COS "co sin 4:v when it should be 1/8. This leads in turn to the printed value 23/64 as given on 



page 116 when it should be 15/64. 



After the two errors in Forsyth's second order term in f had been detected, two papers were 



found which are concerned with the Forsyth derivation, Wassef 1948, [19], and Gougenheim 1950, 



[20]. Wassef purports to give the corrected version of Forsyth's second order term but he includes 



the term *2 in (102) and he gives 15/23 for the numerical coefficient of *1 in (102). Hence Wassef's 



results are erroneous and useless. Gougenheim, unaware of Forsyth's work, had developed his 



formulae independently and he has the term *2 in (102) missing in his derivation and the correct 



numerical coefficient 15/64 for *1 of (102). His formula for the second order term is (in the 



notation of Forsyth) 



( V ^^^^-^ 



^^ - (1/2) cos^Oo sin^Oo + (1/16) {v^ - v^ (cos^Qj, + 15 cos^Oosin^Oo) 



cot V2— cot 1^1 



- (3/4) cos^Oo sin^Oo (sin 2.v^ - sin 1v^ 



+ (15/64) cos''ao (sin 4^2 - sin 4i^i ) 



Since the last two terms of (105) are the same as the last two of (102), as corrected, we have 



only to show that 



(1/16) cos''an + cos^an sin ^a^ s (1/16) (cos^ao + 15 cos^Oq sin^ao)> 



(106) 

 l/(cot i/j - cot i/j) = (sin Oo sin (^I'sin <;62')/sin 200. 



Writing the right member of the first of (106) as 



(1/16) cos^ao + (15/16) cos^ao sin^cto + (1/16) cos^Oo -(1/16) cos^Qo (1 - sin ''ao) 



= (1/16) cos'oo + (1/16) cos'ao + (15/16) cos'oo sin 'oo 



- (1/16) cos^Oo + (1/16) cos^ao sin ^a,, 



= (1/16) cos''ao + cos^ao sin^Oo. 



From relations (103) we have 



sin Oo sin {v^ - v-i) = cos li cos I2 sin 2(f>o or 

 sin Uq cos li cos I2 



sin 2(po sin {v^ - 1^1) (107) 



cos li sin (^ 1 cos I2 sin 0; 

 sin ao sin (;6 j sin ^ 2 cos li sin i • cos Ij sin 1^2 sin u^ • sin i/j 



sin 2(^0 sin 1^2 cosi^i - cos 1^2 sin v^ cot v^ — cot v^ 



77 



