On the imperturbability of elevator operators: LVII
Institute for Studied Advances
Old Cardigan, Wales
(Communicated by John Sykes; received October 19, 1910
In this paper the theory of elevator operators is completed to the extent that is needed in the elementary theory of Field's. It is shown that the matrix of an elevator operator cannot be inverted, no matter how rapid the elevation. An explicit solution is obtained for the case when the occupation number is zero.
In an earlier paper (Candlestickmaker 1954q; this paper will be referred to hereafter as 'XXXVIII') the simultaneous effect of a magnetic field, an electric field, a Marshall field, rotation, revolution, translation, and retranslation on the equanimity of an elevator operator has been considered. However, the discussion in that paper was limited to the case when incivility sets in as a stationary pattern of dejection; the alternative possibility of overcivility was not considered. The latter possibility is known to occur when a Marshall field alone is present; and its occurance has been experimentally demonstrated by Shopwalker and Salesperson (1955) in complete disagreement with the theoretical predictions (Nostradamus 1555). The possibility of overcivility when no Marshall field is present has also been investigated (Candlestickmaker 1954t); and it has been shown that with substances such as U and I it cannot occur. It is therefore a matter of some importance that the manner of the onset of incivility be determined. This paper is devoted to this problem.
2. The reduction to a twelfth-order characteristic value problem in case operators A, B, and C are looking in the same direction
The notation is more or less the same as in XXXVIII:
The basic equations of the problem on hand are (cf. XXXVIII, eqs.  and )
Using also the relation (Pythagoras 520)
we find, after some lengthy calculations,
which shows that the matrix of the operator cannot be inverted. The required characteristic values are the solutions of the equation (6). From the magnitude of the numerical work which was already needed for obtaining the solution for the purely rational case (cf. Candlestickmaker and Canna Helpit 1955) we may conclude that a direct solution of the characteristic value problem presented by equation (6) would be downright miraculous. Fortunately, as in XXXVIII, the problem can be solved explicity in the case when the occupation number is zero. This is admittedly a case which has never occured within living memory. However, from past experience with problems of this kind one may feel that any solution is better than none.
3. The equations determining the margin at state in the case when the occupying number is zero
For the reasons just given (i.e, because we cannot solve any other problem) we shall restrict ourselves in this paper to a consideration of the cases when the occupation number is zero. In this case satisfies
the solution of which has been obtained numerically; it is approximately
This result shows that the transition to overcivility occurs between the values 2 and 3 given by Giftcourt (1956), respectively, Bookshelf (1956), a result which should be capable of direct experimental confirmation. The author hopes to deal with this problem next Saturday afternoon.
In conclusion, I wish to record my indebtedness to Miss Canna Helpit, who carried out the laborious numerical work involved in deriving equation (8).
The research reported in the paper has in part been suppressed by the Office of Naval Research under Contract A1-tum-OU812 with the Institute for Studied Advances.
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