﻿$30 O^ EXTENDING A GEOGRAPHICAL SURVEY 



It will appear, that there is a great difference in 

 the above observed angles of tiie star with the N. 



end 



54— «? X ,00763 



equal 1 00 — feet ; for the steel beinsr contrafted will 



iz ° 



evidently extend over a bhorter space than it did at 54° by the 



34— ""■'x .00763 

 quantity . leet. 



Next, suppose the brass standard to be reduced to «^ or 54 »<« below 



the temperature of coincidence. Then, had the expansion of brass and 



, , , , 54— «'' X ,00763 

 steel been the same, the space 100 — lect, would now 



54— /^^ X ,00763 54— «<» X ,00763 

 increase to 1 00 — + equal 1 00 feet by 



54 — /i' X ,00763 



the brass scale, since that scale has contrafled feet in 



12, 

 100 feet. 



54 — ;;'' X ,01237 



Bat 100 feet of brass will have contracted feet, and 



la 

 therefore the space in brass measure will be expressed by 1 00 — 



___^ o 



54--«°X ,00763 54— ^'^X ,01237 54— n* X ,01237— 54— ;r X ,00763 



1 r:ioo + 



la 12 12 



feet, when the standard temperature is ;/°. But if the standard tenu 

 perature be j^ then the space will measure 

 54—-'' X ,01237— 54— ».« X ,00763 



100^ feet, when measured by the brass 



12 ' •' 



scale at s^ of temperature. 



Case 3d. Let the temperature of coincidence be beiiveen the 

 standard temperature and the temperature of measurement. 



1 . Let the temperature of coincidence be 54° as before, and let the 



standard temperature be below 54°, so that 54 — s° shall express the 

 number of degrees below 54 for che reduction, and let «° be 



above 54, so that » — 54' expresses the excess of the temperature of 



measurement above that of coincidence, and ;/—j<» the excess of the 



temperature of measurement above the standard teniperature. 



Now, 



