Thus trestle after trestle is added until the bridge has grown right across the water to the further bank. The trestles cannot fall over sideways because of their own width, they cannot fall forwards or backwards because of the "baulks" which pass between them and carry the floor, but as a precaution diagonal ties of rope are always added here and there along the bridge, that is to say, two trestles are tied together with two ropes, each rope passing from the bottom of one trestle to the top of the other, a form of tying which is very effective and very easy and simple to carry out. One interesting thing to notice is the form of the "baulks," in which connection I would like to remark that when I use the word without inverted commas I mean it in the ordinary sense as implying a big heavy timber, but when I use the commas I mean it in its technical sense as it is used in military engineering. In this latter sense it describes the timbers specially provided for the purposes just described. Large supplies of the ordinary heavy baulks could not be carried with an army: but strength is required nevertheless. Hence the military engineers have invented a form which combines strength with lightness. If you stand a plank upon its edge, supported at each end so as to form a beam, its strength will vary as its width and as the _square of its height_. If then you double its width you only double its strength, but if you double its height you multiply its strength _four_ times. If you halve the width of a given beam you halve its strength, but if you then double its height you quadruple that half, in other words, without making the beam any heavier by these two operations you double its strength. Moreover, if you support a beam at each end and pass a load over it or spread a load permanently upon it, its greatest strength is required in the middle. You can shave away the ends without making the beam as a whole any less strong. So these "baulks" are made like planks, very oblong if looked at endwise, also thinner at the ends than in the middle. But if by chance they tipped over on to their sides they would for that very reason be very weak, and that is why the notches are provided in the transomes and the centre beams of the pontoons, in order that the "baulks," having been laid edgewise in them, cannot tip over. Thus a considerable saving is made in the weight of the bridging material to be carried.