270 



CATALOGUE OF POLAR STAKS. 



Simplifying tliis equation, we have : 



X 



w- 



X 



to* 



g = -l .4G361 -^ + 0.53090 0.07105 ^- + 0.0038194 0.00006944 • + 0.000001 9290 



X 



X 



= r0.16543«] — + [9.72501] — + [8.85156h] ~ + [7.58200] -^ + [5.841C4;0 ~ + [4.28534] 



X 



(53) 

 a; 



w 



12 



From equation (53) we derive the following numerical values of the effect 

 of the error x for ic — 1, lo — S, tc — lG, w = oO, and ic = 40: 



M) = 1 



to = 1 



3=8 



JO = 8 



to = 16 



r" -0.0057173.r 



r'^ + 0.0000081009X 



U^ -0.0000000042349X 



r''™ + 0.00000000000088929a; 



V^ -0.000000000000000063160X 



to = 16 



LogaritbniB. 



[7.75719«]x 



[4.90853]j; 



[1.62684»i]x 



[7.94904]x 



[3.80044m]x 



+ 0.00000000000000000000G8534.r [9.83591]x 



to = 30 



Logaritbms. 



[7.21119«].J; 



[3.81G5.3]x 



[9.98883/*]x 



[o.76503]x 



[1.07043;i]x 



[6.55989]x 



to = 40 



Logaritlims. 



[6.9G131«].« 

 [3.31677]x 



[9.23920n]x 



[i.76552]x 



[9.82104n]x 



[5.06062]x 



We illustrate the computation by assuming 



X = one unit in the third decimal jilace of a for 1875.0. 

 Then, assuming 



= 10 for to = 1 



= 40 for tc = 8 



= 40 for to = 16 



= 100 for to = 16 



= 120 for ic = 16 



= 120 for to = 30 



= 120 for w = 40 



we have for the total effect e of the error .r 



