In the first Beis Hamikdash, the tables in the Beis Hamitbachayim were made of silver;1 in the second Beis Hamikdash they were made of marble.2 (However, even in the first Beis Hamikdash there were marble tables in other places,3 such as the table next to the ramp where they put the meat of the Korbanos until they were offered.4)

1 Divrei Hayamim I 28:16. The Passuk just mentions silver tables, without explaining what they were used for, the Mefarshim (Mefaresh, Radak, and Medrash Divrey Hayamim from R' Shmuel Masnos) explain based off of Yechezkel (40:39-41) where he mentions stone tables that the were used while skinning and cutting up the Korbanos, and say that these are the tables that we are referring to here as well (these tables of yechezkel correspond to the eight tables in the Beis Hamibachayim, see Rashi Yoma 16b).

The question arises why do the Mefarshim explain like this, and we have to say that the First Beis Hamikdash is different than both the second and the third, as in both of them these tables were made of stone, why don't they explain the Passuk as referring to the silver tables known to be in the second Beis Hamikdash, like the table next to the ramp where the Keilim were stored (Shekalim 6:4), or the table in the Ulam where the Lechem Hapanim was placed on before bringing it in to the Heichal, which according to some opinions was made of silver (see Tosafos to Menachos 99b)? This is especially problematic as this is not just a detail you can say they just changed, and the material of the tables were not part of the instructions handed down; we cannot say this, as the Passuk in Divrei Hayamim that mentions the silver tables is describing the details of the Beis Hamikdash that David told Shlomo, when he gave him the scroll of the Megillas Hamikdash!

One answer we can give is that the mefarshim would rather say that the Passuk in Divrei Hayamim is relying on a different Passuk in Tanach, rather than on something that is not mentioned in Tanach at all. Another (more probable) answer is that they want to explain the Passuk according to the opinion that the table in the Ulam was marble, and there was therefore only one silver table in the second Beis Hamikdash, while the Passuk mentions silver tables, more than one.

From the above it comes out that this is one of the changes that they changed in the second Beis Hamikdash to be like the third. There is also a reason for this change, as marble does not heat up, while metal does, and makes the meat spoil faster (See Yerushalmi Shekalim 6:3 and Bavli Tamid 31b).

2 Middos 3:5

3 See Mefaresh to Divrei Hayamim I 29:2
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4 Shekalim 6:4

   The north wall of the expanded Har Habayis was mostly destroyed, and virtually no remains can be seen above ground, besides for a few stones in the northeast and northwest corners. (The Kaftor Vaferach already observed this fact, as he writes (chapter 6) that the northern wall is destroyed, as opposed to the other walls, where he found remains of all the gates mentioned in the Mishnah, see my earlier post about this Kaftor Vaferach.) However, it seems that there are still remains of this wall underground, as the present north wall of the Har Habayis is on the same line as we would make the Herodian north wall be, based on the remains at both corners.

   On the north side of the Har Habayis, in the eastern part, there is a large pool, called by the Arabs Birket Isra'in, a corruption of Birket Beni Israil, pool of the sons of Yisroel. It is first mentioned by this name by Muqadassi, an Arab geographer, in the tenth century. There are different opinions about its date, with some dating to Herodian times, and some dating it to later times, like when the Romans rebuilt Yerushalayim as a pagan city, called aelia capitolina, during the times of Hadrian yemach shemo. Towards the end of the 19th century, the pool was being used as a garbage dump, as well as a vegetable garden. In 1934 the pool was filled in because its condition posed a threat to public health. In 1981 a small square equipped with benches was constructed on part of the covered pool. Today the area is known as el-Ghazali Square, and is used as a parking lot, as well as a collection point for garbage, before it is dumped outside the city. Some small shops also exist at the site.

  Above the ground, the northeast corner of the (expanded) Har Habayis can be clearly seen, and to the north of it is the more modern eastern city wall of Yerushalayim. However, underground the Har Habayis wall does not end at this point, but runs further, for another 38.4 meters (126 feet).

   Warren writes the following about this (Survey of Western Palestine, Jerusalem, pp 129-130): Gallery along east wall of Sanctuary, Commenced 5th June,1869. From a point (P) 18 feet south of the north-east angle, a gallery was driven along the wall (level 2,363 feet 3 inches [720.31 m]) to north, past where the straight joint between the Castle of Antonia and city wall should occur; but no straight joint was found to exist. The wall runs on without a break of any kind, and there is no projection... To a distance of 65 feet (19.81 m) the stones were all like those at the Wailing Place, but beyond this to 75 feet (22.86 m) they had rough projecting faces (projections about 6 to 10 inches [15-25 cm]) with well-cut marginal drafts. 

    The northern part of the eastern wall of Har Habayis, from the northern joint to the northeast corner of the Har Habayis, a distance of around 121 meters (397 feet) is from Hurdus's expansion. This wall crossed over the Bezesa valley and continued onto the hill north of Har Hamoriah. By the northeast corner, there is a tower that was (mistakenly) called "The Tower of Antonia" (The Antonia fortress, mentioned by Josephus, was actually by the northwest corner of Har Habayis). 

     The Parah Adumah was burned on top of Har Hamishchah, which is Har Hazeisim, the Mount of Olives. (The ashes of the Parah Adumah-red heifer were used to purify people from Tumas Meis.) This place was located directly to the east of the Beis Hamikdash, as learned from the Passuk (Bamidbar 19:4) "Elazar the kohen shall take some of its blood with his finger and sprinkle it directly towards (אל נוכח) the face of the Tent of Meeting seven times". From the words directly towards (אל נוכח) we learn that number one, he sprinkled the blood towards the entrance of the Kodesh Hakodoshim, and number two, that the location he was in must be directly opposite the Kodesh Hakodoshim. (The face of a building is the door, although from the fact that the passuk does not just simply say door, we learn that over here it also means the most important part of the Heichal, the Kodesh Hakodoshim. In order to see the entrance to the Kodesh Hakodoshim, however, you had to look through the door of the Kodesh. [Tosafos Chadashim, Parah 3:9]​)

         Leading from Sha'ar Shushan, in the eastern wall of the Har Habayis, there was a long Kevesh-כבש ("bridge") that led to the place where they burned the Parah Adumah, on Har Hazeisim. (The ashes of the Parah Adumah-red heifer were used to purify people from Tumas Meis.) This place was located directly to the east of the Beis Hamikdash, as learned from the Passuk (Bamidbar 19:4) "Elazar the kohen shall take some of its blood with his finger and sprinkle it directly towards the Tent of Meeting seven times. 

     Josephus (Wars 5:4:2) writes amount the east wall of Yerushalayim, that at its end, "it was joined to the eastern stoa of the temple". Some (R' Yehosef Shwartz, in Tevu'os Ha'aretz chapter 7, Michael Avi-Yonah, in his famous model; the Holyland model, and others,) have understood this to mean that it joined the southeast corner of the Har Habayis, and the east wall of Har Habayis was also part of the east wall of the city, like it is today. However, this cannot be, as Rashi (סוכה נא ע"א ד"ה שלא היתה מאירה מאור בית השואיבה) seems to imply that (at least part) of Yerushalayim was to the east of the Har Habayis. Furthermore, the Gemarah (Shavuos 16a) talks about two areas on Har Hazeisim, which is located east of Yerushalayim, that were added to Yerushalayim. 

   The southeast corner of the (expanded) Har Habayis is built on the lowest point of the bedrock, so in order to help stabilize it, the lower rows of stone are set back from the ones under them more than in the other walls, they are set back between 7.6-10.1 cm (3-4 in), and in one case 15.2 cm (6 in). Higher up (around seven rows under the master course), however, they are set back very little, only a quarter or a third of an inch (around 7 mm). On some of the lowest stones of this corner there are letters and symbols on the stones, either painted with red paint or engraved. The margins of some of these lower stones are very irregular, with some having huge margins on one side, and very small or no margins on the other, it seems that they used unperfect stones for here, since they were below street level, and would never be seen anyway.

    When the stones for the Har Habayis were quarried, the masons left small square projections of about 12 cm (4 in), on either side of the stone. These projections had ropes placed around them, and were used to lift and transport the stones. When the stones were put into the Har Habayis walls, these projections were usually cut off, however sometimes they were left, and you can still see stones in the southern edge of the eastern wall which have these projections.

   The eastern wall of the Har Habayis is 466 meters (1530 feet) long. This wall is not exactly on the north-south axis, rather it is on an angle of 6 degrees to the north. The southern part of this wall is at an angle of around 93 degrees compared to the southern wall of Har Habayis, but at 73.2 meters (240 feet) away from this corner, the wall turns slightly to the east, so at a point 198.12 meters (650 feet) from the south-east corner, the wall is 2.43 meters (8 feet) to the east of a line in production of the first 73.2 meters (240 feet).

   In the southeastern corner of the expanded Har Habayis, there was a tower, the remains of which can be seen in the eastern wall. This made a nice visual balance to the eastern wall of the Har Habayis, as it had towers on both ends.