638 REPORT—1899. 
2. On the Controversy concerning the Seat of Volta’s Contact Force.' 
By Professor Ortver Lopcs, 7.2.8. 
MONDAY, SEPTEMBER 18. 
The Section was divided into two Departments. 
The following Reports and Papers were read: 
DrparTMeNT I.—MATHEMATICS. 
1. Report on Tables of certain Integrals. See Reports, p. 65. 
2. Report on Tables of certain Mathematical Functions. 
See Reports, p. 160. 
3. The Median Estimate. By Francis Gauron, D.C.L., F.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 suit- 
able 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 com- - 
pensation 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 80V.,’ than to enable him to say, ‘I do 
not think the bonus should be so much as 100/., certainly it should not be more 
than 1002.’ 
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 it understood that A and B are intended to serve as 
divisions, 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 Society of 
London. 
