﻿ACROSS THE PENINSULA OF INDIA. 331 



end of the base ; but that arose from tlic unfavour- 

 able weather in the mornings, at which time the 



telescope 



Now, by Case 1st, the space over which the chain extends on the 



n— 54*' X ,00763 



ground will be 100 ^ — feet, compared with the brass 



scale at 54°. Had the contraction of brass been the same as that of 



n—s'^ X ,00763 



steel, lOO-i — feet, would be the measure, by the brass 



scale at 54 — f** below the temperature of coincidence. Bat it has con- 

 ,01237 — ,00763 



trafted more by j4 — i^ ^ feet in loO feet; and con- 



iz 



sequently the space which the chain extends over, at n° of tempera- 

 lure, will, at 7/ — i« of temperature, measure, by the brass scale, 



iJH^^X ,00763+54— j°x ,01237— ,00763 



100+—^ feet. 



li 

 2. Let the standard temperature be above 54°, and the temperature 

 of measurement below it. 



Then, by Case 2d, the space over which the chain extend.^ is — 



54—" ° X ,00763 



J 00 feet, measured by the brass scale at 54". — And 



12 



s—n^ X ,00763 _ 



100 : feet would have been the measure at s° by the 



12 



brass, had the expansion of steel and brass been equal. But the ex- 

 pansion of brass is more by •'—54''+, 01 23 7— ,00763 feet. And there- 



12 

 fore, if the space over which the steel chain extended, when the tem- 



perature was 54 — K*? below the temperature of coincidence, be measured 



by the brass standard, when the temperature is s — 54° above that of co- 

 incidence, the value of that space, in brass measure, will be 100 — 



V^— «°X, 00763 + J— 54° X, 0123— 0076 j * 



12 



Hence, universally, if s° anda° denote as above, and /" temperature 

 of coincidence, and S z=. the space on the ground over which the steel 



chain 



