The principle which guided Mr. Cowper to a solution of the problem which he has successfully overcome, is the well known mathematical fact that the position of any point in a curve can be determined by its distance from two rectangular co-ordinates. It follows, then, that every position of the point of a pencil, stylus, or pen, as it forms a letter, can be determined by its distance from two fixed lines, say the adjacent edges of the paper. Moreover it is obvious that if these distances could be transmitted by telegraph and recombined so as to give a resultant motion to a duplicate pen, a duplicate copy of the original writing would be produced. But inasmuch as the writing stylus moves continuously over the paper, the process of transmission would require to be a continuous one; that is to say, the current traversing the telegraph line, and conveying the distances in question (or what comes to the same thing, the up and down, and direct sidelong ranges of the stylus) would require to vary continuously in accordance with the range to be transmitted. Mr. Cowper effects this by employing two separate telegraphic circuits, each with its own wire, battery, sending, and receiving apparatus. One of these circuits is made to transmit the up and down component writing of the pencil's motion, while the other simultaneously transmits its sidelong component. At the receiving station these two components are then recomposed by a pantograph arrangement of taut cords, or levers, and the resultant motion is communicated to the duplicate pen at that place. The plan adopted by Mr. Cowper to transmit each continuously varying component is to cause the resistance of the circuit to vary very closely with the component in question. Fig. 5 shows how the apparatus is theoretically arranged for this purpose. P is the writing style, which is held in the writer's hand in the ordinary way, while he shapes the letters one by one on paper pulled uniformly underneath by means of clockwork. To P are attached, at right angles, two arms, a a, one for each circuit; but as it is only necessary to consider one of the circuits, say that sending up and down motions, we will confine our attention for the present to the arm, a. One pole of the sending battery, B, is connected to the arm, a, the other pole being connected to earth. Now the arm, a, is fitted with a sliding contact at its free extremity, and as the pencil, P, is moved in writing, a slides lengthwise across the edges of a series of thin metal contact plates, C, insulated from each other by paraffined paper. Between each pair of these plates there is a resistance coil, C, and the last of these is connected through the last plate to the line, L. It will be seen that as a slides outward across the plates the current from the battery has to pass through fewer coils, since a short-circuits a number of coils proportional to its motion. But the fewer of these coils in circuit