Smyth apparently had predicted based on the Pyramid that the year 1882 would be significant. The book mentions the possibility that 1882 would mark "the beginning of the end" or the beginning of the transition between dispensations, and that there would be a neutral zone between them, when Christ would first return for his saints before the tribulation and then later return to establish his kingdom on earth. This was the same reasoning that Barbour/Russell used in the book "The Three Worlds" to explain the apparent failure of Barbour's expectations for 1874.
Morton Edgar appears to have been a good and intelligent man, and it is regrettable that he and others like him wasted their time and talents on the Pyramid. I once perused the library of a believer in the Pyramid who had many books on the Pyramid. The books did not agree, they had different measurements, set different dates, had different meanings and events assigned to the passages. All very confusing. Russell had differing measurements in Vol. 3 in his chapter on the Pyramid, and Morton Edgar's measurements differed from both of Russell's measurements.
That the Pyramid was built by Shem/Melchizedek is purely conjecture. Even though there is a coffer in the Pyramid we are to believe that the Pyramid was not built to be a tomb for Pharoah, and that God picked Egypt to build a building rather than Palestine, and that we are to trust the handful of people who made the measurements.
These books on the Pyramid are often quite unreadable with lengthy discussions of measurements and secret passages that only a privileged few will ever see. There are arguments over a fraction of an inch. When I measure my bedroom I don't always get the same results. Are we to believe that we can get exact measurements from the Pyramid with its worn surfaces and rubble?
The Edgars saw correspondences between places in the Pyramid and events in sacred history. Seen as products of human imagination, there is much ingenuity in this. Unfortunately, the curious can be tempted to mistake their imaginings for divine secrets, and lose touch with reality.