After Geometrical Similitude has been retained by making two structures, animal, machine, or steamship, from the same drawing but to a different scale, there is still the remaining variable of the material of construction to be taken into account ; and a further question arises of the Mechanical Similitude in a calculation of the relative velocity and stress in the parts.

The first statement of the problem is to be found in the Principia, Book II, Section VII, Prop. XXXII, Theorem XXVI.

In its application to the steamship the principle goes by the name of Froude's Law; it is applied to infer the performance of the full size steamer by calculation on the record of the model in the experimental tank.

1. 1. In previous reports issued by the Association, general reforms have been suggested which apply to the teaching of Arithmetic as well as of other subjects, and some detailed suggestions have been madewhich applyexclusivelyto Arithmetic. The present report deals at greater length with Arithmetic only—its relation toother subjects, its scope and its treatment.

2. 2. There are certain parts of the subject-matter of the Arithmetic Course that are regarded by many teachers as of little educational value to the ordinary student.The Committee suggest that these should not be considered a necessary part of the Mathematical Course.This suggestion in no way interferes with a teacher who, either from personal preference or local considerations,wishes to take a more detailed course ; at the same time, it allows others to omit certain parts of a more specialised character. The Committee hope that in the course of time the parts omitted will cease to be required by examining bodies.The omissions will be discussed in detail below.

3. 3. The Committee recommend that the time set free by the elimination of a part of the usual subject-matter should be spent, partly in securing a higher standard of accuracy in straightforward computation and partly in extending the range of the ordinary school course in Mathematics.

The directions in which this course may be extended are discussed in detail in a recent report issued by the Association entitled “A General Mathematical Syllabus for Non-Specialists in Public Schools.”

The following is a simple method of establishing the formula for the determination of the duration of day, at any latitude, for a known declination of the sun.

terminator or limit of the sun's illumination of the earth (at right angles to the line showing the direction of the sun's rays), ά is the point at which the terminator, άO'c', cuts the elevation of the line of latitude λ.

Referring to the plan, α and α are the points in plan corresponding to ά in elevation ; 0 is the plan of the polar axis.