Terrestrial Refraction. 565 



where A</> is tne total refraction, we have the following- 

 value for Q for the ray considered : 



Qa (l-«)B A j (50 ) 



7 



If tfQ = Q-478, (51) 



we have, on writing '850 for R/R' in (47), 



dR' = 2-772dQ (52) 



Whence 



tfs '122dR' 



7 = ~2/r " (53) 



4_5401 



Y 2 



This last formula gives us the fractional error in range, as 

 calculated with the equation (45). The error results when 

 we replace the value of R' in (45), which is given by (47) 

 and (50), by the value R' (c) — 7497. Numerical (percentage) 

 values for lOOds/s are given in Table VII. and the corre- 

 sponding curves are plotted in fig. 6. The values for 

 (£ = 90° are only rough indications, since ds is not small. 

 The curves for 1i=l km. and Jl = 2 km. are practically 

 coincident. 



Table VII. (Values of lOOds/s.) 



<p Q 90°. 89° 30'. 89°. 88°. 



h. Q. 100 ds/s. Q. 100 ds/s. Q. 100 ds/s. Q. 100 ds/s. 



1 577 -204 550 -1-31 538 --388 529 --096 



2 521 -183 517 -T20 511 --388 505 -'098 

 'A 495 -11-4 494 - -635 491 --210 487 -'047 



4 479 - -98 476 4- "090 471 + -138 468 4- "068 



5 464 4-164 460 + 1"04 455 + -548 450 4- -264 

 •6 448 -j-40-2 443 +2-26 438 +108 431 +-445 



7 434 +64-8 427 4-3-62 422 +1-68 415 4- "681 



8 419 +95 412 +5t)9 405 +2+0 396 +-985 



00 



I 



57°. 





86°. 





85°. 



h. 



Q. 



100 ds/s. 



Q. 



100 ds/s. 



Q. 



J 00 ds/s. 



1 



525 



-041 



524 



-023 



524 



-015 



2 



502 



-•041 



502 



-•024 



500 



-•014 



3 



485 



-017 



485 



-•010 



4S5 



-•007 



4 



465 



+ -043 



465 



+ •025 



465 



+ •016 



5 



446 



+ 429 



446 



+ •076 



446 



+ •049 



6 



429 



+ •233 



427 



+ •142 



425 



+ •003 



7 



410 



+ -3IS8 



408 



+ •226 



408 



fl49 



8 



393 



+ •520 



390 



+ •323 



300 



+ •212 



Phil. Mag. 



S. 6. 



Vol. 38. 



No. 227. Nov. 



1919. 



2 R 



