So-called “standard form.”

Method I have used with success as regards clearness and accuracy. (I believe this is Mr. Pendlebury’s arrangement.)

Ride. Put singles (or units) figure of multiplier under the last figure of multiplicand.

Arguments in favour of this second plan :

Instead of such a mechanical rule as Mr. Borchardt’s (p. 69, Borchardt’s ,Arithmetical Types and Examples), we get the continued use of the sound and fundamental rule of “putting each first figure of a partial product underneath the figure to which that partial product is due.” And this also corresponds to the method of algebraic multiplication.

1. (1) We have, above, assigned an intelligible meaning to this expression if the body be considered as a member of a system. But, taken absolutely, it has no meaning.

2. (2) If our shot, now considered separately, meet directly a target of mass M′ and there be inelastic collision, and if the relative velocity be U, then the velocity u′ of the shot relatively to the c.m. of this new system will be , and the velocity V′ of the target relatively to this c.m. will be .

The total internal energy of this system as measured by the heat given out will be , and of this the shot may with some reason be said to contribute the first term, and the target the second, in virtue of its K.E. [see VII., (3) and (4)].

That every person in the realm who teaches mathematics should be a member of our Association is an ideal towards which we are converging non-uniformly, if at all. Were this ideal state of things a reality no apology would be needed for a paper dealing with topics which though educationally important are from a mathematical point of view very familiar. As it is, the feeling haunted me as I wrote that I was writing a sermon, and that the people whom it might benefit would not be in the room, were not even members of our Association. As, however, other writers of sermons must, I suppose, sometimes find themselves in a similar position, 1 have ventured to go on.