Marine Barometer for Errors due to Swinging. 167 



in millibars will be in error by approximately 1*4 mb. 

 For a deviation of one degree the corresponding error 

 will be 0*15 mb. For observations at sea, the swinging 

 of a barometer with the rolling or pitching of the ship 

 is therefore a matter which requires consideration, and 

 it is the object of this communication to indicate a means 

 whereby it may be largely, if not completely, rendered 

 ineffective in disturbing the height of the mercury column. 



(2) Consider the effect of a series of small oscillations 

 about the point of support. 



The introduction of a constriction into the barometer 

 tube — the invariable custom in marine work — provides 

 damping which prevents the mercury from "pumping" 

 during each swing. The mercury assumes a level which 

 is determined by -the mean deviation during the period 

 of each swing. We may calculate the mean deviation 

 for oscillations of varying amplitude thus : — 



If a is the amplitude of oscillation of the simple pendulum 

 of length I to which the barometer is equivalent, and 6 the 

 angular deviation of a point describing a circle of radius cl 

 witli uniform angular velocity a), 



I sin a. = a sin 6 (1) 



Whence the average value of sec a from = to = tt/2 

 is given by 



which may be shown to be equivalent to 



l + isin 2 «o + -<& sin 4 a + . . . , 

 where sin a = a/l, 



a being the full angular amplitude. 



If we neglect powers of a higher than the second, it 

 appears that the effect, of swinging the barometer through 

 an angle a is equivalent to giving it a permanent deflexion A 



where A= — ^. The error in the barometric height, oTi, 



^ 2 . . . • i 



is unfortunately still likely to be appreciable, and it obviously 

 amounts to 



A (sec A -1) =ft(seo-^--lJ 



or more completely 



-i f sin 2 a , 9 • 4 \ 



