﻿328 ON Extending a geographical survey 



Observations for the Latitude of the southern e.rtre- 

 miti) of the Base, and the Meridian at that point. 



For the meridian, I observed the angle which the 

 line made with the polar star when at its greatest 

 western elongation ; and computed its azimuth, at 

 that time, fiom having the latitude of the place, and 

 the ajjparent polar distance given— at that season of 

 the year a double azimuth could not be taken in the 

 night time, and my telescope had not sufficient 

 powers to observe the star in tbe day time. 



The 



Now, since the expnnslon of brass is clifFerent from that of steel ; it 

 follows, that when the measurement is mdde in a higher or lower tem- 

 perature than that in which the steel and brass coincided, there will 

 be an equation ; which must bd" applied to the apparent measure of the 

 chain, in order to bring it to the brass measure. I shall call this 

 higher or lower temperature, the temperature of meafiirement. 



After the steel chain has been reduced to brass measure, it may be 

 fourd necessary to reduce the brass standard itself, to the space it 

 would have measured, or extended over, in a higher or lower tempe- 

 rature. Let that be called the standard temperature. Now upon a 

 .slight examination of these, it appears that they will resolve them- 

 selves into three cases. 



Case 1st. When the standard temperature and the temperature of 

 measurement are both aho've the temperature of coincidence. 



Let the brass standard and steel chain coincide, when the therma- 

 meter is at 34° ; and let a space be measured by the chain at the temi 

 peraturc of n degrees, so that "i^^^^'' shall express the number of de- 

 grees above the temperature of coincidence, when the measurement is 

 made. Now, the length of the chain at 54° was precisely a given 

 number of feet, (we will suppose lOO feet,) by the brass scale. And 

 since ,00763 inches is the expansion of 100 feet of steel for one degree 

 of the thermometer, it follows, that when the chain is applied at the 

 temperature of «° it will extend anjer a space oh the ground equal to 



K — 54" X J00763 



100 + • feet, if measured by the brass scale in the tem- 



12 

 perature of .54^. 



So far as to the temperature of 54° when the brass and steel coincide ; 

 that is, when 100 feet of brass coincide with lOO feet of steel at that 

 degree of temperature. But suppose it should be thought necessary to 

 change the standard temperature to ;i°, the temperature of coincidence 

 being still at 54° : — tnat is to say, let the space above-mentioned be 

 measured by the brass standard at the same temperature «° as when the 



cljain 



