1887.] Its Reduction to Sea Level. 263 



The latituie correction has now to be considered. The weight 

 of a body on the earth, decreases from the poles towards the equator in 



(cos ^ 

 1 — - — ^ I so that the weight of the atmosphere 



below any altitude, or the term 30 — B will increase in that propor- 

 tion towards the poles, hence the latitude must be replaced by the 

 co-latitude, and as the cosine of the co-latitude is the same as the 

 sine of the latitude, we have the latitude correction as 1 + '00346 

 sin^^. Colonel Clarke from pendulum observations has altered the 

 co-efficient to '002606. 



The formula for heights based on the foregoing is 



H = 65,000 (1 - -002606 sin^^) log. ^ (3) 



and for reduction 



, B H (1 + -002606 sin20) 



^^^- B^ - 65,0-00 • ^^) 



The reduction to the gravity of latitude 45^ is given by La Place 

 as 1 + '00284 cos 20.* Professor Archibald, from Colonel Clarke's 

 observations, has altered this to 1 — '002606 cos 2^. 



Between Cape Town and Kimberley this correction for gravity 

 makes a difference of '013 of an inch, so that the reduced readings 

 at the latter should have this correction applied subtractively. 



The foregoing gives the argument upon which I have considered 

 this question. Of course the formula given will only be applicable 

 for stations on elevated plateaus. For mountain stations they will 

 not answer, as temperature and humidity have such different effects 

 at such stations to what they have on elevated lable lands. More- 

 over the atmosphere between the station and the foot of the mountain 

 has to be taken into consideration with all its varying conditions.^ 

 For these stations I would introduce the temperature correction 



/' = t + — where t represents the mean temperature of the date 

 2c 



of observation for a great number of years, and — the variation due 



2c 



to altitude, c being the number of feet in which the temperature de- 

 creases one degree. This variable c is different for different latitudes 

 and temperatures. 



In the tropics the perpetual snow limit is 16,000 feet above the sea 

 level. Taking this as a datum we find that with a sea level tempera- 

 ture of 80^, the decrease is P in every 333 feet of altitude, but with a 



* Co-Latitude. 



