

-© 



Bowditch on correcting the ajrpai^ent distance 



\ 



the value of the quantity 59'^ 4S^'' — L\l for all altitudes, and at 



the same entry the Proportional Logarithm of —^ 



2.LM 



cos.m 



by 



means 



of 



which the quantity LM — LK called i\\e. second correction is com. 

 puted. This requires only one additional logarithm ; because 



log. sin. d and log. costc. g were found in making the computation 



BK. 



of the jii^st correction. 



The next term in the values of MS is 18''' + BM 

 Now it is well known that when the arch MK is very small in 

 comparison with BK, the diiierence BM — BK will be very 



to ± i- MK-. cot. BK, or ± 4-. MK^ cot. d : so that 



■ly equal 



the terra now treated of is 18^' ± ^ MK^ cot. d. The uppe 

 being used if d 90, the lower if d>QO°. 



gn 



This is found by 

 means of Table XX, which contains two vertical ccdumns corres- 

 ponding to each value of d, the arguments at the side being the 



J 



quantites 60' —LM and 60' — LK, or in other words the correc- 

 tion of Tab. XIX, and corr. Tab. XIX + second correction ; the 

 tabular numbers corresponding when d < 90% being respectively 



IS^'^ -' 4 L^Ti^ cot. d and i LK^ cot. d, whose difference is 18^^ + 



(X^M 



LK"), cot. d or 18 



// 





MK^ cot.rf 



When d 



the tabular numbers 



90% 



LK\ cot. d, Rid^ LM'. cot. d 



y 



whose difference is 18^^ 

 led the third correction. 



iMKI^ cot. d, as above. This is cal- 



Therefore if we neglect the two very small terms BC + (MS 



MC) in the value of MS, it will become 



MS=(a|)p.{list.-2^)-f.cf>rr.Tab.XVlI-f.rorr.Tab.X!: 



. 



and all the terms of this expression will have the affirmativ 



2''corr.-f3'»corr. (A) 



zy 



As an example of this formula, let us take the foUowinjr, which 



t.4!. The ap- 



first in the Practical Navigator, Pag. 155, Ed 



pai 

 alt 



being 3? 

 Horiz. Parall 



app 



14/ 



app 



./ Qr;" 



35 



y 



m 



