It occasionally happens that logarithms and anti-logarithms are required to many figures, and in default of tables must be calculated. If a series of such logarithms are required, they are probably most easily obtained by interpolation between nntnbers, the logarithms of which have been calculated to many figures by Briggs, Gardiner, Sharp and others.

If only a few values aro required, this method is practically inapplicable, since it is tedious and requires somewhat large tables. Many ingenious methods have been suggested to meet such cases, but in general they necessitate special artifices and tables, which require considerable practice to use with safety.

Note 1. The object of the Central Committee in formulating these enquiries has been solely that of acquiring information. The Committee does not itself take up any definite standpoint in the matter as to how far the teaching of the subject in the schools is desirable.

In the Greenwich meteorological observations, Table XIII, gives the excess of the arithmetic mean of the daily maximum and minimum over the true mean daily temperature for each day in the year.

A little experience of problems in which it is necessary to divide by sine or cosine of an angle will prepare a boy for the definitions of secant, cosecant and cotangent as the reciprocals of the cosine, sine arid tangent respectively, though, as a matter of fact, he can get on very well without them. At this stage a boy will probably appreciate the fact that since an acute angle is determined if me know any one of the six trigonometrical ratios, it should be possible, if any one of the ratios is given, to find the others. Problems such as this : “Given sin A = ·64, find tan A” should be done (i) by drawing a figure to scale, i.e. constructing the angle A whose sine is ·64, and finding the tangent by measurement (ii) by drawing a right-angled triangle, hypotenuse 100 units, one side 64 units, and calculating the other side by Pythagoras’ theorern; (iii) by taking from the tables the angles whose sine is ·64 and looking up its tangent.