IBM 704 preparatory to running a 
production problem. 
Neutron-Transport Codes 
Because of the special emphasis the 
neutron-transport codes have received, 
a few comments on the actual tech- 
niques involved in these calculations 
are in order. The usual objective of 
any of these calculations is to obtain 
the neutron fluxes and the critical 
parameters for a given reactor system. 
The over-all mathematical technique 
for calculating a reactor can be only 
indicated here. The article by Ehrlich 
and Hurwitz (4) illustrates the multi- 
group method for solving the age-diffu- 
sion equation, and the report by Carl- 
son (4) illustrates a method for solving 
the transport equation. In mathe- 
matical language, the problems are 
reduced, in the steady-state cases, to 
finding the fundamental eigenvalue (a 
critical parameter) and eigenfunction 
(the neutron fluxes) of homogeneous 
differential-integral equations. Nu- 
merically, it is necessary, of course, to 
reduce the problem to finding the funda- 
mental eigenvalue and eigenfunction of 
associated matrices. Although the cal- 
culations and codes actually deal with 
matrices, it is not particularly advan- 
tageous to think of the problems in 
such terms. The power technique of 
matrix theory is customarily used to 
find the eigenvalue and eigenfunction. 
In the language of physics, this power 
technique is equivalent to first guessing 
a source due to fission, and then com- 
puting—in continuing sequence—fluxes 
from a source and a source from fluxes. 
When succeeding sources have the 
same shape, the processes converge. A 
ratio of succeeding sources gives a value 
to v,, the calculated average number of 
neutrons emitted per fission required 
to maintain criticality. 
The number of groups in a problem 
refers to the number of values or inter- 
vals of energy (or velocity or lethargy) 
in which the neutrons are assumed to 
diffuse. The number of mesh points 
refers to the number of space points at 
which the flux will be evaluated. The 
number of regions refers to the number 
of materials of homogeneous composi- 
tion which constitute the reactor. 
The validity of multigroup calcula- 
tions is best judged by comparison of 
the calculated results with experimen- 
tal observations on actual reactors. 
The number and scope of such com- 
parisons available so far are inadequate. 
One may hope that future multigroup 
calculations will someday have a better 
experimental foundation. 
Computing Machines 
Memory. The speed, reliability and 
cost of digital computers are closely 
connected with the type of memory. 
At present, magnetic-core memories are 
used in the fastest, most reliable, and 
most expensive machines, such as the 
IBM 704 and the Remington-Rand 
1103A. Cathode-ray-tube memories 
are cheaper and as fast but have not 
always proved reliable. The 701, 1103, 
and other Princeton-type computers 
all have electrostatic memories, but 
only MANIAC II is now being built 
with such a memory. The acoustic 
mercury-delay-line type of memory is 
used on the UNIVAC I and the SEAC. 
This acoustic memory has proved to be 
reliable and not too expensive, but 
where speed is concerned, it has the 
disadvantage of not having random 
access to the information being circu- 
lated as acoustic pulses in the delay 
line. Magnetic drums are also reliable 
and relatively cheap, but they do not 
have the speed advantage of random 
access. 
The size and the speed of the memory 
usually determine the scope of a caleu- 
lation. Ordinarily, in discussing the 
size of the memory, only the number of 
words* of the ‘‘fast’’ memory is men- 
tioned. Many machines also have 
auxiliary, or ‘‘slow,’’ memories con- 
sisting of magnetic drums, tapes, or 
disks which can store a few million 
words of information. The UNIVAC 
I has a 1,000-word memory, and the 
TABLE 1—Commercial Computers 
Installed On order 
Machines 
Medium machines 
IBM 650 560 1200 
Datatron 55 55 
UNIVAC File 10 200 
ELECOMS 13 5 
ALWAC 16 5 
Large machines 
UNIVAC I and II 40 20 
UNIVAC Scientific 
(1103 and 1103A) 20 10 
BIZMAC 3 3 
IBM 701 16 0 
IBM 702 14 0 
IBM 704 38 66 
IBM 705 46 118 
Princeton-type machines have 1,024- 
and 2,048-word memories. Magnetic- 
drum machines have 1,000-, 2,000- and 
4,000-word memories. The latest mag- 
netic-core machines, the 704 and 1103A, 
have 4,000-, 8,000-, 12,000-, and will 
have 32,000-word memories. 
Speed. The speed of a computer 
can be measured in various ways. A 
common method is to give the access 
time, or fundamental machine cycle 
time. This time interval indicates the 
time it takes the central processing unit 
to transmit to or receive from the mem- 
ory a word of information. Another 
method is to give the time of a typical 
multiplication. Ina floating-point ma- 
chine, this time is approximately the 
same whether the multiplication is car- 
ried out by means of fixed point or 
floating point.t In a fixed-point ma- 
chine, a floating-point operation may 
take as much as twenty times as long 
as the corresponding fixed-point oper- 
ation. Table 2 lists the number of 
operations per second performed by 
various digital machines. 
Type. High-speed computers can 
also be separated according to whether 
they are one-of-a-kind machines or pro- 
duction models. Until 1956 one-of-a- 
kind machines, such as Whirlwind I, 
ORACLE, MANIAC I, ORDVAC, 
ILIAC, AVIDAC, SEAC, SWAC, 
NORGC, and the MARK I, II, III and 
IV, played an important role in reactor 
calculations and, indeed, in all high- 
speed computing. The present trend 
is strongly toward renting or buying 
one of the production models built by 
a computer manufacturer. With the 
flood of machines being produced com- 
mercially now, it is unlikely that one- 
of-a-kind machines will again play a 
major part. 
The figures in Table 1 give the ap- 
proximate number of machines de- 
livered and on order as of early 1957. 
Including one-of-a-kind machines, there 
are about 700 medium machines in- 
stalled and 1,500 on order, and about 
200 large machines installed and 250 on 
order. 
Although any of the machines listed 
* A word is a set of characters, such as 
10 alpha-numeric characters or 40 binary 
digits, i.e., a sequence of 40 0’s and 1's, 
which occupies one storage location and is 
treated by the computer as a unit. 
+ In a fixed-point machine, numbers in 
the machine normally must be between 
some fixed limits, such as —1 and +1. Ina 
floating-point machine, a number com- 
monly consists of both an exponent and a 
signed proper fraction. 
33 
