There will then obviously be two flags corresponding to each of the numbers, the top flag being that at the head of the vertical column in which the particular number is found, and the lower one that at the left of the corresponding horizontal column. For example, supposing we have three flags, red, white, and blue, they might be arranged as below: Red White Blue ----+-------+----- Red 1 | 4 | 7 ----+-------+----- White 2 | 5 | 8 ----+-------+----- Blue 3 | 6 | 9 ----+-------+----- The signal corresponding to 6 will then be a white flag over a blue one. If the signals to be thus denoted number considerably more than 100, it is convenient to form the table of 10 squares to a side, giving 100 squares in all. The first 100 numbers will then be written in, and by the addition of suitable pendants to represent 100, 200, 300, etc., it will be possible to denote any signal number from 1 upwards. The disadvantage of this method is that the individual flags have no fixed numerical value, and a reference to the table is necessary before the number represented by the combined flags can be ascertained, and _vice versâ_. In spite of this drawback, this was the method first chosen by Howe for all his signals[382], and it was used by him in his second numerary code for those of his signals which were intended for the use of private ships when communicating with the flagships, the numeral signals of the La Bourdonnais method being in this code only used for the Admiral's orders to his fleet. In the 1799 Signal Book the tabular method was discontinued. Some time before June, 1776, probably on being appointed to command the North America Squadron in February of that year, Howe had compiled a signal book on the old plan of single flags in particular positions, condensed from the "general signal book," and containing all the signals "likely to be needful on the present occasion." The flags he employed were as follows, those marked * being also used inverted: Union. St George. Red } Yellow } plain flags. Blue } White } *Red and white } *Red and blue } *Blue and white } in two horizontal stripes. *Red and yellow } *Blue and yellow } *Red, blue, white } *White, red, blue } in three horizontal stripes. Blue, white, red } A year or two later, probably in consultation with Kempenfelt, he drew up the first of his codes on the numerary system. The signals were divided into those for the Admiral and those for private ships. For the former a "table" of 16 squares on each side was employed with the following flags: