Mr. Ivory's Tables of mean 



[No. 157. 



introduced are of no practical importance, the following detail of the 

 interpolations is inserted here as a guarantee for the course which has 

 been adopted. 



TABLE I. Interpolations between num- 

 bers as in the Original Table of 1838. 



TABLE II. Interpolations between Ta- 

 bular refractions for Z.D. 89° $ Z. #.90° 



Zen. 

 dist. 



8900 

 05 

 10 

 15 

 20 

 25 

 SO 

 35 

 40 

 45 

 50 

 55 



90.00 



Mean 

 refrac- 

 tion, 



24:16.80 



25:05.97 



25:46 80 



26:29.46 



27:14.20 



28 : 06 

 * ... 



28:49.50 



Tab. 

 diff. 

 M.R. 



87.40 



95.30 



29:40.24 

 30: 33.20 



103.70 



31:28.12 



* 



32: 25.10 



111.90 



33: 26.30 



* 



34: 32.00 



126.90 



d. 



39.17 



40.83 



42*66 



44" 74 



46*.66 



48*64 



50.74 



58.96 



51.92 



£6*98 



6*6*20 



65*70 



d. 



1.66 

 1*83 

 *'*.08 

 1**92 



l".98 

 2*10 



2,22 

 1.96 

 2! 06 

 '"'.22 

 '"'.50 



+.17 



+.15 

 —.16 

 +.06 

 +.22 

 +.12 

 —.26 

 +.10 

 +1.16 

 +2.28 



Mean | Tab. 



refrac- 

 tion. 



24 : 26.80 



25 : 06. 



25 : 4*6. 9 



26:29. 6 



27:14*. 2 



28 : 00. 8 



28 : 49*. 4 



29 : 40- 2 



30:33. 3 



31:28". 9 



32:27. 1 



33:28*. 



34:32. 



diff. 

 M.R. 



80,1 



87.3 



95. 



103.9 



113.8 



124.9 



39.2 

 40.9 

 42.7 

 4*4.6 

 46.6 

 4*8.6 

 50.8 

 5*3.1 



5*8.2 

 6*1. 



1.1 

 l'.8 

 1*9 



2**0 

 2*0 

 2*.2 

 2.3 

 '"' 5 

 2*.6 

 2! 8 

 *2*9 



r 1 * 2 



|Z + o 



+.1 +0.03 

 +.1+0.10 

 +.1 '+0.14 



+.0 



+.2 

 +.1 



+ 2 



+0.00 



-0.06 

 -0.10 

 -0.14 

 +.1 +0.10 

 +.2 +0.78 

 +.1 J +0.20 



... 1+018 



I 



The numbers to which asterisks are affixed, are those of the original 

 Table. 



With a view to facilitate the computation of numbers still interme- 

 diate between those in the present Table, Log. differences correspond- 

 ing to one minute of altitude and to one second of refraction, have been 

 given in separate columns. 



The Tables (II and III of 1838) containing the Log co-efficient for 

 Barometric pressure and for temperature, have been extended by con- 

 tinuing the application of the tabular differences to the limits of prac- 

 tical utility, and the co-efficients of the correction for altitudes under 

 10° have been taken from their respective columns in the original Ta- 

 ble I. and extended by interpolation as above. 



The following examples, will explain the use of the Tables. 



Let P. denote the height of the Barometer. 

 „ T. ,, the temperature, Fahrenheit. 

 „ T. „ the Zenith distance of the object. 



