378 THE SCIENTIFIC PAPERS OF 



barometer that its indications are not affected by changes of 

 atmospheric pressure, excepting the small correction for change 

 of atmospheric density before referred to, which could be avoided 

 in excluding the atmosphere from the extremities of the mercury 

 column. 



The total attraction of the earth varies in the inverse ratio of 

 the square of the distance from the centre of the earth ; and the 

 ratio of the attraction on the surface of the earth, and at a height 

 h above the surface (supposing the earth to be a sphere), will be 



expressed by = ^ > which for relatively small values of h 



iv R + 2A w-w' h 



may be written = 77 or = ^i proving that attraction 

 iv Li w |R * 



decreases with elevation in the simple ratio of |R. The decrease 

 on account of depth of sea takes place, as shown on p. 362, nearly 

 in the ratio of R, or the readings of fathoms on the bathometer 

 may be taken for yards in raising the instrument above the sea-level. 



The corrections for latitude necessary for reading depth of sea 

 are also applicable for height ; but in the latter case another 

 correction will have to be made for the attractive force exercised 

 by the mass composing the mountain or elevation abo^e the 

 sea-level supporting the instrument, and this will vary greatly 

 with the breadth, being a maximum in the case of an elevated 

 plateau. The instrument will, in such cases, give indications of 

 height considerably below the real elevation, and it is doubtful on 

 that account whether it can be made available for such a purpose. 



TEST FOR ELEVATION. Being desirous to test the instrument 

 for height, I decided to take it up a tower ; and having obtained 

 the permission of the Board of Works, through my friend, Dr. 

 Percy, to make use of the Clock Tower for the purpose, the 

 instrument was tested on the 18th of December, the readings 

 being as below : 



being a difference of 45'25 divisions, equivalent to a difference of 

 * Including correction for variation in atmospheric density. 



