# THE ENGINEER'S "SLIP-STICK"

### By DEAN 0. J. FERGUSON

The slide rule is a corollary to the logarithm, and, interestingly enough, its elements appeared within a decade after Napier had announced his revolutionary invention of logarithms.   His publication came in 1614—over three centuries ago. He found extended calculations to be laborious, and subject to "slippery errors." (Who has not?) And so, he set for him-self the task of abbreviating the labor, and eliminating errors in the process. How successful his deliberate quest was, in the invention of logarithms, all know, for no other advance ever made in mathematical cal-culation approaches logarithms in effectiveness. Napier, himself, would probably be surprised to realize the magnitude of their use.

What, to the inventive mechanical mind, could be more logical than the addition of logarithms by meas-urements upon a scale? So Gunter (1620) built a scale of logarithmic lengths and used dividers to lay off his measures. This was the elementary rule—but there was no "slide".

Soon thereafter (1632), Oughtred (England) pub-lished a description of his two circular scales arranged for multiplication. His former pupil Delamain dis-puted his title to the claim, as he had published an article in 1630. However, Oughtred claimed to have used it since 1621, and a bitter quarrel ensued. Per-haps the battle over the circular scale was not worth the fighting, for this type gave place to the straight rule, the percursor of our present rule. This develop-ment is Oughtred's (1633).

One by one the various elements of the present rules appeared. About 1675, Newton offered the idea of the indicator. About 50 years later Warner com-bined simple with double and triple scales for squares and cubes, respectively.   Later the inverted scale appeared. Roget (1815) invented the log-log scale.

Perhaps the date 1859 is as significant as any, in that, at that time, Lieut. Mannheim (French artillery) invented the arrangement of several scales, which is still known as the Mannheim rule. It is capable of handling three-quarters of all the calculations de-manded of slide rules. It is a sturdy form, and its durability and dependability are marked.

The many patent dates borne by other rules attest the fact that, constantly, improvements are being made. The most elaborate rule that has come to my attention carries fourteen scales, although, for pur-poses of association one with another, there are sev-eral duplicates among these.   Of course, even for direct use in multiplication, two identical scales are used. Again, one of the fourteen extends four times across the full length of the rule, adding to the very-complicated appearance which it presents to the novi-tiate. It appears forbiddingly complex and confusing. But a few hours of analysis of the scale groupings, with practice in their use, relieve the mind quite effectively.  The rules really are practical and ex-tremely useful.

The slide rule was pretty largely a mathematician's toy, until the engineer came to adopt it. Probably no one more fully than he is able to use it in all of his calculations. His data generally carry about that de-gree of accuracy represented by slide rule settings and readings. Therefore slide rule calculations are suffi-ciently accurate for his purposes. He has no use for the 707 places to which the decimal part of pi has been extended.  Nor, for that matter, has any one else, except to "point with pride."  For, take the greatest distance measured by man—that to one of the most distant spiral nebulae observed, so far away that astronomers measure the distance in terms of that enormous unit, the light-year.   One hundred million of these units is the space so measured. Conceive of the sphere of which this is the radius. Then calculate the number of electrons which could be packed into this sphere, and in introducing pi, we should have no use for the last 590 decimal places! (We should note, of course, such a calculation repre-sents precision, but not accuracy.)

Probably every engineer who has been on the campus during the last 30 years recalls seeing the home-made, eight-foot, demonstration slide rule that used to hang in the old steam class-room in Mechanic Arts Hall, and later until recently graced the wall of one of the design rooms. It was the first large dem-onstration rule on the campus, and was made by Dan Gutleben, U. of N. '00, who used it to justify his faith in slide rules. He it was who brought to our campus, back in the 90's, the first "slip-stick." And so enthusiastic a promoter of its use was he that he always had his slide rule with him. He came to be known as "Slide Rule Dan." But his missionary work was successful, for others followed his lead and the "rule ceased to be the exception."

Dan, if you happen to note this reference, away off there in your Philadelphia office, perhaps you will be gratified to know that a voluntary slide rule class we are conducting now enrolls one hundred and twenty-five students. I hope we may do our work as well as you did yours.