LVIII. C. J. MERFIELD. 
multiply all quantities, given in either of the tables, by this value 
with the exception of ¢, also K atid log. m. The quantity X is 
simply the circular measure of 2¢. The value of log. m may be 
found for the radius R, by subtracting twice the logarithm of #& 
from the tabulated value of log. m. A practical example will 
perhaps make the preceding remarks more explicit. 
Let # equal 4, then if we multiply each value of « in the first 
column of Table I. by four, we obtain the several lengths along 
the axis X, where the ordinates y of the second column are to be 
set out, these values being also multiplied by four ; thus— 
R=4 
wv y 
0-20 000018 68 
0-40 0:00149 32 
0-60 0:00503 92 
etc. ete. 
e, = 2°00 y, = 018664 04 
We also have the following 
@ = 15° 38’ 24”-50 
xe’ = 107837 80 
H = 0:03853 52 
: s = 2°01550 96 
Should a longer transition be required, then use Table II. or IL., 
so that with the above value of R we have the choice of three 
transitions namely 
R.S.—Cubic Parabola 2 
050 x 4 
0-68 x 4 
and asa in other cases. It is not necessary that & be integral, 
but any value may be taken. 
Limits of application.—The angle of deflection w of the straights 
must either be equal to or greater than 24; if less than this angle 
then the transitions will overlap, this will be inadmissible ; whe? — 
2¢ equals w, then the circular curve disappears, the points ¢ and c 
= 2°00 
0°60 x 4 = 2°40 
= 292 
n 
oa becoming one and the same, and such a case is admissible. 
