METERS FOR POWER AND ELECTRICITY. 367 



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 act- 

 ing 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 straight 

 line 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 lono-er the figure will be ; \ ______ 



'.' ' ^"~~ 



either cause makes both the quantity ^~ 



Kir 1 



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 quan- 

 tity 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 j^ractical and auto- 

 matic instrument of which I shall speak presently. The guiding prin- 

 ciple 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 



