In the figure 1 following, the knot 9Aj has a triangular section Prr cutting away on each side of it a (3 + r)-gonal mesh, and 9Ar2 has such a section Rpp, through one crossing only. Make in these knots creases at rr that approach to meet at R in 2, and creases pp that meet at P in 2. In 3, 2 is prepared for a rotation through two right angles about the fixed axis PE, through the crossing P and the crease-kiss R, or, as a more learned man would say, through the decussation P and the plicatorial osculation R–taking 2 for 9Aj: exchange here P and R if 2 is 9Ar2.

The Indians, to whom the preparation of these heads is traced, are scattered over a wide tract of country on the eastern side of the Andes. They are known under the general designation Macao, the name of the region they inhabit—a designation which includes the Jivaros, Pastazas, Mendes, Tumbas, and more than twenty other tribes. Early brought into contact with the first Spanish invaders, they suffered much at their hands. Many references to them occur in the history of the Spanish settlers. Their appearance, social habits, and superstitious practices have much prominence given to them in the recent literature of South American travel. At present I limit my remarks mainly to the specimens of “shrunk” or reduced heads now before us. They are from several points of view remarkable, and raise several questions of great ethnological interest, but trustworthy references to them are comparatively few. Indeed, the only sources of information worth mentioning are a communication by Mr William Bollaert, F.R.G.S., to the Ethnological Society of London, 1860, and another, by Sir John Lubbock, to the Anthropological Institute of Great Britain in 1873. The former is entitled “On the Idol Human Head of the Jivaro Indians in Ecuador;” the latter, “Note on the Macas Indians.” In Mr Bollaert's paper special attention is given to a specimen obtained by M. José Felix Barriero, of the Secretariat of the Provincial Government, Quito, and sent by him to Don R. de Silva Ferro, Chilian Consul, London. This specimen was placed in the Ecuador Court of the International Exhibition, 1862. Sir John Lubbock's paper is devoted chiefly to a general description of the Macas Indians.

For many years past some little amount of isolated work has occasionally been accomplished in photographing certain of the brighter stars. But lately, stellar photography has gone forward with leaps and bounds; so that at a dozen different Observatories in Europe, America, South Africa, and Australia, so much is now being done in that line, that there is a speedy prospect of, in a manner, the whole sidereal heavens being photographed, and after a fashion that would not only have astonished Hipparchus, but been equally surprising to either Sir William Herschel, or Argelander or Struve up to within a very few years ago.

How this reading is to be done is well known; but it may be useful to have more examples. Consider the two following circles of two unifilars each of fourteen crossings—

which are the simplest possible that have their janal symmetries. I wish to show that the knots are completely given by their circles, as are also their symmetries.

The purpose of this paper is to give rules for the construction of knots Mn of n crossings, having each one or more linear sections PR, such that by unkissing at P and at R, shall be obtained two unifilar knots of n – 1 crossings. See my paper “On the Twists of Listing and Tait,” page 363 of the Proc. R.S.E. The knot Mn is always made by a section ffc, i.e., by uniting the P's and R's of two 2-gons (PR) on Ke+2 and Ln-e, after cutting away the four edges PR.

The law of variation of the electromotive force of polarisation with current-density has been very thoroughly investigated. It is found that it may be represented by an equation of the form

where x is the current-density, and a, b, c are constants. So for very feeble direct currents the reverse polarisation current is proportional to the current-density; but for strong currents it cannot be expressed by an algebraical formula as a function of the current-density in a finite series of terms. The above formula gives the maximum value of the polarisation current. So far as I know, no observations have been made regarding its variation with time from its commencement until the maximum is reached. This question is of interest chiefly from a theoretical point of view. The object of this note is to describe the result of some experiments made on this subject. Platinum electrodes, heated to redness before each experiment, were used.

The lacquer tree (Rhus vernicifera) is indigenous to Japan; it supplies a valuable timber, and its fruit yields vegetable wax, but it is chiefly cultivated on account of its juice–lacquer (Urushi)–which forms the basis of the famous Japanese varnishes. The juice is obtained by making incisions in the tree, and it is made into a varnish by simply stirring in the sun in order to drive off an excess of moisture. Different colours may be imparted to the varnish by the addition of various metals, oxides, and sulphides; and after it has been applied to an object it must be hardened by exposure to a moist atmosphere at a moderately high temperature.