62 C. J. MERFIELD. 
Table 4 is similar to Table 3. The value of y used in the” 
equation to obtain the angles, is found by the formula No. 16. 
This table may be called the approximate as it is exactly the | 
same parabola, as that given by Table 2. The radius of curvature ; 
being in error to a small extent at the point of contact C. 
‘Table 5 contains the exact value of log “‘m,” to be used in the 
rigorous method. These values have been computed from equ® — 
tions 3 and 4. 
Table 6. This table gives the log cubes, also the log squares | 
of the distance along the axis of X for every ten links. The us? — 
of these quantities will be made apparent by the following 
examples. : 
Required the offsets to the transition to the ten chain radius 
arc at the distances 3-50, 3-60 and 3:70 from O along the axis of X. 
= me: takes = 4< 
log m. = 7°6489271 (See table ‘. ) 
log x, = 1-8061800 
log y, = 9°4551071 
Yo = 0°28517 
Yo = 94551071 = 9°4551071 = 9-4551071 : 
en 50) =9-8260240 (3-60) = 9:8627275 (3-70)= 9°898425! 
[log offset = 9-2811311 9-3178346 9-3535322 
offset = 0:19104 0-20789 0-22570 
Again required the angles 6’, for a transition to the twelve chai | 
radius arc, %, = 4. The distances along the axis of X being 3:60, 
3°70 and 3-80, 
We find from the equation tan @ = ma,? = ° that 
log tan 9 = 8-7477807 approximate — ; 
log tan CO B=8-7477807 = 87477807 =  8-7477807 
Table (3-60) = 9-9084850 (3- 70) = 9-9322834 (3-80) =9- 9554472 
log tan 6’ =8-6562657 8-6800641 87032279 
@ =2° 35’ 41-0” 9° 44’. 26-4” 9°, 53’. 260° 
