It is tempting to think that if you have a 50lb longbow you need to buy arrows spined at 50lbs. This is not however the case. The measurement of an arrow’s spine is related to a recurve bow and because the longbow arrow has to go round the handle of the bow rather than straight ahead as with a recurve, the arrow needs to be more bendy. This is all to do with the archer’s paradox.
The best explanation of the archer’s paradox on the web is by Nigel Cook and it can be found at: Nigel Cook’s Longbow
I have included an extract:
Any discussion concerning longbow arrows must begin with the archer's paradox. The essence of it is thus. You draw your bow and sight the point of the arrow onto the target. For that moment that you aim, imagine the line of the arrow shaft from nock to point. If you extend that imaginary line forwards you will go past the left of the target (assuming that you are right eyed). Longbows are not centre shot bows, you lay the shaft against the bow, and the arrow flies around the bow. That is the essence of the archer's paradox, that the arrow begins by pointing off to the side but flies straight ahead.
The following diagram seeks to illustrate how this happens.

4. ...flexing the other way, 5 & 6. and thus clears the bow. 
This process takes a matter of about 25 milliseconds. The arrow stops bending in 'flexural oscillations' as it flies towards the target, and will follow the line of the string, ie. forwards rather than to the side.
In order for the arrow to flex around the bow shaft as it is loosed there must be a precise degree of flexibility. If this is not the case the arrow will clatter against the bow, it will 'fishtail' in flight, and it will certainly not behave in a responsible manner. This property is known as the spinage of the arrow.
A spine tester measures the deflection of a spine when it is supported between two points, 26 inches apart and a 2lb weight applied to the centre of the spine. The resulting bend in the spine can be measured in inches. The deflection can then be converted into a spine value in pounds using the following formula:
Spine (in lbs) = 26/d where d=the deflection in inches (or if your eyesight is keen mm can be used!)
So, if the deflection is half an inch the maths is 26x2=52
In eights of an inch the approximate values are:
4/8^{ths} =52lbs
5/8^{ths} =42lbs
6/8^{ths} =35lbs
7/8^{ths }=30lbs
1 =26lbs
1 1/8 =23lbs
1 2/8 =21lbs
1 3/8 =19lbs
This means that an arrow that deflects the least is stiffer and therefore of a higher poundage that one that deflects the post and is whippier and of a lower poundage.
The values of spines are given in pounds for a 26” shaft suitable for a recurve bow. Hilary Greenland recommends that you select arrows which are spined for two thirds or three quarters of the actual draw weight of your bow at your draw length. Quicks have provided a table based on the draw weight of the bow with values for different arrow lengths (nock to pile) from which the following is an extract:
Longbow 
24”
arrow
length 
26” 
28” 
30” 
32” 
3038lbs 
 
20/25 
25/30 
30/35 
35/40 
3845lbs 
20/25 
25/30 
30/35 
35/40 
40/45 
4553lbs 
25/30 
30/35 
35/40 
40/45 
45/50 
5360lbs 
30/35 
35/40 
40/45 
45/50 
50/55 
6068lbs 
35/40 
40/45 
45/50 
50/55 
55/60 
The values of the spines are given in ranges of 5lbs as this is the usual accuracy at which they are sold. So if you were hoping to make a set of a dozen arrows between 3436lbs, you will need to buy two dozen shafts!
What else affects the choice of your arrows?
You will also need to consider the weight of the pile, the
diameter of the shafts and the size of the fletchings. These all affect the flight of the arrow. I
suggest you start with piles of 7080 grains and feathers no more than 3
inches. For an article on spine: http://homepage.ntlworld.com/joetapley/spine.htm
And this is not enough for you to be going on with, you also need to consider the overall weight of the arrow. A heavy arrow will have a greater inertia than a lighter one. As a general rule for the same bow a heavy arrow will need to be stiffer than a light arrow (or to put it another way a bow can shoot an arrow of any stiffness provided you get the weight right!).