Marine Barometer for. Errors due to Swinging. 169 



By equating the values of Sh found in §§ (2) and (3) we 

 find that there will be no disturbance of the mercury level if 

 l=2d. 



(-i) The preceding investigations have been made on 

 the assumption that the two causes of displacement are 

 independent. The following argument shows that this is 

 justified even bej^ond the limits of accuracy to which it 

 is useful to proceed. 



The acceleration along the tube at any instant is 

 g cos a -\-£l 2 d j which would cause the mercury to occupy 

 a length of tube h l instead of A for a fixed barometer. 

 Whence 7 7 , , ~ 9 7 



A 2 r= Jig/g COS OL + lVd. 



The constriction in the tube causes the observed value 

 of h' to be the average value of the rioht-hand side of the 

 equation. 



Using our previous equations (1), (2), and (3), we 

 have for the average value of hi 



_ ^ ^ 1-gsin'g ^ 



which reduces to 



T 2hC 7r/2 / la 2 .„, d\l * a \ja 



whence 



i-»{. + 5(i-¥)}. 



since ajl = u where a is small. 



Thus the displacement y of the mercury above its un- 

 disturbed level is given by 



, = 7,-/* =¥(!-¥) <*) 



which may also be written 



y^i^-w) (5) 



(5) We next consider the possibility of arranging that 

 the errors discussed in (2) and (3) shall neutralize one 

 another. 



KpO we have from equation (4), d/l-h whence it 



