1904-5.] Mr T. Oliver on Diameters of Twisted Threads. 487 
with the calculus. Plot to a large scale on squared paper the 
values of 0 as abscissae and the corresponding values of AD as 
ordinates, and draw a curve through the tops of the ordinates in 
the usual way. The values of AD may be found by drawing 
figures for the ten values of 6 , i.e. 0°, 10°, 20° .... 90°, and 
measure off the lengths for each case, or the values of cos 6 may be 
taken from a four-figure table of cosines. 
The area inclosed by the base line, the curve, and the two end 
ordinates may be found by the planimeter, or any of the rules for 
summing areas in mensuration. Of the latter, the mid-ordinate 
rule, being the simplest and sufficiently accurate, might be used. 
