work on the subject is a desideratum. In the carrying out of this rather laborious task, I have received much encouragement from Professor Tait and from Professor Chrystal, who has pointed out the want of a text-book on physical arithmetic in his reports as examiner of High Schools.

The writings which I have studied most in this connection are those of Clerk-Maxwell, Sir W. Thomson, Professor Tait, and Professor Everett; while for numerical data I have consulted principally the Tables of Landolt and Börnstein. I have gone on the principle of comparing the values given by the different authorities so as to retain the common figures, and cut off the uncertain remainder. As a general rule every one of the figures given may be relied on as significant, with the exception of perhaps the last

The examples have been partly selected from the recent examination papers of the several Universities, and partly prepared by myself either for examinations or to illustrate kinds of calculation which were otherwise not illustrated.

EDINBURGH, 31st July, 1884.

ALEXANDER MACFARLANE.