Complete Argument Research Articles

Some Remarks on Herbach's Paper, "Optimum Nature of the F-Test for Model II in the Balanced Case"

The purpose of this note is to present a lemma which will settle a question of completeness left open in Section 6 of the above mentioned paper [5]. We give two applications of the lemma, (i) by proving that, in addition to Herbach's results, also the standard $F$-test for $\sigma^2_{ab} = 0$ is a uniformly most powerful similar test, (ii) by pointing out that the standard form introduced in [5] together with our lemma provide convenient tools to prove that in a balanced model II design (with the usual normality assumptions) the standard estimates of variance components are minimum variance unbiased. This result is well known ([2], [3]) and it has in fact been pointed out by Graybill and Wortham [3] that a completeness argument may be used to demonstrate the minimum variance property of the usual estimators for the variance components. The present lemma shows that the estimators do indeed have the necessary completeness property. We will follow Herbach's notation throughout.

On the Site of the Battle of Ethandun

Three places are now recognized as possible sites of the battle of Ethandun: Edington, on the Polden Hills in Somerset; Edington, near Westbury in Wiltshire; and Heddington, about six miles south-east of Chippenham, also in Wiltshire. The object of the present paper is to endeavour to disprove the possibility of Edington on the Polden Hills being the scene of the battle, and to show that an overwhelming mass of evidence favours Edington, near Westbury.The latest and most complete argument in favour of the Polden Hills as the site of the battle is to be found in Messrs. Whistler and Major's Early Wars of Wessex. After a careful examination of the evidence and of the topography of this site, I am of opinion that the plan of campaign suggested by these authors is most unlikely, if not altogether impracticable, from a military point of view.

Supplement.—Further Detail of Proofs that Colebrooke's Essay “On the Duties of a Faithful Hindu Widow” was not indebted to the Vivâdabhangârṇava

If the crucial instance which has already been adduced and laboured, for the intent indicated above, should be regarded as anywise inconclusive, the ensuing particulars will be found to complete my argument.