host, I hardly like to pick out those inventions which I consider of value. I can not describe all; I can not act as a judge and say these only are worthy of your attention, and I do not think I should be acting fairly if I were to describe my own instruments only and ignore those of every one else. The only way I see out of the difficulty is to speak more particularly about my own work in this direction, and to speak generally on the work of others.

I must now ask you to give your attention for a few minutes to a little abstract geometry. We may represent any changing quantity, as, for instance, the strength of an electrical current, by a crooked line. For this purpose we must draw a straight line to represent time, and make the distance of each point of the crooked line above the straightFig .1line a measure of the strength of the current at the corresponding time. The size of the figure will then measure the quantity of electricity that has passed, for, the stronger the current is, the taller the figure will be, and the longer it lasts the longer the figure will be; either cause makes both the quantity of electricity and the size of the figure greater and in the same proportion: so the one is a measure of the other. Now, it is not an easy thing to measure the size of a figure, the distance round it tells nothing; there is, however, a geometrical method by which its size may be found. Draw another line, with a great steepness where the figure is tall, and with a less steepness where the height is less, and with no steepness or horizontal where the figure has no height. If this is done accurately, the height to which the new line reaches will measure the size of the figure first drawn; for, the taller the figure is, the steeper the hill will be: the longer the figure, the longer the hill; either cause makes both the size of the figure and the height of the hill greater, and in the same proportion: so the one is a measure of the other; and so, moreover, is the height of the hill, which can be measured by a scale, a measure of the quantity of electricity that has passed.

The first instrument that I made, which I have called a "cart" integrator, is a machine which, if the lower figure is traced out, will describe the upper. I will trace a circle, the instrument follows the curious bracket-shaped line that I have already made sufficiently black to be seen at a distance, the height of the new line measures the size of the circle, the instrument has squared the circle. This machine is a thing of mainly theoretical interest; my only object in showing it is to explain the means by which I have developed a practical and automatic instrument of which I shall speak presently. The guiding principle in the cart integrator is a little three-wheeled cart, whose front wheel is controlled by the machine. This, of course, is invisible at a