OCR Rendition - approximate

~i3s REPORT-1$9f). On Glee Controve,,sg concerning the Seat of Volta's Contact Force.' By Professor OLIN-Eiz LouoE, XO1'DAI, SEPTE_lf]iER 1 The Section was divided into two Departments. The following Reports and Papers were read DEPARTMENT T.-MATHEMATICS. 1. Re~po)'t on Tables c!f certain Lztegrals. See Reports, p. 6.5. 2. Report on Tables of certain Jlathematical Fit-actions. See Reports, p. 160. 3. The Median Estimate. By FRANCIS GALTO~t, D.C.L., P.R.S. The usual method is very unsatisfactory by which the collective opinion of Councils, Senates, and other Assemblies is ascertained, in respect to the most suitable amount of money to be granted for any particular purpose. The opinions of individual members are sure to differ as to rewards for past services, as to compensation for damage, or as to the cost of carrying out some desirable object for which provision has to be made. How is that medium amount to be ascertained which is the fairest compromise between many different opinions ? The method usually adopted is for some person in authority to consult his colleagues and then to lay a definite proposal before the meeting, to which another person may move an amendment ; the amendment and the original motion are then put severally to the vote, and are carried or rejected by a simple majority. Jurymen are said to adopt a different way of assessing damages ; each writes his own estimate on a separate paper, the estimates are added together, and the average of them all is occasionally accepted by the whole body of the jury and returned as their verdict. Averages are, however, objectionable to large assemblages on account of the tedious arithmetic that would then be needed. Moreover, an average value may greatly mislead, unless each several estimate has been made in good faith, because a single voter is able to produce an effect far beyond his due share by writing down an unreasonably large or unreasonably small sum. The middlemost value, or the median of all the estimates, is free from this danger inasmuch as the influence of each voter has exactly equal weight in its determination. Again, few persons know what they want with sufficient clearness to enable them to express it in numerical terms, from which alone an average may be derived. Much deeper searching of the thought is needed to enable a man to make such precise affirmation as that ' in my opinion the bonus to be given should be 801.,' than to enable him to say, `I do not think the bonus should be so much as 1001., certainly it should not be more than 1001.' The plan that I would suggest for discovering the median of the various sums desired by the several voters is to specify any two reasonable amounts, A and B, A being the smaller, making t understood that A and B are intended to serve as dicisiowtz, and therefore no votes are to be given for either of those two precise ' This paper will be published in the Proceedings of the Physical Soeiety of London.