Rmr 

 g 



The first term in the denominator is to be multiplied by <o w at T, to get the 

 water-head at 4 C. ; the second term to be divided by p* to get the volume 

 of the air-bubble. These reductions, therefore, cancel each other. Mercury, 

 water, and air are necessarily at the same temperature, at least in apparatus, 

 figure in. The partial exhaustion was produced by a Geryk air-pump 

 with an interposed exhaustion chamber to insure the required slowness of leak. 



Thus it jfollows that variations of g are determinable with the same accuracy 

 as T and H. The former, being of the order of 290, 0.03 C., must be guaran- 

 teed if g is to be correct to io~ 4 . Furthermore H, which is about 60 cm. of 

 mercury, must be read to 0.006 cm. for the same accuracy. Both of these 

 requirements are moderate. By tapping the table from below, the light 

 swimmer is slightly separated from the thermometer above, and the degree of 

 flotation may thus be estimated with great precision by the speed with which 

 the swimmer rises again into contact. An accuracy of o.oi per cent in g may 

 thus be expected, provided m is adequately constant. It is thus the chief 

 purpose of this paper to see to what degree this may be insured ; for under 

 the very severe conditions of a heated room, in winter, with very variable 

 temperatures, it would be futile to aim at precision. 



The absolute determination of g is dependent on the value of m. To measure 

 this, large swimmers would be needed, such as would make the apparatus too 

 cumbersome. With regard to small quantities, or small changes of the quan- 

 tities TT, /'m, ;w, equation (i) may be stripped of its less important terms and 

 written in the approximate form 



