Considering the abundance of this gadoid, it is a matter for surprise that our knowledge of its life-history is not more complete. The work of Prof. Sars upon the cod in Norwegian waters is well known, and need not be referred to in any detail here. It is, however, important to avoid the assumption that his account will apply in every detail to the cod of British waters.

In 1883 Prof. M'Intosh showed that the cod spawned in early spring and that spawning was effected outside the territorial limit. Dr Fulton, from an examination of a number of captured specimens, was led to the same conclusion; and further, that the cod, whilst having an extended spawning period reaching from January to June, must be regarded as having a main period of February, March, and April, the great majority of individuals spawning in the month of March. Thus whilst 40 per cent, of the fish examined in March were mature, the proportion fell to 16 per cent, for February and April, and 10 per cent, for May. In estimating the growth of this species, by the method pursued below, it is probably most correct to regard the true spawning period as including the months of February, March, April, and May. A study of the distribution of pelagic eggs off the Frith of Forth leads to a similar conclusion. From this latter source the spawning period of the cod can be defined as extending from the third week in February to the second week in May, with a maximum in early April.

Using Bellenden's translation of Boece, he tells us, “Attoure in all the desertis and muris of this realme growis aue herbe, namit hadder, but any seid, richt nutritive baith to beistis and fowlis; specialie to beis. This herbe, in the moneth of July, has ane floure of purpure hew, als sweit as huny. The Pichtis maid this herbe, sum time, ane richt delicus and hailsum drink. Nochtheless, the maner of the making of it is perist, be exterminioun of tlie said Pichtis out of Scotland; fur they schcw nevir the craft of the making of this drink but to thair awin blud.”

(26) Of the various determinant forms thus far obtained the most promising is that of §8 or that of §14; and to these it is desirable now to return in order to obtain an expression for the eliminant in the ordinary non-determinant notation. In doing so it will also be well to make a slight change in the coefficients of the three quadrics, viz., to write f, g, h for 2f, 2g, 2h, as in this way the diversity in the cofactors of the determinants occurring in the last three rows of either form of the eliminant disappears.

1. The present paper deals with a, series of experiments made in the Physical Laboratory, Edinburgh University, from January to October 1899, with the object of determining the convective loss of heat from a cooling body owing to the action of currents of air.

(1) The simplest possible case of the development referred to in the title is one which is seen to follow instantly from the determinant definition of a Pfaffian. Thus, by the said definition,

and therefore

the result reached being that a Pfaffian with certain zero elements is expressible as a determinant. It should be noted that, as in many instances where this form of definition is used, there is an ambiguity as to sign : it is of less importance to note that here the appropriate sign is –.

It is my intention in this, the second part of my memoir on the Craniology of the Races of India, to give the results of my examination of skulls obtained from the districts occupied by the aboriginal tribes in Chúta Nágpúr, the Central Provinces, the people in the province of Orissa, and to compare them with the skulls of some other aboriginal people.

The majority of the specimens described belong to the Indian Museum, Calcutta, and through the courtesy of the Trustees I was permitted to have them on loan for purposes of study. Many of these crania had been those of persons who had died in jail. The names, tribes, and castes, and not unfrequently the age, stature, and other physical characters, had been recorded in the prison books, and were embodied in the lists which were sent to me along with the skulls by the authorities of the museum. Several of these skulls were especially interesting, as having been presented to the museum by Colonel Dalton, the author of the valuable treatise on the Ethnology of Bengal, Other specimens in the museum had been obtained from the Medical College, Calcutta, and several were presented by Professor D. B. Smith; in all probability they were from bodies which had been used for anatomical purposes. Mr W. H. P. Driver also had presented a series of crania from Ranchi.

The vertical movements of the earth's atmosphere from which the energy is derived which causes the horizontal movements of the air which we call winds, and by means of which the moisture evaporated from the surface of land and water is collected and carried to the higher regions of the atmosphere, where it is condensed to cloud and again distributed in the form of rain over the earth's surface, are of great interest, and a thorough knowledge of the laws governing these vertical movements is necessary to enable us to arrive at a correct forecast of the coming weather over any area.

The accompanying Tables I. and II. contain the readings from May 1888 to December 1899 of the new set of deep rook thermometers erected in June 1879 at the Calton Hill Observatory, to replace the old set which were destroyed in September 1876. The tables are in continuation of, and are similarly arranged to, those published by the Royal Society of Edinburgh in Vol. XXXV. part 3 of the Transactions, along with a paper by the late Prof. Piazzi Smyth. The tables published with Prof. Smyth's paper contain the observations made between October 1879 and April 1888, being the beginning of the series with the new set of thermometers.

(l) Cayley in his paper entitled “Note sur l'addition des fonctions elliptiques” obtains among other similar things an expression for

in terms of

where

The form of the expression is the quotient of two determinants, and as the expression becomes useless for such cases as u = v, u = w, … on account of the simultaneous vanishing of numerator and denominator, he is led to seek a means of throwing out the common evanescent factors.

(1) There being n2 independent variables in a general n-line determinant, the Hessian of the determinant with respect to the said variables must be a determinant with n2 lines: and as a general n-line determinant has all its terms linear in the elements involved, it follows that each element of the Hessian being a second differential-quotient cannot be of a higher degree in the variables than the (n − 2)th, and that consequently the degree of the Hessian itself cannot exceed n2(n − 2). The object of the present short paper is to show that this degree is attained by the n(n − 2)th power of the given determinant being a factor of the Hessian.

(1) The continuant

is conveniently denoted by

and, when the elements b1, b2, b3 of the variable minor diagonal are each equal to 1, a further simplification is obtained by leaving them out;—thus,

stands fo