Aero-mercurial Tide-Gauge. 257 



dh 



It is evident that the reduction-factor -— of the apparatus 



tin 

 may have any value whatever, which is less than - , by 



suitably choosing the values of s ly s 2 , s 3 , In my case it was 



., „ OP7 . It is easy to find experimentally the value of the 

 lo*o7 " L 



factor, by raising the immersed jar by a known height and 

 comparing this height with the vertical line recorded on the 

 cylinder. 



The effect of temperature may be calculated in a similar 

 way. For this purpose, the product of the volume and the 

 pressure in Boyle's law must be put equal to FT, where T is 

 the absolute temperature and F a constant. Here h is con- 

 sidered to be constant ; we have the equations 



dF=-dh 1 = pdhJl+'l 3 \ 



pdh 3 (l+^){ Sl (a -hd + v + s 2 (b-h 2 )l-¥(s 1 dh 1 + s 2 dh 2 )=~RdT, 



s 2 dh 2 = —s$dli%. 



Eliminating dh ly dh 2 , dP, w T e have approximately 

 dh 3 F . F 



dT 



P {K 1+ !W '^ P ( 1+ J) 



If we neglect v in comparison with the volume of the jar, R h 

 equal to P^a/T ; hence 



dh z _ a 



dA~ 



^ + t) 



In my case, a = 12 cm., p = 13'6, and 1 -\ — = 1*26; hence 

 at 10 b 0., " 2 



^ = 0-0025 cm. 



When the temperature changes, the vapour-tension also 

 changes; but the change of vapour-tension per degree rise of 

 temperature is about 1/3 the change of pressure due to the 

 thermal expansion of air. Hence as the combined effect of 

 these two, we may take 



^ = 0-0033 cm. 

 Phil. Mag. S. 6. Vol. 10. No. 56. Aug. 1905. S 



