8 Carl C. Engbcr^^ 



meaningless refinement of the computations ; and that, as a rule, 

 in spite of the high powers of the constants, three or four decimal 

 places will be sufficient to give results as reliable as the data 

 warrant. 



The equations 



IV 



y=yo cos ^'" 6 e-^^ 

 x=a tan 



have a rather forbidding appearance, and the mere sight of them 

 is often sufficient to deter a man from going farther with the 

 work. If handled properly, however, they are not so bad as 

 they look. Taking logarithms, we have 



log tan ^=log X — log a 

 log j'=\og j'o + 2;n log cos 6 — vM6 log e, 



where M is the factor which converts from circular to radian 

 measure. 



We now take a card and write on it the values of log a, log jyo, 

 log (vMloge), and log 2m, thus: 



loga= 



, log (vJl/log e) = 



logJ'o= 



, log 2;;/= 



The proper use of this card will enable us to plot the curve in 

 one-fifth of the time required did we use no labor-saving devices.' 

 Similar methods may be employed in computing other forms of 

 probability curves. 



94 



