64 PROCEEDINGS OF THE AMERICAN ACADEMY 



1.7 = 32A-{-16B-\-8G-^4:I) + 2B-\-^- 



1.8 = 243 ^ + 81 B-\-27 0+9 B -\- 3 B -^ F. 



1.9 = 1024^4-256^+ 64 (7+ 16 B -\- 4c F -\- F. 

 2.0 = 3125 A 4- Q'25 B -^ 125 C-\-2oB-\-5F-\-F. 



From these equations A B C B E F are found, and the required 

 equation is : — 



y = —0.0005 a:* + 0.006 x^ — 0.0245 x" + 0.139 x + 1.48. 



Next, the same volume of water used in the preceding experiment was 

 heated to 36°. The can was then placed on the same wooden props 

 used before, and by means of the same thermometer the temperatures 

 were read off every five minutes. The temperature of the air and of 

 the water at starting was 23°. The following were the temperatures 

 every five minutes : — 



I consider here only the temperatures included by the first equation ; 

 that is, from 9.8 to 7.3. 



The equation of this second curve is found by the same process as 

 in the first curve to be y = 0.12 a: -|- 1-46 ; therefore, the curve is a 

 right line. The thickness of the layer of sand was 2.7 cm. = x. To 

 determine A, I took the mean radius of the layer = 1.35 cm. 



.-. A = 2 7i . 1.35, 7.1 = 00.21 cm.^ 

 h = height of the can = 7.1 cm. 



F= volume of water. The water weighed 906 grammes; 

 therefore, its volume was 906 cm.'' 



V 



J X is constant, and = 40.62. 



.■ . K = A0.Q2 (Brt, + BrQ j^. 

 Brt^ = IB^y'] and B^t.., always = .12. 



[i),y], = o = 0.139 ; . . . i)^/, + Brf, = . 259, 



and /„ — < = 1 00 — 30.7 = 69.3 ; 



.•.A'=.1518. 



