Let us for the moment accept the truth of the various traditions relating to them, and suppose that they left traces of their worship; what, in the light of the last chapter, should we expect to find? The thing most likely to remain would be ancient shrines in all probability serving for the foundation of nobler structures built in later times. This brings us to the question as to the probabilities of temple-building generally in relation to the heavenly bodies; but before I deal with it, it is important to consider a view first put forward, I believe, by Vitruvius, and repeated by all since his time who have dealt with the question, that the temples were built purely and simply to face the Nile.[5] The statement is so far from the truth that it is clear that those who have made it had not studied the larger temple-fields. Indeed, we have only to note the conditions at Karnak alone to determine whether there is any truth in the view that the temples face the river. We see at once that this idea cannot be true, because we have the chief temples facing in four directions, while the Nile flows only on one side. Other archæologists who have endeavoured to investigate the orientations of these buildings have found that they practically face in all directions; the statement is that their arrangement is principally characterised by the want of it; they have been put down higgledy-piggledy; there has been a symmetrophobia, mitigated perhaps by a general desire that the temple should face the Nile. This view might be the true one, if stars were not observed as well as the sun. With regard to all the temples of the ancient world, whether they are located in Egypt or elsewhere, we must never forget that if astronomy is concerned in them at all, we have to deal with the observations of the rising or setting of the heavenly bodies; whereas the modern astronomer cares little for these risings or settings, but deals only with them on the meridian. The place of rising or setting would be connected with the temple by the direction of the temple's axis. Now, the directions towards which the temples point are astronomically expressed by their "amplitudes"--that is, the distance in degrees from the east or west point of the horizon. For instance, a temple facing east would have an amplitude of zero from the east point. If we suppose a temple oriented to the north, it would have an amplitude of 90°; if half-way between the east and north, the amplitude would be 45° north of east, and so on. So that it is possible to express the amplitude of a temple in such a way that the temples in the same or different countries or localities, with the same or equivalent amplitudes, may be classified; and the more temples which can be thus brought together, the more likely is any law relating to their structure to come out. Let us take this, then, as a general principle. Now how would it be carried out?