OF ARTS AND SCIENCES. 133 



time. After the basket has descended into the water, it commences 

 to give out heat to the water; this, in turn, radiates heat; and the 

 temperature we measure is dependent upon both these quantities. 



Let T = temperature of the basket at the time t 



a 'fl __ u u U (( 



u TV/ — — « " »< " oo 



" d = " " water " t 



U 01 -— " « " " 



" 0" = " " " u . 00 



6" = T" 

 We may then put approximately 



T— T"= (7" — T")s-7, 

 where c is a constant. But 



f> T" T' T 



e" — e' ~ " e — qi ' 

 hence , 



— d'= (0" — 0') (1 — 8~^). 



To find c we have 



1 , 6" — 0' 



= — ]o<r„ 



t ° e" — o 



where U" can be estimated sufficiently accurately to find C approxi- 

 mately. 



These formulae apply when there is no radiation. When radiation, 

 takes place, we may write, therefore, when t is not too small, 



o -*- o' = {d" — 0') (l — «"-£) — G (t — o, 



where C is a coefficient of radiation, and t {) is a quantity which must be 

 subtracted from t, as the temperature of the calorimeter does not 

 rise instantaneously. To estimate t u , T a being the temperature of the 

 air, we have, according to Newton's law of cooling, 



C 



( ' " ' o) = ¥^T a ft 6 ~ T ^ dt nearl >'' 







e" — e> 

 h = c „ _ Ta nearl 7. 



where it is to be noted that —, ~r is nearly a constant for all values 



0" — 1 a J 



of 0" — T a according to Newton's law of cooling. 



