76 
The N.Z. Journal of Science and Technology. 
[Mar. 
Section. 
Weight 
of 
Section. 
Weight per 
Inch run. 
Distance 
from B to 
End of Section. 
Moment about Crosshead-pin. 
First Moment. 
2W xxdx. 
Second Moment 
SW x xUx. 
lb. 
lb. 
in. 
AB 
11-4 
3-65 
-34 
-18 
-37 
BC 
12-8 
4-1 
H 
20 
42 
CD 
14-65 
5-1 
6 
67 
315 
DE 
1350 
1-73 
84 
6072 
341668 
EP 
571 
7 62 
914 
5015 
440329 
FG 
327 
9-35 
95 
3052 
284595 
GH 
31-6 
9-03 
98J 
3057 
295868 
HJ 
13 25 
7-58 
1001 
1318 
131005 
Total 
308-5 
18583 
1493785 
Total weight—estimated, 308Jlb. ; actual, 3081b. 
Centre of gravity from crosshead pin—estimated, 60-23 ; actual, 60"45. 
Square of radius of gyration about crosshead-pin : 
(fc 2 ) = 
1493785 
.308-5 
4842 (inches). 
n 
Jo 
r 2 
W* -dx = 
/ 2 
W/c 2 
1493785 
95' 2 
= 165. 
Fig. 2 and the accompanying table show how the work was actually 
performed for an existing rod. The rod is first divided into such portions 
as may be considered with sufficient accuracy for the purpose to have 
constant weight per inch run, and this weight is carefully calculated. 
The first and second moments are then calculated from the relationships 
and 
a 2 — b' 2 
~~2 
a 8 — b 8 
It will be noticed that the results checked closely with those obtained 
by weighing. 
The following table shows how the correct treatment of the rod dealt 
with in fig. 2 compares with the ordinary approximations in use. It 
must be remembered that the primary horizontal forces are given cor¬ 
rectly by all methods and it is only the secondary forces (those dependent 
on cos 2 6 and higher multiples of 0) that are in error for horizontal 
components. 
Method of calculating Rod. 
Revolving Part for 
Vertical Forces. 
Reciprocating Part for 
Horizontal Forces. 
' 
By Calculation. 
Error. 
By Calculation. 
Error. 
lb. 
lb. 
lb. 
lb. 
Correct method 
165 
0 
112 
0 
One-half revolving 
154| 
lOf 
1541 
42J 
Weight on big end revolving .. 
196* 
31* 
112 
0 
Five-sixths weight on big end revolving . 
164 
1 
1441 
321 
W k‘ z i 
revolving 
165 
0 
1431 
314 
Two-thirds revolving .. 
206 
41 
102^ 
H 
