364 Mr. A. R. McLeod on 



In applications of these formulae the quantities iu brackets 

 are taken ^ as constant. Consider the case of (44) when it 

 is a question of determining 5 as a function of li and D. 

 Writing (44) in the form 



/* = *tanD-^-, (45) 



we have for the range error, ds, due to a small variation dR\ 

 in the value of R' : 



ds KW) dR 



7 = ~^jbP ( 46 ' 



Also 



where Q = (1 - €)m ' (48) 



In any numerical formula, we must assume a value for R'. 

 This requires the assumption of a mean value for Q, which 

 quantity varies from one ray to another, as well as along any 

 particular ray. 



To take a particular case, let us examine a formula in 

 practical use. In Chauvenet's ' Manual of Spherical and 

 Practical Astronomy,' p. 180, the following formula occurs : 



I) = 22-14^ + 39-07^, 



where D is the dip in seconds, x the height in feet, and 

 d, the range in statute miles. Changing the units to radians 

 and kilometres, we get the equivalent formula : 



D= 7 + 27W7 < 49 > 



Writing R /W = 7497, we have for this formula : 



» _ 637 o_. s . n . 

 ^-7497- 8o0 ' 



and therefore 



Q (c) = 478. 



Xow if we take for ml, in (48), the expression 



