For a number of years I have been collecting specimens and conducting an investigation into the craniological characters of the native inhabitants of our great Indian Empire, and several hundred skulls have now been under examination, and almost all have been measured. The sources to which I have been indebted for material are in part the collection of crania belonging to the Henderson Trustees, long known as the Edinburgh Phrenological Museum, and now deposited by the Trustees in the Anatomical Museum of the University; in part, a few specimens belonging to the University collected by my predecessors in office; in part, the valuable series of Indian crania belonging to the Indian Museum, Calcutta, which through the intercession of Dr John Anderson, F.R.S., the former Director, the Trustees of that Museum, with great liberality, most courteously permitted me to have the loan of for purposes of study; and lastly, a number of crania which have been forwarded to me by friends and former pupils, engaged in the public service in India, to whom I take this opportunity of expressing my indebtedness for the valuable material which I have received from them.

The various structures in the marsupial shoulder girdle are so unquestionably homologous with similar structures in the girdle of the human subject and of the Eutheria generally, that there has never been any difficulty in interpreting the parts in terms of human anatomy; but when the elements are compared with those in what we may consider to have been the ancestral condition, such as is exemplified in the shoulder girdle of the Monotremes, or of the Anomodonts, or in the more distantly related conditions met with in modern Reptiles and Amphibians, we are confronted with quite a number of difficulties, to which the most varied solutions have been applied by different morphologists. The chief difficulty in the way of comparing the typical mammalian girdle with that of the lower forms, is that in the girdle of the higher mammals certain structures are rudimentary, and, further, that the forms that have hitherto been examined have been so far removed from the ancestral stock that even a study of the early developmental conditions fails to give any clues that are more satisfactory than those afforded by comparative anatomy. Though it has been suspected that further results would be obtained from the study of the early condition in Marsupials and Monotremes, the embryos of these groups that have hitherto been studied have been too old to yield much further evidence than that obtained by a study of the adult forms.

1. The following paper is a contribution to the theory of non-alternate ± knots, together with a census of these knots for Order Ten; that is, all the knots are given which have in reduced form just ten crossings, and in which the thread does not proceed alternately over and under.

The census was begun in the fall of '93, and carried so far that the forms were drawn. The matter was then laid aside and taken up anew in the spring of '99.

2. Having postulated an endless one-dimensional continuum which may change its length and form in any way, subject only to the condition that it can never have a double point, and consequently no one portion can be made to break through another, I understand by a knot a continuum which can not be brought to a circular form.

The publication by the Royal Society of Edinburgh in 1890 of the hourly observations made at the observatory on the summit of Ben Nevis along with corresponding observations at five different hours at Fort-William at the sea level was an important contribution to meteorological science. As I held at the time the Lectureship in Geography at the University of Cambridge it furnished a welcome supply of facts for the illustration of important points in physical geography. What struck me most at the time in the study of this work was the unique character of the observatory of Ben Nevis itself, without reference to its companion at the sea level, as a first-class observatory in a locality where the atmosphere is for the greater part of the year completely saturated with moisture. Being also situated on a true peak, and that the highest point in the British Islands, the observations may fairly be taken to represent the meteorology of the clouds, or at least of such clouds as are in contact with mountain slopes, and in any case they must afford rich material for the study of the physics of the atmosphere.

In the autumn of last year (1897), Sir A. Geikie, F.R.S., Director-General of the Geological Survey, kindly placed in my hands for description an important collection of fossil fish-remains from the Silurian rocks of the Lesmahagow district, which had been made by Messrs Macconochie and Tait, collectors to the Survey. I accordingly prepared a brief report on these fishes, which was included by the Director-General in his Summary of Progress for that year.

The collection was, however, considerably increased by additional work on the part of Mr Tait in the spring of the present year (1898). Many better and more complete specimens were procured, and I was able to define one new genus and species, which had previously been represented only by undeterminable fragments. The results gained by the examination of the entire collection I now propose, with Sir Archibald Geikie's sanction, to lay before this Society in detailed form.

The laps referred to below are parts of the external boundary of the figure, and are supposed to be described with the sun. The first specification of a lap refers to the side of the figure, the second to its position on the side.