Touches Down

Association football owes its phenomenal success to its intrinsic simplicity.
This is best illustrated in the means in which goals are scored. Australian, Rugby, Gaelic and American codes  have secondary means of scoring points. In Association it's a goal or nothing. 
The Football Association Laws of 1863 state:
A goal shall be won when the ball passes between the goal-posts or over the space between the goal-posts (at whatever height), not being thrown, knocked on, or carried.
Essentially no change there. Apart from the restriction of height, first by tape (1866) and then by a crossbar (1883) the means of scoring a goal has remained unaltered since 1863.

But then, in the records from 1866 one can find the following examples of scores:
10.3.66- Barnes 2 touches down, Crystal Palace 0.
31.3.66- London 2 goals 4 touches down, Sheffield 0.

In order to understand this we must return to one of the fundamental differences between 1860s Association  Football and the modern game. In those days when the ball crossed the touchline or the goal line it hadn't, as such, gone 'out of play'. There was still the matter of the advantageous restart to be settled. Once the ball had crossed these lines the team whose player first touched it down would have the restart. When the ball crossed the goal line (outside the posts) there were two possible outcomes:
1- if the defending team touched it down first, they would have a free kick from  the goal line in line with where the ball was touched down.
2- If the attacking team touched the ball down they would have a free kick from a point in line with where the ball was touched down 25 yards from goal. The free kick had to be a direct shot at goal and the defenders had to be behind the goal line until the ball was kicked.
This sounds like the 'conversion' in Rugby (more of which later).
The Football Association was all about unification, and as such they would have drawn on the practices of the various current codes.
So where did these codes stand as to whether getting the ball across the line should be used as a means of  facilitating an attempt at goal or of actually scoring?

1: Rugby school 
It is worth remembering that the laws of Rugby Union were not formulated until 1871. According to the rules of football played at Rugby school, a touch-down did not score points, but allowed an attempt to kick at goal (hence 'try'). This practice continued with the development of Rugby Union- points scoring was introduced in 1886, but even then a drop kick over the cross bar was more valuable than a touch down alone.  

2: Eton 
Rouge flags were placed an additional 4 yards (3.7 m) each side of the goal. If the ball was kicked between the rouge flags and subsequently touched down the team scored a rouge. If the score was tied at the end of the game then rouges were used to decide the winner. 

3: Sheffield Rules
The Eton rouge was the solution adopted by Sheffield in 1861. Rouges were used as a secondary method of scoring to decide games in the case of  actual goals scored being level. Rouges were abandoned in 1868 to be replaced by the goal and corner kicks.
( Cheltenham College had a similar rule, recorded though in 1869, when the rouge and touch down had passed out of Sheffield and Association Football).

4: Cambridge rules:
When a player has kicked the ball beyond the opponents' goal line, whoever first touches the ball when it is on the ground with his hand, may have a FREE kick bringing the ball straight out from the goal line.

So, the Football Association began with a position as set out in the Cambridge Rules.Two of the most influential figures in shaping the Football Association laws , E.C Morley and C.W Alcock, were advocates of this set of rules, and came close to adopting them lock stock and barrel. 
A report of a match between C.C.C (Clapham Common) and Crystal Palace in Bell's Life (January 1865)  tells us:
The C.P.C soon obtained a touch down, but the place kick (sic) was unsuccessful...
Following their AGM in February 1866 the FA adopted the Sheffield principle of using secondary scoring to decide matches finishing equal on actual goals:
...if a player of the opposite side first touches the ball after it has gone behind the goal line of his adversary, one 'touch down' shall be scored by his side, and in the event of no goal being got by either side, or an equal number of goals being got on each side, the side obtaining the greater number of 'touches down' shall be the winners of the match.

 It was a relatively short lived experiment, the touch down disappearing from the rules altogether following the 1867 AGM, being replaced by a free kick for the defending team to be taken within 6 yards of their goal. 

see: The Football Association 1863-1883: A Source Book by Tony Brown (2011)