My friend, Mr. Carl G. Barth, when the matter was referred to
him, soon developed the fact that the number of elements of a cycle
which may be observed together is subject to a mathematical law, which
is expressed by him as follows:
The number of successive elements observed together must be prime to the
total number of elements in the cycle.
Namely, the number of elements in any set must contain no factors; that
is, must be divisible by no numbers which are contained in the total
number of elements. The following table is, therefore, calculated by Mr.
Barth showing how many operations may be observed together in various
cases. The last column gives the number of observations in a set which
will lead to the determination of the results with the minimum of labor.
[Transcriber's note -- Table omitted]
When time study is undertaken in a systematic way, it becomes possible
to do greater justice in many ways both to employers and workmen than
has been done in the past. For example, we all know that the first time
that even a skilled workman does a job it takes him a longer time than
is required after he is familiar with his work, and used to a particular
sequence of operations. The practiced time student can not only figure
out the time in which a piece of work should be done by a good man,
after he has become familiar with this particular job through practice,
but he should also be able to state how much more time would be required
to do the same job when a good man goes at it for the first time; and
this knowledge would make it possible to assign one time limit and price
for new work, and a smaller time and price for the same job after being
repeated, which is much more fair and just to both parties than the
usual fixed price.
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