solving, if its roots be k, and 2, the equation of the section we are now dealing with will be evidently

To find the directions of the principal sections at any point of the surface U = 0.

=

If a, B, y, be the direction angles, we have, from equations (15), substituting L, M, N, as before for a1, b1, c1.

The condition that the first three of equations (6) should hold simultaneously, viz:

has already received a geometrical interpretation in the case of the section of a quadric, viz: that certain three lines should lie in one plane. The application of this to the curvature of surfaces is not difficult.

For if we substitute L, M, N, for a, b, c, and d x, dy, dz, (proportional to the direction cosines of the directions of maximum and minimum curvature) we get

the known equation of a line of curvature but which is in fact the reduced form of

and this is the expression of the condition that the lines whose direction cosines are proportional to L, M, N; L+ d L, M + d M, N + d N, d x, d y, d z, namely two consecutive normals and the arc between them on the surface, should lie in the same plane. Hence we see that substituting in equations of (15) we can get the equations of the lines of curvature in the shape

Note on Zinc Sulphide.

By THOMAS MACFARLANE.

(Read May 27, 1882).

I desire to call the attention of the Society to a peculiar property of anhydrous Zinc sulphide. It possesses in an extraordinary degree the opacity and divisibility which, combined, make up the property known to manufacturers of pigments and painters as "body" or covering power. Heretofore it has been supposed that no substance could exceed sesquibasic Carbonate of Lead (common white lead) in this respect, but I have ascertained that anhydrous zinc sulphide far excels it in covering power.

Such substances as sulphate of Barytes and Carbonate of Lime which are used for the adulteration of white lead are very low in covering power, possessing only one-fortieth of the body of Zinc Sulphide.

The ordinary practical way of testing the "body" of a white pigment is to mix it in oil with an equal weight of any standard colour and then spread the resulting paint on glass. The lighter the tint, the more the white pigment is capable of masking the coloured one, and the greater is the "body" of the former. According to this test, zinc sulphide has the greatest covering power of any known substance and indeed four times that of white lead.

On account of its immense body, zinc sulphide may be used as a standard for deter mining covering power. By mixing it with various proportions of ultramarine blue I

have arranged a scale of tints by comparison with which the "body" of any pigment may be very closely arrived at. The preceding table shows the composition of the various. shades of blue constituting the scale, their numbers, and the names of the ordinary pigments of commerce with whose ascertained covering powers they correspond.

In drawing attention to the covering power of Zinc sulphide, I have not, of course, attempted to discuss the nature of this property itself. As it is of considerable importance in the arts, its investigation seems worthy the attention of chemists and physicists.

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