THERMO-ELECTRIC DIAGRAM FROM - 200° C. TO 100° C. 



745 



Each observation gives an equation (9), and from these in the usual way we get the 



normal equations 



*2(U 2 ) -2/2(UV)-*2(U) = 2(U 3 ) x 



z2(UV)-i/2(V 2 ) -z2(V) = 2(U 2 V)l .... (11) 



*3(U) -yS(V) -*2(1) = S(IP) ) 



for which we require the values of 2 of each of the following seven terms, for the 

 eleven observations specified below in Table I., 



U U 2 U 3 

 V UV U 2 V 



V 2 . 



The values of these 2's are respectively — 



1,807-99, 392,494-58, 95,351,762- 



2,220-65, 317,498-61, 58,212,092- , 

 534,690-35, 



The solution of equations (11), with these numbers as coefficients, is 



x = 2u = 2{a+M) = 278-57307, j 



y = p =psecu> = 90-208406,1 . . . (12) 



z = u 2 -p'v = (a + km) 2 -p sec w (k-am)= -8105-33015; ' 

 which give finally 



a= 118-7125 | 



k = 312-7267 - ..... (13) 



p= 90-01381 ' 



with the experimentally measured value 



tan co = 



15-2 



(14) 



Table I. 

 Details of Calculation for Callendar's Platinum, with cot w= 15*20. 



pt°. 



rc. 



E. 



C.G.S. 

 Units. 





T. 



200 H = 

 E + 50,000. 



U. 



V. 



E 

 200" 



200' 



Error = 



E„- E c 



200 ' 



100-2 

 73-7 

 455 

 155 



- 16-2 



- 62-4 



- 81-1 

 -122-9 

 -164-5 



- 188-0 

 -195-5 



100-05 



73-21 

 44-99 

 15-36 



- 15-51 



- 59-69 



- 77-29 

 -116-07 

 -153-88 

 -174-89 

 -181-55 



- 43550 

 -29320 

 -16440 



- 4740 

 + 4620 

 + 11910 

 + 12770 

 + 9090 



- 1490 

 -10810 



- 16140 





300-05 



27321 



244-99 



215-36 



184-49 



140-31 



122-71 



83-93 



46-12 



25-11 



1845 



6450- 

 20680- 

 33560- 

 45260- 

 54620- 

 61910- 

 62770- 

 59090- 

 48510- 

 39190- 

 33860- 



302-17 



280-01 



256-03 



230-25 



202-46 



160-67 



143-36 



103-37 



62-08 



38-00 



29-59 



12-51 

 85-43 

 151-68 

 212-13 

 260-96 

 300-32 

 305-78 

 289-93 

 239-52 

 194-30 

 168-09 



- 217-75 

 -146-6 



- 82-2 



- 23-7 

 + 23-1 

 + 59-55 

 + 63-85 

 + 45-45 



- 7-45 



- 54-05 



- 80-7 



-219-13 



- 146-6 



- 80-36 



- 22-77 

 + 22-84 

 + 59-09 

 + 62-81 

 + 46-18 



- 8-22 



- 57-69 



- 76-61 



+ 1-38 



nil. 

 -1-84 

 -0-93 



+ 0-26 

 + 0-46 

 + 1-04 

 -0-73 

 + 0-77 

 + 3-64 

 -4-08 



The data employed and the intermediate results obtained in this calculation are 

 shown in Table I., the headings of the various columns being either clear in themselves 

 TRANS. ROY. SOC. EDIN., VOL. XLVII. PART IV. (NO. 25). 110 



