Directly Nelson learned this he changed the flags and reported the matter to the Admiralty. On the 4th November, the Admiralty, despite the objection of Lord Keith that a change of signal numbers would be better, issued a circular letter to all commanders-in-chief telling them to alter their numeral flags in accordance with a painted copy enclosed with the letter. These are the flags shown in the third column of the plate. Further, as their Lordships had reason to apprehend that Lieut. Lemprière was not the only officer under commander's rank who had obtained a copy of the signal book, the strictest injunctions were to be given that such improper proceedings were not to take place in future, and existing irregular copies were to be impounded. The flags in use in the Mediterranean were changed in numerical value in accordance with the Admiralty order on the 16th January, 1804, and these new numeral flags were the ones used at Trafalgar, and, in fact, until the end of 1810[390]. We have seen that Howe's second code, first in its original form, next as re-arranged by McArthur, and finally as simplified and expanded for the 1799 Signal Book, in each case with practically the same numeral flags, sufficed, when supplemented by Popham's Vocabulary, for the navy's needs throughout the most sustained and strenuous struggle that until the recent war had ever fallen to its lot[391]. Towards the close of this period, however, Popham, who seems to have devoted all the time not required for his professional duties, or for defence against the attacks made upon him, to the improvement of his code[392], brought out a greatly enlarged and improved vocabulary, which is best described in his own words: The present edition is wholly new cast and composed; very considerably enlarged by additional materials; and, as I trust, improved by a distribution of those materials which was intended to increase the facility of reference. It consists of nearly 6,000 primitive words, exclusive of the inflexions of verbs, &c., making in all upwards of 30,000 real words; the sentences have also been extended to about 6,000, with 1,500 syllables, a Geographical Table, a Table of Technical Terms, a Table of Stores and Provisions, and a Spare Table for Local Significations. With so large a number of signals the limitation in the number of flags that can be conveniently hoisted at a time made itself at once felt, and Popham found himself compelled to abandon the "simple numerary" method. Taking the limit of convenience at three flags, the ten numeral flags of the Admiralty Signal Book would suffice for only 999 signals. Popham, therefore, after calculating the number of combinations available with various sets of flags, chose 23. These, which were mostly of his own design, he denoted by the numbers 1 to 9 and the letters A to O. With these 23 flags the number of available combinations is as follows: