OF THE EARTH BETWEEN THE DIAMETER SPECIFIED,
REDUCED TO THE DENSITY OF WATER.
-----+------+---------------+-------+-----------------+-------------+
Diam.|Densi-| Volumes | Avgs. | Volumes at |Observations.|
in | ties.| in Cubic | of |Density of Water | |
miles| | Miles. |Density| in Cubic Miles. | |
-----+------+---------------+-------+-----------------+-------------+
| | | | |{Total volume|
7918| |259,923,849,377| 5·6600|1,471,168,987,476|{of the earth|
| |---------------+-------+-----------------|{at density |
| | | | |{ of water. |
| | | | | |
| | | | |{Density at |
| | | | |{7914 miles |
7914|2·0000| 393,724,522| 1·0000| 393,724,522|{in diameter.|
| | | | |{The 2 miles |
7909|2·5000| 491,596,266| 2·2500| 1,106,090,598|{above being |
| | | | |{at density |
| | | | |{of water. |
7900|3·0000| 883,309,189| 2·7500| 2,429,097,520| |
| |---------------+-------+-----------------|{Volume to |
| | 1,768,628,977| | 3,928,912,640|{9 miles deep|
| | | | |{at density |
| | | | |{of water. |
7850|3·0679| 4,870,723,550| 3·0339| 14,777,288,178| |
| | | | | |
7800|3·1359| 4,809,069,650| 3·1019| 14,917,253,147| |
| | | | | |
7750|3·2038| 4,747,808,450| 3·1698| 15,049,403,225| |
| | | | | |
7700|3·2717| 4,686,939,950| 3·2377| 15,174,905,476| |
| | | | | |
7650|3·3397| 4,626,464,150| 3·3057| 15,293,702,541| |
| | | | | |
7600|3·4076| 4,566,381,050| 3·3737| 15,405,599,748| |
| | | | | |
7550|3·4756| 4,506,690,650| 3·4416| 15,510,226,541| |
| | | | | |
7500|3·5435| 4,447,392,950| 3·5095| 15,608,125,558| |
| | | | | |
7450|3·6114| 4,388,487,950| 3·5775| 15,699,815,651| |
| | | | | |
7400|3·6794| 4,329,975,650| 3·6454| 15,784,493,235| |
| | | | | |
7350|3·7473| 4,271,856,050| 3·7132| 15,862,255,885| |
| | | | | |
7300|3·8152| 4,214,129,150| 3·7812| 15,934,465,142| |
| | | | | |
7250|3·8832| 4,156,794,950| 3·8492| 16,000,335,122| |
| | | | | |
7200|3·9511| 4,099,853,450| 3·9172| 16,059,945,934| |
| | | | | |
7150|4·0191| 4,043,304,650| 3·9851| 16,112,973,361| |
| | | | | |
7100|4·0870| 3,987,148,550| 4·0531| 16,160,311,788| |
| | | | | |
7050|4·1549| 3,931,385,150| 4·1210| 16,201,238,203| |
| | | | | |
7000|4·2229| 3,876,014,450| 4·1889| 16,236,236,930| |
| |---------------| |-----------------| |
| | 80,329,049,377| | 285,717,488,335| |
-----+------+---------------+-------+-----------------+-------------+
-----+------+---------------+-------+----------------+-------------+
Diam.|Densi-| Volumes | Avgs. | Volumes at |Observations.|
in | ties.| in Cubic | of |Density of Water| |
miles| | Miles. |Density| in Cubic Miles.| |
-----+------+---------------+-------+----------------+-------------+
| | | | | |
7000|4·2229| 80,329,049,377| 4·1889| 285,717,488,335| |
| | | | | |
6950|4·2908| 3,821,036,450| 4·2568| 16,265,387,960| |
| | | | | |
6900|4·3587| 3,766,451,150| 4·3248| 16,289,147,934| |
| | | | | |
6850|4·4267| 3,712,258,550| 4·3927| 16,306,838,133| |
| | | | | |
6800|4·4946| 3,658,458,650| 4·4606| 16,318,920,654| |
| | | | | |
6750|4·5625| 3,605,051,450| 4·5285| 16,325,475,491| |
| | | | | |
6700|4·6305| 3,552,036,950| 4·5965| 16,326,937,841| |
| | | | | |
6650|4·6984| 3,499,415,150| 4·6645| 16,323,022,067| |
| | | | | |
6600|4·7664| 3,447,186,050| 4·7324| 16,313,463,263| |
| | | | | |
6550|4·8343| 3,395,349,650| 4·8004| 16,299,036,460| |
| | | | | |
6500|4·9022| 3,343,905,950| 4·8682| 16,278,802,946| |
| | | | | |
6450|4·9702| 3,292,854,950| 4·9362| 16,254,190,604| |
| | | | | |
6400|5·0381| 3,242,196,650| 5·0042| 16,224,600,476| |
| | | | | |
6350|5·1060| 3,191,931,050| 5·0721| 16,189,793,479| |
| | | | | |
6300|5·1740| 3,142,058,150| 5·1400| 16,150,178,891| |
| | | | | |
6284|5·2140| 962,684,511| 5·2080| 5,013,660,933| |
| |---------------| |----------------| |
Half volume}| | | |{0·352507 of |
of earth }|129,961,924,688| | 518,596,945,467|{whole volume|
| | | | |{of the earth|
| | | | |{at density |
| | | | |{of water. |
6250|5·2420| 2,129,893,439| 5·2080| 11,092,485,030| |
| | | | | |
6200|5·3098| 3,043,490,450| 5·2759| 16,057,151,265| |
| | | | | |
6150|5·3778| 2,994,795,650| 5·3438| 16,003,588,994| |
| | | | | |
6100|5·4457| 2,946,493,550| 5·4118| 15,954,833,794| |
| | | | | |
6050|5·5137| 2,898,584,150| 5·4797| 15,883,371,567| |
| | | | | |
6000|5·5816| 2,851,067,450| 5·5477| 15,816,866,892| |
| |---------------| |----------------| |
| |146,826,249,377| | 609,405,243,009| |
-----+------+---------------+-------+----------------+-------------+
-----+------+---------------+-------+----------------+-------------+
Diam.|Densi-| Volumes | Avgs. | Volumes at |Observations.|
in | ties.| in Cubic | of |Density of Water| |
miles| | Miles. |Density| in Cubic Miles.| |
-----+------+---------------+-------+----------------+-------------+
| | | | | |
6000|5·5816|146,826,249,377| 5·5477| 609,405,243,009| |
| | | | | |
5950|5·6495| 2,803,943,450| 5·6156| 15,745,824,838| |
| | | | | |
5900|5·7175| 2,757,212,150| 5·6835| 15,670,605,255| |
| | | | | |
5850|5·7850| 2,710,873,550| 5·7515| 15,591,589,223| |
| | | | | |
5800|5·8533| 2,664,927,650| 5·8194| 15,508,275,967| |
| | | | | |
5750|5·9213| 2,619,374,450| 5·8873| 15,421,043,199| |
| | | | | |
5700|5·9892| 2,574,213,950| 5·9553| 15,330,206,336| |
| | | | | |
5650|6·0572| 2,529,446,150| 6·0232| 15,235,360,051| |
| | | | | |
5600|6·1251| 2,485,071,050| 6·0912| 15,137,064,780| |
| | | | | |
5591-1/2 | 412,281,190| 6·1591| 2,539,281,080| |
| |---------------| |----------------| |
0·647819 } | | | |{Half mass of|
of whole } |168,383,592,967| | 735,584,493,738|{whole earth |
volume of} | | | |{at density |
the earth} | | | |{of water |
| | | | | |
5550|6·1930| 2,028,807,460| 6·1591| 12,495,628,024| |
| | | | | |
5500|6·2610| 2,397,498,950| 6·2270| 14,929,225,962| |
| | | | | |
5450|6·3289| 2,354,301,950| 6·2950| 14,820,330,775| |
| | | | | |
5400|6·3968| 2,311,497,650| 6·3628| 14,707,597,247| |
| | | | | |
5350|6·4648| 2,269,086,050| 6·4308| 14,592,038,570| |
| | | | | |
5300|6·5327| 2,227,067,150| 6·4988| 14,473,263,994| |
| | | | | |
5250|6·6006| 2,185,440,950| 6·5667| 14,351,135,086| |
| | | | | |
5200|6·6686| 2,144,207,450| 6·6346| 14,225,958,748| |
| | | | | |
5150|6·7365| 2,103,366,650| 6·7026| 14,098,025,308| |
| | | | | |
5100|6·8045| 2,062,918,550| 6·7705| 13,966,990,043| |
| | | | | |
5050|6·8724| 2,022,863,150| 6·8385| 13,833,349,651| |
| | | | | |
5000|6·9403| 1,983,200,450| 6·9064| 13,696,775,588| |
| |---------------| |----------------| |
| |194,473,849,377| | 905,774,812,734| |
-----+------+---------------+-------+----------------+-------------+
-----+------+---------------+-------+-----------------+------------+
Diam.|Densi-| Volumes | Avgs. | Volumes at |Observations|
in | ties.| in Cubic | of |Density of Water | |
miles| | Miles. |Density| in Cubic Miles. | |
-----+------+---------------+-------+-----------------+------------+
| | | | | About |
5000|6·9403|194,473,849,377| 6·9064| 905,774,812,734| density |
| | | | | of iron |
4950|7·0083| 1,943,930,450| 6·9743| 13,557,554,137| |
| | | | | |
4900|7·0762| 1,905,053,150| 7·0423| 13,418,813,378| |
| | | | | |
4850|7·1441| 1,866,568,550| 7·1102| 13,271,675,704| |
| | | | | |
4800|7·2121| 1,828,476,650| 7·1781| 13,124,988,241| |
| | | | | |
4750|7·2800| 1,790,777,450| 7·2461| 12,976,152,480| |
| | | | | |
4700|7·3479| 1,753,470,950| 7·3140| 12,824,887,528| |
| | | | | |
4650|7·4159| 1,716,557,150| 7·3819| 12,671,453,226| |
| | | | | |
4600|7·4838| 1,680,036,050| 7·4499| 12,516,100,569| |
| | | | | |
4550|7·5518| 1,643,907,650| 7·5178| 12,358,568,931| |
| | | | | |
4500|7·6197| 1,608,171,950| 7·5858| 12,199,270,778| |
| | | | | |
4450|7·6876| 1,572,828,950| 7·6537| 12,037,960,935| |
| | | | | |
4400|7·7556| 1,537,878,650| 7·7216| 11,874,883,784| |
| | | | | |
4350|7·8235| 1,503,321,050| 7·7896| 11,710,269,651| |
| | | | | |
4300|7·8914| 1,469,156,150| 7·8575| 11,543,894,449| |
| | | | | |
4250|7·9594| 1,435,383,950| 7·9254| 11,375,991,957| |
| | | | | |
4200|8·0273| 1,402,004,450| 7·9934| 11,206,782,371| |
| | | | | |
4150|8·0953| 1,369,017,650| 8·0613| 11,036,061,982| |
| | | | | |
4100|8·1632| 1,336,423,550| 8·1295| 10,864,454,250| |
| | | | | |
4050|8·2311| 1,304,222,150| 8·1972| 10,690,969,808| |
| | | | | |
4000|8.2991| 1,272,413,450| 8.2651| 10,516,624,406| |
| |---------------| |-----------------| |
| |226,413,449,377| |1,147,552,171,299| |
-----+------+---------------+-------+-----------------+------------+
-----+------+---------------+-------+-----------------+------------+
Diam.|Densi-| Volumes | Avgs. | Volumes at |Observations|
in | ties.| in Cubic | of |Density of Water | |
miles| | Miles. |Density| in Cubic Miles. | |
-----+------+---------------+-------+-----------------+------------+
| | | | | About |
4000|8·2991|226,413,449,377| 8·2651|1,147,552,171,299| density |
| | | | | of copper |
3950|8·3670| 1,240,997,450| 8·3331| 10,341,355,851| |
| | | | | |
3900|8·4349| 1,209,974,150| 8·4010| 10,164,992,834| |
| | | | | |
3850|8·5029| 1,179,343,550| 8·4689| 9,987,742,590| |
| | | | | |
3800|8·5708| 1,149,105,650| 8·5369| 9,809,800,023| |
| | | | | |
3750|8·6387| 1,119,260,450| 8·6048| 9,631,012,320| |
| | | | | |
3700|8·7067| 1,089,807,950| 8·6727| 9,451,577,408| |
| | | | | |
3650|8·7746| 1,060,748,150| 8·7407| 9,271,681,355| |
| | | | | |
3600|8·8426| 1,032,081,050| 8·8086| 9,091,189,137| |
| | | | | |
3550|8·9105| 1,003,806,650| 8·8766| 8,910,390,109| |
| | | | | |
3500|8·9784| 975,924,950| 8·9445| 8,729,160,715| |
| | | | | |
3450|9·0464| 948,435,950| 9·0124| 8,547,684,156| |
| | | | | |
3400|9·1143| 921,339,650| 9·0804| 8,366,132,559| |
| | | | | |
3350|9·1822| 894,636,050| 9·1483| 8,184,398,976| |
| | | | | |
3300|9·2502| 868,325,150| 9·2162| 8,002,658,247| |
| | | | | |
3250|9·3181| 842,406,950| 9·2842| 7,821,074,605| |
| | | | | |
3200|9·3860| 816,881,450| 9·3522| 7,639,638,697| |
| | | | | |
3150|9·4540| 791,748,650| 9·4200| 7,458,252,283| |
| | | | | |
3100|9·5219| 767,008,550| 9·4880| 7,277,377,122| |
| | | | | |
3050|9·5899| 742,661,150| 9·5554| 7,096,424,353| |
| | | | | |
3000|9·6578| 718,706,450| 9·6239| 6,916,759,004| |
| |---------------| |-----------------| |
| |245,786,649,377| |1,320,251,473,643| |
-----+------+---------------+-------+-----------------+------------+
-----+------+----------------+-------+-----------------+------------+
Diam.|Densi-| Volumes | Avgs. | Volumes at |Observations|
in | ties.| in Cubic | of |Density of Water | |
miles| | Miles. |Density| in Cubic Miles. | |
-----+------+----------------+-------+-----------------+------------+
| | | | | |
3000| 9·6578|245,786,649,377| 9·6239|1,320,251,473,643| |
| | | | | |
2950| 9·7257| 695,144,450| 9·6918| 6,737,200,981| |
| | | | | |
2900| 9·7937| 671,975,150| 9·7597| 6,558,275,871| |
| | | | | |
2850| 9·8616| 649,198,550| 9·8276| 6,380,063,674| |
| | | | | |
2800| 9·9295| 626,814,650| 9·8956| 6,202,697,051| |
| | | | | |
2750| 9·9975| 604,823,450| 9·9635| 6,026,158,444| |
| | | | | |
2700|10·0654| 583,224,950|10·0315| 5,850,621,086| |
| | | | | |
2650|10·1334| 562,019,150|10·0994| 5,675,940,204| |
| | | | | |
2600|10·2013| 541,206,050|10·1674| 5,502,658,393| |
| | | | | |
2550|10·2692| 520,785,650|10·2353| 5,330,397,363| |
| | | | | |
2500|10·3372| 500,757,950|10·3032| 5,059,409,310| |
| | | | | |
2450|10·4051| 481,122,950|10·3712| 4,989,822,340| |
| | | | |{ About |
2400|10·4730| 461,880,650|10·4391| 4,821,618,293|{ density |
| | | | |{of silver. |
2350|10·5410| 443,031,050|10·5070| 4,654,927,242| |
| | | | | |
2300|10·6089| 424,574,150|10·5750| 4,489,871,636| |
| | | | | |
2250|10·6768| 406,509,950|10·6429| 4,326,444,747| |
| | | | | |
2200|10·7448| 388,838,450|10·7108| 4,164,770,870| |
| | | | | |
2150|10·8127| 371,559,650|10·7798| 4,005,338,715| |
| | | | | |
2100|10·8807| 354,673,550|10·8467| 3,847,037,595| |
| | | | | |
2050|10·9486| 338,180,150|10·9147| 3,691,134,883| |
| | | | | |
2000|11·0165| 322,079,450|10·9826| 3,537,269,768| |
| |---------------| |-----------------| |
| |255,735,049,377| |1,422,103,132,109| |
-----+-------+---------------+-------+-----------------+------------+
-----+-------+---------------+-------+-----------------+------------+
Diam.|Densi- | Volumes | Avgs. | Volumes at |Observations|
in | ties. | in Cubic | of |Density of Water | |
miles| | Miles. |Density| in Cubic Miles. | |
-----+-------+---------------+-------+-----------------+------------+
| | | | | |
2000|11·0165|255,735,049,377|10·9826|1,422,103,132,109| |
| | | | | |
1950|11·0845| 306,371,450|11·0505| 3,385,557,708| |
| | | | | |
1900|11·1524| 291,056,150|11·1185| 3,236,107,805| |
| | | | | |
1850|11·2203| 276,133,550|11·1864| 3,088,940,344| |
| | | | | |
1800|11·2883| 261,603,650|11·2543| 2,944,165,858| |
| | | | | |
1750|11·3562| 247,466,450|11·3223| 2,802,888,487|} About |
| | | | |} density |
1700|11·4242| 233,721,950|11·3902| 2,662,139,545|} of lead |
| | | | | |
1650|11·4921| 220,370,150|11·4582| 2,525,045,253| |
| | | | | |
1600|11·5600| 207,411,050|11·5261| 2,390,640,503| |
| | | | | |
1550|11·6280| 194,844,650|11·5940| 2,259,028,872| |
| | | | | |
1500|11·6959| 182,670,950|11·6620| 2,130,308,620| |
| | | | | |
1450|11·7638| 170,889,950|11·7299| 2,004,522,025| |
| | | | | |
1400|11·8318| 159,501,650|11·7978| 1,881,768,566| |
| | | | | |
1350|11·8997| 148,506,050|11·8658| 1,762,143,088| |
| | | | | |
1300|11·9676| 137,903,150|11·9337| 1,645,694,821| |
| | | | | |
1250|12·0356| 127,692,950|12·0016| 1,532,519,609| |
| | | | | |
1200|12·1035| 117,875,450|12·0696| 1,422,709,531| |
| | | | | |
1150|12·1715| 108,450,650|12·1375| 1,316,319,764| |
| | | | | |
1100|12·2394| 99,418,550|12·2055| 1,213,453,112| |
| | | | | |
1050|12·3073| 90,779,150|12·2734| 1,114,168,820| |
| | | | | |
1000|12·3753| 82,532,450|12·3413| 1,018,557,725| |
| |---------------| |-----------------| |
| |259,400,249,377| |1,464,439,812,165| |
-----+-------+---------------+-------+-----------------+------------+
-----+-------+---------------+-------+-----------------+------------+
Diam.|Densi- | Volumes | Avgs. | Volumes at |Observations|
in | ties. | in Cubic | of |Density of Water | |
miles| | Miles. |Density| in Cubic Miles. | |
-----+-------+---------------+-------+-----------------+------------+
| | | | | |
1000|12·3753|259,400,249,377|12·3413|1,464,439,812,165| |
| | | | | |
950|12·4432| 74,678,450|12·4093| 927,507,290| |
| | | | | |
900|12·5111| 67,217,150|12·4772| 838,681,824| |
| | | | | |
850|12·5791| 60,148,550|12·5451| 754,569,575| |
| | | | | |
800|12·6470| 53,472,650|12·6132| 674,461,229| |
| | | | | |
750|12·7149| 47,189,450|12·6820| 598,456,605| |
| | | | | |
700|12·7829| 41,298,950|12·7489| 526,516,184| |
| | | | | |
650|12·8508| 35,801,150|12·8169| 458,859,759| |
| | | | | |
600|12·9188| 30,696,050|12·8848| 395,512,465| |
| | | | | |
550|12·9867| 25,983,650|12·9528| 336,561,022| |
| | | | | |
500|13·0546| 21,663,950|13·0207| 282,079,794| |
| | | | | |
450|13·1226| 17,736,950|13·0886| 232,151,644| |
| | | | | |
400|13·1905| 14,202,650|13·1566| 186,858,585| |
| | | | | |
350|13·2584| 11,061,050|13·2245| 146,276,856| |
| | | | | |
300|13·3264| 8,312,150|13·2924| 110,488,423| |
| | | | | |
250|13·3943| 5,955,950|13·3604| 79,573,874| |
| | | | | |
200|13·4623| 3,992,450|13·4283| 53,611,816| |
| | | | | |
150|13·5202| 2,421,650|13·4963| 32,683,315| |
| | | | | |
100|13·5981| 1,243,550|13·5642| 16,867,761| |
| | | | |{ About |
50|13.6661| 458,150|13.6321| 6,245,547|{ density |
| | | | |{of mercury.|
0|13·7340| 65,450|13·7001| 896,672| |
| |---------------| |-----------------| |
| |259,923,849,377| |1,471,098,672,405| |
| | | | | |
|True volume at density of water|1,471,168,987,476| |
| |-----------------|{ About |
| Deficiency | 70,315,071|{1/21,000th |
| | |{ part. |
-----+-------------------------------+-----------------+------------+
CHAPTER IX.
PAGE
165 Inquiry into the Interior Construction
of the Earth--_continued_.
166 The earth gasiform at one period. Density including the moon
may have been 1/10,000th that of air. Must have been a hollow
body. Proofs given.
169 Division of the mass of the earth alone into two parts.
171 Division of the two masses at 817 miles from surface.
172 Reasons why the earth cannot be solid to the centre.
172 Gasiform matter condensing in a cone leaves apex empty.
173 Proportions of the matter in a cone.
174 Calculations of the densities of the outer half of the hollow
shell of the earth. Remarks upon the condensation.
175 Calculations of inner half of the hollow shell.
177 Remarks upon position of inner surface of the shell.
179 Calculations of the same.
THE INTERIOR OF THE EARTH AND ITS DENSITY--_continued._
When, according to the nebular hypothesis, the ring for the formation
of the earth and moon had been thrown off by the nebula, and had
broken up and formed itself into one isolated mass--rotating or not on
an axis, as the case may have been--it must have been in a gasiform
state. What was its density, more or less, may be so far deduced from
Table III., where it will be seen that when it had condensed to about
one-half of its volume, it must have had a density of only 1/9000th
part of our atmosphere, and in which each grain of matter would have
for its habitat 16 cubic feet of space, or a cube of 2·52 feet to the
side. So that, with an average distance from its neighbours of 2-1/2
feet, a grain of matter could not be looked upon as wedged-in in any
way, and would be free to move anywhere. Now, supposing this earth-moon
nebula to have been in the form of even an almost shapeless mass,
and that it was nearly homogeneous--as it could hardly be otherwise
after the tumbling about it had in condensing from a flat ring--its
molecules would attract each other in all directions, and as the
mass--without having arrived perhaps at the stage of having any well
defined centre--would have an exterior as well as an interior, the
individual molecules at the exterior would draw those of the interior
out towards them, just as much as those at the interior would attract
those of the exterior in towards them; but as the number of those
at the exterior would--owing to the much greater space there, being
able to contain an immensely greater number--be almost infinitely
greater than of those nearer to the central part, the latter would
be more effectually attracted, or drawn, outwards than the former
would be inwards, and there would be none left at the interior after
condensation had fairly begun. The mass would speedily become a hollow
body, the hollow part gradually increasing in diameter. But let us go
deeper into the matter.
Let us suppose that the whole mass had assumed nearly the form of a
sphere. We have already shown that, although the general force of
attraction would cause all the component particles of the sphere to
mutually draw each other in towards the centre, yet the more powerful
tendency of the particles at the exterior--due to their greatly
superior number--would at first be to draw the particles near the
centre outwards towards them, and that there would consequently be
a void at the centre, for a time at least. Of course it is to be
understood that each part of the exterior surface would draw out to it
the particles on its own side of the centre, just in the same manner as
the four masses we placed at the centre were shown to be drawn out by
those at London, Calcutta, and their antipodes. Now we must try to find
out what would be the ultimate result of this action; whether it would
be to form a sphere solid to the centre, or whether the void at first
established there would be permanent.
In order to show how the heat of the sun is maintained by the
condensation and contraction of that luminary, Lord Kelvin--in his
lecture delivered at the Royal Institution, on Friday, January 21,
1887--described an ideal churn which he supposed to be placed in a
pit excavated in the body of the sun, with the dimension of one
metre square at the surface, and tapering inwards to nothing at the
centre. In imitation of him, we shall suppose a similar pit of the
same dimensions to be dug in the spherical mass, out of which we
have supposed the earth to have been formed; only we shall call it
a pyramid instead of a pit. This we shall suppose to be filled with
cosmic matter, and try to determine what form it would assume were it
condensed into solid matter, in conformity with the law of attraction.
The apex of our imaginary pyramid would, mathematically speaking, have
no dimension at all, but we shall assume that it had space enough to
contain one molecule of the cosmic matter of which the sphere was
formed. This being so arranged, we have to imagine how many similar
molecules would be contained in one layer at the base of the pyramid
at the surface of the sphere, and we may be sure that when brought
under the influence of attraction, the great multitude of them would
have far more power to draw away the solitary molecule from the apex,
than the single one there would have to draw the whole of those in
the layer at the base in to the centre of the sphere. A molecule of
the size of a cubic millimetre would be an enormously large one,
nevertheless one of that size placed at the apex of the pyramid would
give us one million for the first layer at the base, and shows us what
chance there would be of the solitary one maintaining its place at the
apex. At the distance of one-twentieth of the radius of the sphere
from the centre, the dimension of the base of the pyramid would be
one-twentieth of a square metre, and the proportion of preponderance of
a layer of molecules there would be as 25 to 1, so that the molecule at
the centre would be drawn out almost to touch those of that layer; at
one-tenth of the radius from the centre, the preponderance of a layer
over the solitary central molecule would be as 10,000 to 1; and so on
progressively to 1,000,000 to 1, as we have already said.
Following up this fact, if we divide the pyramid into any number of
frusta, the action of attraction will be the same in each of them;
the molecules in the larger end of each will have more power to draw
outwards those of the small end, than they will have to draw inwards
those of the larger end; and then the condensed frusta will act upon
each other in the same manner as the molecules did, the greater mass of
those at the larger end, or base, drawing down, or out--whichever way
it may seem best to express it--a greater number of the frusta at the
smaller end of the pyramid, until, in the whole of it, a point would
be reached where the number of molecules in the various frusta drawn
down from the apex would be equal to those drawn up from the base,
leaving a part of the pyramid void at each end, because we are dealing
with attraction, not gravitation, and there would be no falling to
the base or apex, but concurrence to the point, just hinted at, where
the outwards and inwards attractions of the masses would balance each
other. This point of meeting of the two equal portions of cosmic matter
may be called the plane of attraction in the pyramid. The whole pyramid
would thus be reduced to the frustum of a pyramid, whose height would
be as much more than double the distance from the plane of attraction
to its base, as would be required to make the upper part above the
plane of attraction equal in volume, or rather in number of molecules,
to the lower part. It would be impossible for us to explain how, in a
pyramid such as the one we have before us, the action of attraction
could condense, and at the same time cram, the whole of the molecules
contained in it into the apex end.
We must not, however, forget that there are two sides to a sphere, as
well as to a question, and that we must place on the opposite side to
the one we are dealing with, another equal pyramid with apex at the
centre and base at the surface, at a place diametrically opposite to
the first one, and that the tendency of the whole of this new pyramid
would be to draw the whole of the first one in towards the centre of
the sphere. But in the second, the law of attraction would have the
same action as in the first; the molecules of the matter contained in
it near the base would far exceed, in attractive force, those near the
apex, and would draw them outwards till the whole were concentrated
in a frustum of a pyramid, exactly the same as the one in the first
pyramid. And while the whole masses of matter in the two pyramids were
attracting each other at an average distance, say, for simplicity's
sake, of one-half the diameter of the sphere, the molecules in each
of them would be attracting each other from an average distance of
one-quarter the diameter of the sphere; their action would consequently
be four times more active, and they would concentrate into the frusta
as we have shown, before the two pyramids had time to draw each other
in to the centre. There would be then two frusta of pyramids attracting
each other _towards_ the centre with an empty space between them. Here
then we have two elements of a hollow sphere, one on each side of the
centre, and if we suppose the whole sphere to have been composed of
the requisite number of similar pyramids, set in pairs diametrically
opposite to each other, we see that the whole mass of the matter out of
which the earth was formed must have--by the mutual attractions of its
molecules--formed itself into a hollow sphere.
All that has been said must apply equally well whether we consider the
earth to have been in a gasiform state, or when by condensation and
consequent increase of temperature it had been brought into a molten
liquid condition. For up to that time it must have been a hollow
sphere, and we must either consider it to be so still, or conceive that
the opposite sides have continued to draw each other inwards till the
hollow was closed up; in which case, the greatest density would not be
at the centre, but at a distance therefrom corresponding to what has
been called the plane of attraction of the pyramid. That the opposite
sides have not yet met will be abundantly demonstrated by facts that
will meet us, if we try to find out what is the greatest density of the
earth at the region of greatest mass or attraction, wherever that may
be.
Seeing that the foregoing reasoning forces us to look upon the earth as
a hollow sphere, or shell, in which the whole of the matter composing
it is divided into two equal parts, attracted outwards and inwards by
each other to a common plane, or region of meeting, we shall divide its
whole volume into two equal parts radially, that is, one comprising a
half from the surface inwards, and the other a half from the centre
outwards--that is to say, each one containing one-half of the whole
volume of the earth. Referring now to our calculations, Table IV., we
find that the actual half volume of the earth is comprised in very
nearly 817 miles from the surface, where the diameter is 6284 miles,
because the total volume at 7918 miles in diameter is 259,923,849,377
cubic miles. This being the case, we cannot avoid coming to the
conclusion, after what has just been demonstrated by the pyramids that
if one-half of the whole volume is comprehended in that distance from
the surface, so also must be one-half of the mass.
But for further substantiation of this conclusion let us return to the
table of calculations. There we find that from the surface to the depth
of 817 miles--where the diameter would be 6284 miles--which comprehends
one-half of the volume--the mass at the density of water is shown to
be only 518,596,945,467 miles instead of 735,584,493,738 cubic miles,
which is the half of the whole mass of the earth reduced to the density
of water. That is, the outer half of the volume gives only 70·5 per
cent. of half the mass, while the inner half of the volume gives not
only one-half of the mass but 29·5 per cent. more; or, to put it more
clearly, the mass of the inner half-volume is 1·84 times, nearly twice
as great, as the mass of the outer half-volume. On the other hand, we
have to notice that the line of division of the mass into two halves
falls at 1163·25 miles from the surface, where the diameter is 5591·5
miles; so that on the outer half of the earth, measured by mass, 64·74
per cent. of the whole volume of the earth contains only one-half of
the mass, whereas on the inner portion, measured in the same way, 35·26
per cent. of the same whole contains the other half. All these results
must be looked upon as unsatisfactory, or we must believe that two
volumes of cosmic matter which at one time were not far from equal, had
been so acted upon by their mutual attractions that the one has come to
be not far from double the mass of the other; that the vastly greater
amount of cosmic matter at the outer part of a nebula has only one-half
of the attractive force of the vastly inferior quantity at the centre.
This we cannot believe if the original cosmic, or nebulous, matter was
homogeneous; and if it was not homogeneous we have, in order to bring
about such result, to conceive that the earth was built up, like any
other mound of matter, under the direction of some superintendent who
pointed out where the heavier and where the lighter matter was to be
placed.
We shall now proceed to find out what would be the internal form, and
greatest density of the earth, under the supposition that it is a
hollow sphere divided into two equal volumes and masses--exterior and
interior--meeting at 817 miles from the surface; but before entering
upon this subject we have something to say about the notion of the
earth being solid to the centre.
We are forced to believe that, according to the theory of a nucleus
being formed at the centre as the first act, the matter collected there
must have remained stationary ever since, because we cannot see what
force there would be to uniform the nucleus just formed; gravitation,
weight falling to a centre, would only tend to increase, condense, and
wedge in the nucleus more thoroughly. Attraction, as we have shown,
would not allow the matter to get to the centre at all. Convection
currents, or currents of any kind, could not be established in matter
that was being wedged in constantly. Moreover, when in a gasiform
state, it would be colder than when condensed by gravitation to, or
nearly to, a liquid or solid state, and heat would be produced in
it in proportion to its condensation, that is, gradually increasing
from the surface to the centre in the same manner as density, which,
when the cooling stage came, would be conducted back to the surface
to be radiated into space, but could not be carried--by convection
currents--because the matter being heavier there than any placed above
it, and being acted upon by gravitation all the time, would have no
force tending to move it upwards; and above all, when solidification
began at the surface, it is absurd to suppose that the first formed
pieces of crust could sink down to the centre through matter more dense
than themselves; unless it was that by solidification they were at
once converted into matter of the specific gravity of 13·734. Even so
the solid matter would not be very long in being made liquid again
by meeting with matter not only hotter than itself, but constantly
increasing in heat through continual condensation, which would act
very effectively in preventing any convection current being formed to
any appreciable depth, certainly never to any depth nearly approaching
to the centre. If solidification began first at the centre--as some
parties have thought might be the case--owing to the enormous pressure
it would be subjected to there, before it began at the surface, then,
without doubt, the central matter must have remained where it was
placed at first, up to the present day. This would suit the sorting-out
theory very well, as all the metals would find their way to the centre
and there remain; but judged under a human point of view, it would be
considered very bad engineering on the part of the Supreme Architect to
bury all the most valuable part of His structure where they could never
be availed of; or that He was not sufficiently fertile in resources
to be able to construct His edifice in a way that did not involve
the sacrifice of all the most precious materials in it. Man uses
granite for foundations--following the good example He has actually
given we believe, and are trying to show--and employs the metals in
superstructures; but some people may also think that it was better to
keep the root of all evil as far out of man's reach as possible. What
a grand prospectus for a Joint Stock Company might be drawn up, on the
basis of a sphere of a couple of thousand miles in diameter of the most
precious metals, could only some inventive genius discover a way to get
at them!
Returning to our pyramids. We know that the centre of gravity of a
pyramid is at one-fourth of its height, or distance from the base,
and if we lay one of 3959 miles long (the radius of the earth) over a
fulcrum, so that 989-3/4 miles of its length be on one side of it and
2969-1/4 miles on the other, it will be in a state of equilibrium. This
does not mean, however, that there are equal masses of matter on each
side of the fulcrum, for we know that the mass of the base part must
be considerably greater than that of the apex part, and that it must
be counterbalanced by the greater leverage of the apex part, due to
its greater distance from the point of support. This being so, in the
case of a pyramid consisting of gasiform, liquid, or solid matter,
the attractive power of the 989-3/4 miles of the base part would be
greater than that of the 2969-1/4 miles of the apex part, and the plane
of equal attraction of the two parts would be less than 990 miles from
the base of the pyramid. This is virtually the same argument we have
used before repeated, but it is placed in a simpler and more practical
light, and shows that the plane of attraction in a pyramid will not be
at its centre of gravity but nearer to its base, and that it must be
at or near its centre of volume. Thus the plane of attraction in one
of the pyramids we have been considering of 3959 miles in length, and
consequently the radial distance of the region of maximum attraction of
the earth, would not be at 990 miles from the base or surface, but at
some lesser distance.
Now, if we take a pyramid, such as those we have been dealing with,
whose base is 1 square and height 3959, its volume would be the square
of the base multiplied by one-third of the height, that is 1^{2} ×
3959/3 = 1319·66, the half of which is 659·83. Again, if we take the
plane of division of the volume of the pyramid into two equal parts
to be 0·7937 in length on each side, and consequently (from equal
triangles) the distance from the plane to the apex to be 0·7937 the
total height of 3959, which is 3142·258; then, as we have divided it
into a frustum and a now smaller pyramid, if we multiply the square
of the base of this new pyramid by one-third of the height we have
0·7937^{2} × 3142·258/3, or 0·62996 × 1047·419 = 659·83, which is
equal to the half-volume of the whole pyramid as shown above. Thus we
get 3959 less 3142·258 = 816·74 miles as the distance from the base
of the plane of division of the pyramid into two equal parts, which
naturally agrees with the division of the earth into the two equal
volumes that we have extracted from the table of calculations, where we
have supposed the earth to be made up of the requisite number of such
pyramids. So that it would seem that we are justified in considering
that the greatest density of the earth must be at the meeting of the
two half-volumes, outer and inner, into which we have divided it.
Considering, then, that one-half of the volume and mass of the earth
is contained within 817 miles in depth from the surface, this half
must have an average density of 5·66 times that of water, the same as
the whole is estimated to have. Also, as we have seen already, that,
taking its mean diameter at 7918 miles, its mass will be equivalent
to 1,471,168,987,476 cubic miles, one-half of this quantity, or
735,584,493,738 cubic miles will represent the half-volume of the earth
reduced to the density of water. With these data let us find out what
must be the greatest density where the two half-volumes meet, supposing
the densities at the surface and for 9 miles down to remain the same as
in the calculations we have already made, ending with specific gravity
of 3 at 7900 miles in diameter.
Following the same system as before when treating of the earth as
solid to the centre, and using the same table of calculations for the
volumes of the layers: If we adopt a direct proportional increase
between densities 3 at 7900 miles and 8·8 at 6284·5 miles in diameter,
multiply the volumes by their respective densities, and add about 31
per cent. of the following layer, taken at the same density as the
previous or last one of the number, we shall find a mass (see Table
V.) of 735,483,165,215 cubic miles at the density of water, which is
as near the half mass 735,584,493,738 cubic miles as is necessary for
our purpose. It would thus appear that if the earth is a hollow sphere,
its greatest density in any part need not be more than 8·8 times that
of water, instead of 13·734 times, if we consider it to be solid to the
centre.
Let us now try to find out something about the inner half-mass of
the earth, and the first thing we have got to bear in mind is, that
where it comes in contact with it, its density must be the same as
that of the outer half-mass at the same place, and continue to be
so for a considerable distance, varying much the same as the other
varies in receding from that place, and diminishing at the same rate
as it diminishes. This being the case--and we cannot see how it can be
otherwise--if we attempt to distribute the inner half-mass over the
whole of the inner half-volume, and suppose that its density decreases
from its contact with the outer half--where it was found to be 8·8
times that of water--to zero at the centre, in direct proportion to
the distance; then, it is clear that at half the distance between
that place and the centre, the density must be just 4·4 times that of
water. Now, if we divide the outer moiety of the inner half-mass of the
earth--that is, the distance between the diameters of 6284·5 miles and
3142·25 miles--into layers of 25 miles thick each, take their volumes
from Table IV., and multiply each of them by a corresponding density,
decreasing from 8·8 to 4·4, we shall obtain a mass far in excess of
the whole mass corresponding to the inner half of the earth. This
shows that a region of no density would not be at the centre but would
begin at a distance very considerably removed from it. It is another
notice to us that the earth must be a hollow sphere. But why should
there be a zero point or place of no density? And what would a zero of
no density be? It would represent something less than the density of
the nebulous matter out of which the earth was formed; and all that
we have contended for, as yet, is that there is a space at the centre
where there is no greater density than that corresponding to the earth
nebula; but we must now go farther.
If the earth is a hollow sphere, it must have an internal as well as
an external surface. But how are we to find out what is the distance
between these two surfaces? Let us, to begin, take a look at the hollow
part of the sphere. From the time of Arago it began to be supposed that
there is a continual deposit of cosmic matter upon the earth going on,
and since then it has been proved that there is a constant and enormous
shower of meteors and meteorites falling upon it. But although this is
the case on the exterior surface, it may be safely asserted that on
the interior surface, where the supply of cosmic matter must have been
limited from the beginning, there can be no continual deposit of such
matter going on now; nor can there have been from, at least, the time
when the earth changed from the form of vapour to a liquid state. We
may, therefore, be sure that there is no undeposited _cosmic_ matter
of any kind in the hollow of the sphere, and that, as far as it is
concerned, there is an absolute vacuum.
TABLE V.--CALCULATIONS OF THE VOLUMES AND DENSITIES OF
THE OUTER HALF OF THE EARTH--TAKEN AS A HOLLOW
SPHERE--AT THE DIAMETERS SPECIFIED, AND REDUCED
TO THE DENSITY OF WATER.
With mean diameter of 7918 miles. Diameter of half-volume at
6284·5 miles, and density there of 8·8 times that of water.
-----+-------+---------------+-------+----------------+--------------+
Diam.|Densi- | Volumes | Avgs. | Volumes at | Observations.|
in | ties. | in Cubic | of |Density of Water| |
miles| | Miles. |Density| in Cubic Miles.| |
-----+-------+---------------+-------+----------------+--------------+
| | | | |{ Half-volumes|
| | | | |{ of the earth|
7918 | ... |129,961,924,377| ... | 735,584,493,738|{ actual and |
| |---------------| |----------------|{ at density |
| | | | |{ of water. |
| | | | | |
| | | | |{ Density at |
| | | | |{ 7914 miles |
| | | | |{ in diameter.|
7914 | 2·0000| 393,724,522 | 1·0000| 393,724,522|{ The 2 miles |
| | | | |{ above being |
| | | | |{ at density |
| | | | |{ of water. |
7905 | 2·5000| 491,596,266 | 2·2500| 1,106,090,598| |
| | | | | |
7900 | 3·0000| 883,309,189 | 2·7500| 2,429,097,520| |
| |---------------| |----------------| |
| | | | |{ Volume to |
| | 1,768,628,977 | | 3,928,912,640|{ 9 miles deep|
| | | | |{ at density |
| | | | |{ of water. |
7850 | 3·1823| 4,870,723,550 | 3·0912| 15,056,380,638| |
| | | | | |
7800 | 3·3625| 4,809,069,650 | 3·2724| 15,737,199,523| |
| | | | | |
7750 | 3·5437| 4,747,808,450 | 3·4531| 16,394,666,359| |
| | | | | |
7700 | 3·7250| 4,686,939,950 | 3·6343| 17,023,745,860| |
| | | | | |
7650 | 3·9062| 4,626,464,150 | 3·8156| 17,652,736,611| |
| | | | | |
7600 | 4·0875| 4,566,381,050 | 3·9969| 18,251,368,419| |
| | | | | |
7550 | 4·2688| 4,506,690,650 | 4·1781| 18,829,404,185| |
| | | | | |
7500 | 4·4500| 4,447,392,950 | 4·3594| 19,387,964,826| |
| | | | | |
7450 | 4·6312| 4,388,487,950 | 4·5486| 19,926,368,386| |
| | | | | |
7400 | 4·8125| 4,329,975,650 | 4·7219| 20,445,712,022| |
| | | | | |
7350 | 4·9938| 4,271,856,050 | 4·9031| 20,945,337,398| |
| | | | | |
7300 | 5·1750| 4,214,129,150 | 5·0844| 21,426,318,250| |
| | | | | |
7250 | 5·3562| 4,156,794,950 | 5·2656| 21,888,019,489| |
| | | | | |
7200 | 5·5375| 4,099,853,450 | 5·4469| 22,331,491,757| |
| | | | | |
7150 | 5·7187| 4,043,304,650 | 5·6281| 22,756,152,901| |
| | | | | |
7100 | 5·9000| 3,987,148,550 | 5·8093| 23,162,542,072| |
| | | | | |
7050 | 6·0813| 3,931,385,150 | 5·9907| 23,551,749,018| |
| | | | | |
7000 | 6·2625| 3,876,014,450 | 6·1719| 23,922,373,584| |
| | | | | |
6950 | 6·4438| 3,821,036,450 | 6·3532| 24,275,808,774| |
| | | | | |
6900 | 6·6250| 3,766,451,150 | 6·5344| 24,611,498,395| |
| | | | | |
6850 | 6·8062| 3,712,258,550 | 6·7156| 24,930,043,518| |
| | | | | |
6800 | 6·9875| 3,658,458,650 | 6·8968| 25,231,657,617| |
| | | | | |
6750 | 7·1688| 3,605,051,450 | 7·0782| 25,517,275,173| |
| | | | | |
6700 | 7·3500| 3,552,036,950 | 7·2594| 25,785,657,035| |
| | | | | |
6650 | 7·5312| 3,499,415,150 | 7·4406| 26,037,748,365| |
| | | | | |
6600 | 7·7125| 3,447,186,050 | 7·6218| 26,273,762,636| |
| | | | | |
6550 | 7·8938| 3,395,349,650 | 7·8032| 26,494,592,389| |
| | | | | |
6500 | 8·0750| 3,343,905,950 | 7·9844| 26,699,082,667| |
| | | | | |
6450 | 8·2562| 3,292,854,950 | 8·1656| 26,888,136,380| |
| | | | | |
6400 | 8·4375| 3,242,196,650 | 8·3468| 27,061,966,998| |
| | | | | |
6350 | 8·6188| 3,191,931,050 | 8·5282| 27,221,426,381| |
| | | | | |
6300 | 8·8000| 3,142,058,150 | 8·7094| 27,365,441,252| |
| | | | | |
6284½| 8·8000| 962,684,511 | 8·8000| 8,471,623,697| |
| |---------------| |----------------| |
| |129,961,924,688| | 735,484,165,215| |
| | | | | |
True half-volume at density of water | 735,584,493,738| |
-------------------------------------+----------------+--------------|
Deficiency | 100,328,522| |
-------------------------------------+----------------+--------------+
As to how far the internal surface is from the centre, it may be
possible to designate a position, or region, from which it cannot be
very far distant, although we can never expect to be able to point out
exactly where it is. Going back to the time when the whole earth was
in a molten liquid state, and just before the outer surface began to
become solid, it is certain that the interior surface must have been
in the same liquid condition, whatever may have been the condition of
the mass of matter between the two surfaces, owing to the pressure
of superincumbent matter; nay, we may be sure that whatever may be
its state now, it continued liquid long after the other became solid,
because it had no outlet by which to get rid of its melting heat by
radiation, nor weight of superincumbent matter to consolidate it; and
it would always be much hotter than the outer surface. At that time we
have every reason to believe that the outer surface was at least as
dense as it is now, there being no water upon it to lower its average
density, as is the case at the present day; and we have equal reason
to consider that the density at the inner surface, whether liquid or
solid, is now at least equal to what the outer surface was then. Duly
considering, therefore, the absence of water from the interior surface,
we shall suppose that the first layer of 25 miles thick upon it will
have an average density of 2-1/2 times that of water, terminating at
3 times, which is the density we have taken for the outer surface
at 9 miles deep. But there is another contingency, which it will be
necessary to take into consideration before going any farther.
It has been understood--as it is certainly the truth--in the
calculations made with respect to the outer half of the mass of the
earth, that the increase of density in descending was due to the
pressure of the superincumbent matter, caused by the attraction for it
of the inner half, as well as that of the whole of both the outer and
inner halves on the other side of the hollow interior. In the case of
the inner half we have now to consider that the attraction of the outer
half alone would be the effective agent, and that the superincumbent
pressure--that is, of course, the pressure acting from the centre
outwards--would be interfered with, or perturbed, by the attraction of
the mass on the other side of the hollow interior, so that it would
not exert its full power in that direction. But that does not mean
that the density would be in any way diminished. The attractions of
the planets for each other perturb them in their revolutions around
the sun, accelerating or retarding each other, but do not increase
or diminish their density or mass; only it will lead us to expect
that the same depth of 817 miles will not produce the same amount of
pressure outwards at the meeting of the two halves as it does inwards,
and that to obtain an equal pressure a greater depth will be required.
We believe that an expert mathematician, taking as bases two opposite
pyramids in a sphere, similar to those we have used in a former part
of our work, could point out, with very approximate accuracy, what
ought to be the distance of the inner surface of the shell from the
centre--provided a maximum density were determined for the earth--but
that goes beyond our powers, and we shall limit ourselves to the use of
our own implements; which will cause us to depart from the statement
we have made, that the density of the inner half must decrease from
the place of meeting of the two halves, at the same rate as the outer
half had increased. It must decrease much more rapidly than the other
increased. All this premised, and having established a density of 3 for
the interior surface, we may proceed to calculate where that surface
ought to be, so as to give for the interior half of the earth a mass
equal to 735,584,493,738 cubic miles of water.
If we begin our operations with a density of 8·8 times that of water
at the meeting of the two halves of the shell, and diminish it for any
considerable distance at the same rate as it increased when we were
finding the mass of the outer half, that is 0·1812 for each layer, we
soon find that before we could make up the whole mass of the inner
half of the shell, the density would be decreased to at least that of
water, which cannot be, as there can be no liquid or solid matter of
any kind of so low density anywhere in the interior half of the shell.
Furthermore, if we decrease it at the same rate as the volumes of the
different layers of the earth decrease as they approach the centre, it
involves a mass of calculation that serves no useful purpose, as such
calculations bring no contingent of satisfaction with them; because
all the densities with which we are dealing have to be brought to a
rational form before we can frame a proper approximate idea of what
the interior construction of the earth is, as will be seen hereafter;
and because it takes no account of the perturbation--above alluded
to--produced by the attraction of the matter on the opposite side of
the hollow. But, in order to get such a result as we can with our
limited powers, if we begin with a density of 8·8 at the diameter of
6284·5 miles and fix the density of 3--which we have adopted above--at
the diameter of 3200 miles, we shall get a mass somewhat less than
one-half of the earth; and with a density of 2·91 at 3150 miles
diameter we get a mass of 735,713,884,116 cubic miles of water, which
is rather greater than one-half of the mass required (see operations
of Table V.). This density of 2·91 reduced to 2·5, as we mentioned,
might be done when we were fixing the number 3, would make very little
difference on the resulting mass, compared with what we have been in
quest of.
Here we may state that we found that, had the calculations been made
with documents of density proportioned to the decrease of the volumes
of the layers of the earth as they approached the centre, the density
would have been reduced to 2·25 at 3150 miles in diameter; which tends
to show that should that process be considered to be more accurate, it
would not have made any great difference on the result.
With all, we may consider that it has been demonstrated, that the
greatest density of the earth is not necessarily greater at any part of
its interior than 8·8 times that of water.
TABLE VI.--CALCULATIONS OF THE VOLUMES AND DENSITIES
OF THE INNER HALF OF THE EARTH, ON THE SAME
DATA AS THOSE FOR THE OUTER HALF.
------+---------------+---------+----------------+--------------+
Diam. | Volumes |Densities| Volumes at | Observations.|
in | in Cubic | |Density of Water| |
miles | Miles. | | in Cubic Miles.| |
------+---------------+---------+----------------+--------------+
6284½|129,961,924,688| | 735,584,493,737|}Half-volumes |
|---------------| |----------------|}of the earth.|
6250 | 2,129,893,439| 8·800 | 18,743,062,263| |
| | | | |
6200 | 3,043,490,450| 8·705 | 26,493,584,367| |
| | | | |
6150 | 2,994,795,650| 8·610 | 25,785,090,546| |
| | | | |
6100 | 2,946,493,550| 8·515 | 25,089,392,578| |
| | | | |
6050 | 2,898,584,150| 8·420 | 24,406,078,543| |
| | | | |
6000 | 2,851,067,450| 8·325 | 23,735,136,521| |
| | | | |
5950 | 2,803,943,450| 8·230 | 23,076,454,654| |
| | | | |
5900 | 2,757,212,150| 8·135 | 22,429,920,840| |
| | | | |
5850 | 2,710,873,550| 8·040 | 21,795,423,342| |
| | | | |
5800 | 2,664,927,650| 7·945 | 21,172,850,179| |
| | | | |
5750 | 2,619,374,450| 7·850 | 20,562,089,432| |
| | | | |
5700 | 2,574,213,950| 7·755 | 19,963,029,182| |
| | | | |
5650 | 2,529,446,150| 7·660 | 19,375,557,509| |
| | | | |
5600 | 2,485,071,050| 7·565 | 18,799,562,493| |
| | | | |
5550 | 2,441,088,650| 7·470 | 18,234,932,216| |
| | | | |
5500 | 2,397,498,950| 7·375 | 17,681,554,755| |
| | | | |
5450 | 2,354,301,950| 7·280 | 17,139,318,196| |
| | | | |
5400 | 2,311,497,650| 7·185 | 16,608,110,615| |
| | | | |
5350 | 2,269,086,050| 7·090 | 16,087,820,094| |
| | | | |
5300 | 2,227,067,150| 6·995 | 15,578,334,714| |
| | | | |
5250 | 2,185,440,950| 6·900 | 15,079,542,555| |
| | | | |
5200 | 2,144,207,450| 6·805 | 14,591,331,697| |
|---------------| |----------------| |
| 56,339,575,889| | 442,428,177,291| |
-------+---------------+---------+----------------+--------------+
5150 | 2,103,366,650| 6·710 | 14,113,590,222| |
| | | | |
5100 | 2,062,918,550| 6·615 | 13,646,206,207| |
| | | | |
5050 | 2,022,863,150| 6·520 | 13,189,067,738| |
| | | | |
5000 | 1,983,200,450| 6·425 | 12,742,062,891| |
| | | | |
4950 | 1,943,930,450| 6·330 | 12,305,079,748| |
| | | | |
4900 | 1,905,053,150| 6·235 | 11,878,006,390| |
| | | | |
4850 | 1,866,568,550| 6·140 | 11,460,730,897| |
| | | | |
4800 | 1,828,476,650| 6·045 | 11,053,141,349| |
| | | | |
4750 | 1,790,777,450| 5·950 | 10,655,125,828| |
| | | | |
4700 | 1,753,470,950| 5·855 | 10,266,572,412| |
| | | | |
4650 | 1,716,557,150| 5·760 | 9,887,369,184| |
| | | | |
4600 | 1,680,036,050| 5·665 | 9,517,402,223| |
| | | | |
4550 | 1,643,907,650| 5·570 | 9,156,565,611| |
| | | | |
4500 | 1,608,171,950| 5·475 | 8,804,741,426| |
| | | | |
4450 | 1,572,828,950| 5·380 | 8,461,819,751| |
| | | | |
4400 | 1,537,878,650| 5·285 | 8,127,688,665| |
| | | | |
4350 | 1,503,321,050| 5·190 | 7,802,236,249| |
| | | | |
4300 | 1,469,156,150| 5·095 | 7,485,350,584| |
| | | | |
4250 | 1,435,383,950| 5·000 | 7,176,919,750| |
| | | | |
4200 | 1,402,004,450| 4·905 | 6,876,831,827| |
| | | | |
4150 | 1,369,017,650| 4·810 | 6,584,974,897| |
| | | | |
4100 | 1,336,423,550| 4·715 | 6,301,237,038| |
| | | | |
4050 | 1,304,222,150| 4·620 | 6,025,506,333| |
| | | | |
4000 | 1,272,413,450| 4·525 | 5,757,670,861| |
|---------------| |----------------| |
| 96,451,524,689| | 671,704,075,372| |
-------+---------------+---------+----------------+--------------+
| | | | |
3950 | 1,240,997,450| 4·430 | 5,497,618,693| |
| | | | |
3900 | 1,209,974,150| 4·335 | 5,245,237,939| |
| | | | |
3850 | 1,179,343,550| 4·240 | 5,000,416,652| |
| | | | |
3800 | 1,149,105,650| 4·145 | 4,763,042,919| |
| | | | |
3750 | 1,119,260,450| 4·050 | 4,533,004,823| |
| | | | |
3700 | 1,089,807,950| 3·955 | 4,310,190,441| |
| | | | |
3650 | 1,060,748,150| 3·860 | 4,094,487,859| |
| | | | |
3600 | 1,032,081,050| 3·765 | 3,885,785,163| |
| | | | |
3550 | 1,003,806,650| 3·670 | 3,683,970,405| |
| | | | |
3500 | 975,924,950| 3·575 | 3,488,931,696| |
| | | | |
3450 | 948,435,950| 3·480 | 3,300,557,106| |
| | | | |
3400 | 921,339,650| 3·385 | 3,118,734,715| |
| | | | |
3350 | 894,636,050| 3·290 | 2,943,352,605| |
| | | | |
3300 | 868,325,150| 3·195 | 2,774,298,854| |
| | | | |
3250 | 842,406,950| 3·100 | 2,611,461,545| |
| | | | |
3200 | 816,881,450| 3·005 | 2,454,728,757| |
| | | | |
3150 | 791,748,650| 2·910 | 2,303,988,572| |
|---------------| |----------------| |
|113,596,348,539| | 735,713,884,116| |
| | | |{ True |
| | | 735,584,493,738|{ half-volume |
| | |----------------| |
| | | 129,390,378| Excess |
-------+---------------+---------+----------------+--------------+
CHAPTER X.
PAGE
184 Inquiry into the interior construction
of the earth--_continued_.
185 Density of 8·8 times that of water still too high for the
possible compression of the component matter of the
earth as known to us.
186 Reasons for this conclusion drawn from crushing strains
of materials.
187 A limit to density shown thereby.
188 The greatest density need not exceed 6·24 of water.
189 Gases shut up in the hollow centre. Their weight must so far
diminish the conceded maximum of 6·24.
190 Density of inner half of earth at 3000 miles diameter. Greatest
density may be less than 5·833 of water.
191 Supposed pressure of inclosed gases very moderate.
193 Meaning of heat limit to density. Temperature of interior half
of shell and inclosed gases must be equal.
194 State of the hollow interior.
195 Results of the whole inquiry.
INQUIRY INTO THE INTERIOR CONSTRUCTION OF THE EARTH--_continued_.
It may be well to revert here to the experiment we made of putting
a cubic foot of rock, of specific gravity 13·734 in the scale of a
balance at the centre of the earth, where we saw that it could not
depress the scale one hair-breadth, and make the same experiment by
placing a cubic foot of rock of 8·8 specific gravity in the same scale,
at what we have called the region of greatest density of the earth,
that is, at 817 miles from its surface. Here, also, we shall find that
the scale is not depressed for the very same reason as in the former
case, that is because it had nowhere to be depressed to; and it might
be argued that for the same reasons advanced formerly there can be no
matter at that place, but the cases are entirely different. In the
first case, there is nearly the whole mass of the earth drawing the
matter away from the centre were it at liberty to move; whereas, in
the second case, the meeting of the two halves of the shell, at the
region where there is the greatest mass of matter, is also the meeting
place of the action of attraction in its greatest force; the place to
which matter is attracted from all sides, remains stationary, and it
is held there both by attraction and weight of superincumbent matter
or gravitation. The attraction of the whole earth acts as if it were
concentrated at its centre, but that is for external bodies. That kind
of attraction on the inner half of the shell would be far inferior to
that outwards of the outer half, owing to its greater distance and
conflicting nature, and would perturb, as we have said, but not do
away with it. The same could not occur at the centre, because it is
not the centre of the mass, that is, it is not the place where the
greatest quantity of matter existed originally, or is now to be found,
and consequently never was, nor can now ever be, the actual centre of
interior attraction.
It has been said when treating of the earth as being solid to the
centre, that it is not easy to comprehend what may be the nature of
the rocks we are acquainted with, when compressed to one-fourth or
one-fifth of their volume, and we do not find ourselves much better off
when we contemplate them as reduced to one-third or one-fourth of their
bulk, that is, when a cube of one foot is reduced to three or four
inches in height, as would be the case with it at a maximum density of
8·8 times that of water when placed at a depth of 817 miles from the
surface of the earth. We find, therefore, the idea thrust upon us that
there may be a limit to density, perhaps not an absolute limit, but a
practical one; in which case, the greatest density of the earth may not
greatly exceed 5·66 times that of water. For, if we conceive that it
increases to its maximum at 100 miles from the surface, and continues
nearly uniform thereafter, a little calculation will show that the
greatest density of the outer half of the shell need not much exceed
6 times that of water; and, of course, the same will be the case with
the inner half should its density be almost uniform till 100 miles from
the inner surface is reached. It might even so happen that at a depth
of 25 to 30 miles the practical limit might be reached; for a column
of granite of one foot square and 25 miles high would weigh, and exert
a pressure upon its base of 10,000 tons, a pressure equal to nearly
fifteen times what would be sufficient to crush it into powder; in
which case the greatest density of the earth might not much exceed the
5·66 that we are accustomed to think of--without thinking.
It may be deemed absurd to think that there is even a practical
limit to the density of matter, but on the other hand it is much
more absurd to suppose that there is not an absolute limit to it. We
cannot conceive of density being other than the result of compression,
and we cannot believe that matter can be compressed more and more
continually for ever. There must be some end to compression. Perhaps it
was the difficulty in conceiving of rock being compressed to so small
a fraction of its volume as would enable it to take its place at the
centre of the earth--where it has been said that, "it must weigh like
lead"--that originated the idea of its centre being occupied by the
metals, arranged as they would be in a rack in a store, the heaviest
pieces at the bottom of the rack, and the lighter ones higher up.
When fairly looked at, density would really seem to have a limit,
except in so far as it may be combined with heat. We know that water
is compressed 0·00005 part of its volume for every atmosphere of
pressure to which it is subjected. But 0·00005 for round numbers, is in
fractional numbers 1/20,000; therefore a pressure of 20,000 atmospheres
would compress a cubic foot of water into 1/20,000 of a foot in height,
or practically into nothing. We know, also, that as a column of water
33·92 feet high balances one atmosphere, one mile in height will be
equal to 155·66 atmospheres, and 20,000 atmospheres will produce a
pressure equal to a column of water 128 miles high; therefore, a cubic
foot of water, subjected to such a pressure, would be compressed into
virtually nothing. Again, supposing that we have a column of liquid
rock, of 2-1/2 times the density of water, of the same height of 128
miles, we should have a pressure of 2-1/2 times that of the column of
water; and as we have no reason to believe that granite in a liquid
state has to obey a different law of compression to the one obeyed by
liquid ice; then a column of granite 51 miles high would be sufficient
to squeeze its own base, not only off the face of the earth but out of
the bowels thereof. It will be seen, therefore, that at 100 miles deep
from the surface, the density of the earth might well be equal to not
only 5·66 times the density of water but to a great deal more; and that
our estimate of 3 times the density of water, at 9 miles deep, was far
within the mark.
The authors of text-books on the strength of materials tell us that
"the Modulus of Elasticity of any material, is the force that would
lengthen a bar of that material of 1 inch square to double its length,
or compress it till its length became zero; supposing it possible to
stretch or compress the bar to this extent before breaking." This is
neither more nor less than a counterpart of the law of gases, upon
which the air thermometer is constructed, applied to solid matter, and
may be used in the same manner. But we can never produce a perfect
vacuum, and so annihilate a gas and temperature; neither can we
annihilate matter, nor easily reduce it to one half of its volume. Now,
we have seen, a little way back, that a column of granite 25 miles high
would exert a pressure at its base 15 times as great as would crush it
to pieces; so that a column of 25÷15, or 1·66 miles high would destroy
the elasticity of the material, because, when crushing takes place,
all elasticity is gone. We cannot, therefore, get much satisfaction
out of any calculations made upon the theory of the strength of
materials; still, by them, we can make more plain the absurdity of any
notion of the indefinite compressibility of matter. But if, in the
face of contravening its conditions, we follow the reasoning used for
the formation of the theory, and take the modulus of elasticity for
granite as 2,360,000 feet, then the same modulus would compress a bar
of granite of 1 inch square in section till its height became zero. And
as that length is equal to 447 miles, at that depth from the surface of
the earth, granite or any other rock or stone of a similar nature would
be compressed out of existence by the weight of the superincumbent
matter.
Thus we have arrived at two measures of force which would compress
to zero the rocks that are known upon the earth. One where rocks are
looked upon as in a molten, liquid state, and analogous to water, where
the force is equal to that exerted by a column of the material 51 miles
high; and the other where the column requires to be 447 miles high.
In either case the same method of calculation will show that columns
one-half of these heights, will compress the material into at least
one-half of its volume--that is half-way between what it is at the
surface and would be at the specified depths--and consequently into
double its density. So we find in the one case that the density of the
earth ought to be about 5·66 times that of water at a depth of 25-1/2
miles; and, in the other, at somewhere less than 225 miles deep. But,
before proceeding to use and reason upon these depths, we must recall
to mind that the calculations from which we have derived them, in the
second case, have been made in violation of the theory that was adduced
for the purpose, and that in consequence the latter depth must be
excessive. For, were we to erect a structure of any kind, calculating
the stresses it would have to bear, under the same violation of the
theory, we should inevitably find that the structure would give way
under the strains that would be brought upon it; that is the columns
25-1/2 and 225 miles high would compress the same kind of matter
composing them into very far below one-half of its volume.
This premised, let us go back to our layers of 25 miles thick with
their respective volumes. Nine of them counted from the diameter of
7900 miles inwards, will be equal to 225 miles and will bring us to
234 miles deep, which at the same time that it leaves us the same
volume and mass that we have always retained for the first 9 miles in
depth, will facilitate our calculations considerably without making
any appreciable difference in them. We shall then have to find for the
9 layers 9 corresponding densities increasing from 3 to 5·66, and if
we multiply these together respectively, and add the numbers of the
volumes and masses of the outer 9 miles in depth, we shall get, at
the diameter of 7450 miles, a simple volume of 43,418,587,327 cubic
miles, and mass volume of 195,312,523,450 cubic miles. Deducting this
latter sum from 735,584,493,738 cubic miles, which represents the
half mass of the earth at the density of water, we have a remainder
of 540,271,970,288 cubic miles. On the other hand we find that the
simple volume of the earth comprehended between the diameters of
7450 and 6284·5 miles is 86,543,337,361 cubic miles; so that if we
divide 540,272,970,288 by this sum, we find that a density of 6·24
times that of water over the whole intervening space--between the
two diameters just cited--will make up the whole half-volume, at the
density of water, from the surface of the earth to the diameter of
6284·5 miles. Then, for the inner half-mass:--If we multiply the simple
volume between the diameters of 6284·5 miles, and 3150 miles, which
is 113,596,348,539 cubic miles by 6·24, we get 708,841,214,870 cubic
miles at density of water; and if from there we run down the density to
3 at 2700 miles in diameter we get 27,400,652,354 cubic miles, which
added to the last mentioned amount gives 736,241,867,224 cubic miles,
somewhat in excess of the inner half-mass of the earth at density of
water. Thus we see that in order that the average density of the earth
of 5·66 may be made up, there is no necessity for appealing to matter
of any kind with a density of more than 6·24 times of water. And there
is still something else of importance to be taken into consideration
before we can bind ourselves to a density even so great as that.
We have said, a few pages back, that there can now be no undeposited
cosmic matter in the interior of the hollow earth, and that as far
as such matter is concerned the hollow part may be a perfect vacuum.
This is not absolutely true, for gases may be cosmic matter, just the
same as any others of the elements out of which the earth is formed,
but what is generally meant by cosmic matter is solid--at least, we
have always looked upon it in that light--and all solid matter must
have been deposited upon the interior surface at an immeasurably long
period of time before the nebula forming the earth came to have even
the density of water; certainly before it came to be in a molten liquid
state; and we did not want to introduce any posterior evolutions in
order not to complicate our calculations, and also to obtain some
tangible bases to which the consequences of these evolutions might be
applied. But as we have now both form and density to work upon we may
take them into account, and it will be found that neither of these two
bases will be very materially altered by them.
When the earth was in a molten liquid state, it is believed--as we
have said on a former occasion--to have been surrounded by a dense
atmosphere, composed of gases and vapours of metals, metalloids, and
water, and we have no reason to doubt that the hollow of the sphere
was filled with a similar atmosphere, only the vapour of water would,
most probably, be dissociated into its elements of oxygen and hydrogen.
Also we have every reason to believe that even at the present day
gases are being produced in the interior, one part of which find their
way to the surface and are dissipated into the atmosphere in the same
manner as the gases from the chimney of a furnace; and another part
into the interior, where they could not escape but would be stored
up in the hollow. Thus at the present day there may be an atmosphere
there, composed near the surface of vapours of the elements with gases
above them, so to speak, at a very high degree of pressure. These gases
could not have gone on accumulating always, but must have found an
exit in some particular place, or places, when the pressure exceeded
the resistance, or when this was diminished by some convulsion such
as an earthquake; but we do not want to define too much, or make more
suppositions on this point than what present themselves to us in a
reasonable way. All that we need say is, that the resisting power
of some thousands of miles of solid, or even viscous, matter must
be enormous, and the pressure necessary to force its way through it
must have been equal to many thousands of atmospheres. We know that a
pressure of 773·4 atmospheres condenses air to the density of water,
and it must be the same with any similar gas; so we have only to
suppose that the pressure is 4827 atmospheres--which is equal to 773·4
multiplied by 6·24--in order to bring the whole of the gases, and
vapours of elements, in the hollow to the same density of 6·24 times
that of water, which we have shown need not be exceeded in any part of
the earth. And such being the case, we can place the division between
solid and gasiform matter in any point of the radius that may seem to
us reasonable, only we must always have as much solid matter in the
inner as in the outer half-mass of the earth.
Following nearly the result we have obtained in another way, by
placing the division of the hollow part at 3000 miles in diameter,
the volume of which is 14,137,200,000 cubic miles, and multiplying
this by 6·24, we get a mass equal to 88,216,128,000 cubic miles at
density of water, composed of vaporous and gaseous matter in the hollow
centre, and consequently much greater than is required to make up the
total mass of the earth at the density of water; which shows that the
density of the mass between the diameters of 7450 and 3000 miles must
be less than 6·24 times that of water. How much less is very easily
found, by dividing the surplus of 88,216,128,000 cubic miles over the
whole volume between 7450 miles in diameter and the centre, because
in this way we shall include the whole mass arising from both solid
and gasiform matter. This whole volume--that of a globe 7450 miles in
diameter--is 216,505,262,050 cubic miles, which, divided by the surplus
gives the amount 0·407 as the density to be deducted from 6·24 on its
account, and therefore the greatest density of any part of the earth
need not be over 5·833 times that of water.
This result derived from our operations will be acknowledged, we doubt
not, to be much more satisfactory, we might say, more comprehensible,
than to have to believe that our known rocks and stones could be
compressed till they were 13·734 or even 8·8 times heavier than water.
At first sight 4827, say 5000, atmospheres or 75,000 lb. on the square
inch, appears to be an enormous pressure, but it is nearly almost as
nothing compared to the pressures we have been dealing with. A column
of granite 1 mile high would exert a pressure upon its base of 6050 lb.
per square inch, and one of 25 miles high of 151,200 lb., or double the
number of atmospheres we have applied to the gases in the hollow of
the earth. If we take a column 225 miles high, such as we considered
to be the least that would be necessary to compress granite into
one-half of its volume, we get 1,360,860 lb. per square inch, or over
90,000 atmospheres of pressure; and if we go into thinking of columns
of 447 and 817 miles--this last being the depth from the surface of
the division of the matter of the earth into two equal portions--we
could have gases compressed to 174,600 and 326,700 atmospheres or,
dividing the numbers by 773·4, 222 and 422 times the density of water;
so there is no cause to stumble over high pressure. With even 10,000
atmospheres, more than double the number assumed, we should have gases
as heavy as the material we found at the centre of the earth, when we
were looking upon it as solid to the centre--which was 13·734 times the
density of water--and so get rid of burying the precious metals where
they would be "matter in the wrong place," and according to D'Israeli's
definition, justly entitled to the epithet applied to them, sometimes,
by people who have never been blessed with a superabundant supply of
them. At the same time, we find out what we knew before, viz. that we
may have gases heavier than the heaviest metals and as rigid as steel,
if we can only find a vessel strong enough to compress them in, along
with the means of doing it; and also that the thousands of miles of
highly compressed matter, between the hollow centre and the surface of
the earth, are far more than sufficient to imprison gases of far, very
far, greater elasticity than our modest measure of 5000 atmospheres.
And we hope to be able to show presently good reason for believing that
the gases compressed in the hollow, at what may really be considered
as very high pressures, have had, and may probably still have, a very
important part to play in the evolution of the earth.
We have just seen that the pressure produced by a column of granite 1
mile high would be 6050 lb. per square inch, consequently one of double
the height, or 2 miles, would exert a pressure of 12,100 lb. per square
inch at its base, equal to the crushing strain of the very strongest
granite we know, while at the same time that strain would not amount to
one-sixth of 4827 atmospheres; so that if the gases in the hollow of
the earth were at a pressure of only 800 atmospheres, their pressures
would be able to crush granite of that class to pieces, and therefore
the estimate of specific gravity of 3 for the density of the interior
surface--which we made at the beginning of our calculations for the
hollow sphere--cannot be looked upon as by any means exaggerated.
We might now reform our calculations of the two halves of the interior
of the earth, giving a more rational and curve-like form to the
densities, under the supposition that at much less distance than 234
miles from the surface, matter might be compressed to its utmost limit;
but as, according to our demonstration, the solid matter of the earth
must have been divided into two equal parts at the place where the
greatest mass was, long before it could have been condensed into a
state to compress gases; and as the total mass of solid matter must,
in order to make up the total mass of the earth, depend to some extent
on the mass of imprisoned gases; we are unable to make any reform much
different to what our calculations show. Besides, as the difference
between average densities of 5·66 and 5·67 makes a difference of
2,600,000,000 cubic miles on the mass of the earth reduced to the
density of water, very approximate accuracy cannot be attained in any
calculations.
What is meant by a limit to density except in so far as it is combined
with heat, is that whatever density may be given to matter by
compression when it is in a heated state, a greater density will be
found in it when it is deprived of that heat; that whatever may be the
density of any part of the interior of the earth in its present state,
that density will be increased when the earth becomes cooled down to
the temperature derived from the heat of the sun, or to absolute zero
of temperature, if such there be, on account of shrinking in cooling;
and that therefore there can be no absolute limit to density as long as
there is any heat in matter.
It may not be unnecessary for us to recognise now that the weight of a
column of granite would decrease as the depth increased, for the force
of gravitation would be diminished by having a part of the attraction
of the earth above instead of below it; but at 100 miles in depth the
diminution would be only about one-eighth--if distance is taken into
account--of the 817 miles down to the plane of greatest density, and
1/2200th part if the mass left above is considered; differences that
would make extremely little alteration on our calculations.
It will not be out of place either to take a look at what may be
the temperature of the interior of the shell, and of the gases shut
up in the hollow part of the earth; and we have not much to say on
the subject, because we shall not depart from the system we have
followed up till now, with considerable strictness, of not theorising
or speculating on what may be; but will restrict our observations
to theories that have been very generally adopted by astronomers,
geologists, and scientists in general. The air thermometer will be
of no use to us, for whatever may have been the temperature when
the earth was in the process of formation, it must have diminished
very greatly during the cooling process it has undergone since, and
we know that gases heated in a closed vessel in such manner that
pressure and temperature will agree to the theory on which the air
thermometer is constructed, may be cooled down afterwards to almost
any degree required, and the relation between temperature and pressure
destroyed thereby. At one time it was thought that the earth had only
a solid crust, and that, under it, the whole of the interior was in
a molten liquid state. Then some physicists thought that, through
pressure of superincumbent matter, solidification must have begun at
the centre; others that it began almost simultaneously at the surface
and centre, and that there may still be a liquid mass between the two
solidifications--this is repeating what we have said before, but it is
done only to bring it to mind. We, at present at least, do not want
to have anything to do with any of these theories, only we believe
that we have shown in an indisputable manner that there could be no
solidification at the centre, because there could be no matter there
capable of being solidified--gases could not be solidified under such
pressure, and at all events heat, as there must have been there. We
believe at the same time that no one will deny that the heat of the
earth increases as the centre is approached, and that the temperature
of the interior may be very great. The crust of the earth was at one
time supposed to be only 25 to 30 miles thick, because the increase of
heat at that depth would be sufficient to melt any of the substances
we are acquainted with on the surface--repetition again; but for many
years past it has been deemed necessary to increase the thickness to
even hundreds of miles, for reasons some of which will be alluded to in
due time; and if, even at these depths, the increase of heat were only
sufficient to fuse all the substances we know, it is very certain that
at the interior surface of the shell it must be very much greater, as
heat from there could only be _conducted_ outwards, and the difference
required to cause conduction, of any considerable degree of activity,
through more than 2000 miles must be enormous, according to the
experiments made by various physicists upon metals, which have a very
much higher conducting power than rocks, and especially strata, of any
kind. Therefore there can be no doubt, we think, that the inner surface
of the shell must be at a very much higher temperature than what would
preserve it in its liquid state, and that the matter composing it is
liquid to a depth where it might be solidified by the pressure of
superincumbent matter. We do not see how convection currents could be
instituted, much less kept up, in melted matter, under the viscosity,
and, at least quasi-solidity, sure to be produced by pressure of tens
of thousands of pounds on the square inch, and therefore we do not take
them into account. Any way, whatever may be the temperature of the
interior surface of the shell, the same must be that of the imprisoned
gases, because there convection currents could and must exist--were
they even only created by the rotation of the earth and attraction
of the moon--and cannot fail to keep the whole of the hollow part at
the same temperature. It would be absurd to suppose that these gases
could be at a lower temperature than the upper layers, counted from the
region of greatest density, of the interior surface of the shell.
This section of our work may now be brought to a close by stating the
conclusions at which we have arrived, leaving the results involved
by them to be discussed separately, which we shall proceed to do
immediately without binding ourselves so strictly, as we have done
hitherto, to the avoidance of anything that may be looked upon as
theorising or speculating. We believe we have conducted our operations
in the most strict conformity to the law of attraction, and have no
doubts whatever about the form of the interior of the earth resulting
from them; but there may be some room for small variations in the
details of the various densities, and the position of the interior
surface of the shell, arising from the pressure of the gases in the
hollow centre, and the weight they will, in consequence, add to the
general mass of the earth. The conclusions are as follows:--
(1) That the earth is not solid to the centre, nor is it possible that
it could be, according to the law of attraction, but is a hollow sphere.
(2) That its greatest density must be at the region where the greatest
mass of matter is to be found--as must have been always the case from
the time it was a globe revolving on its axis, whether gasiform,
liquid, or solid--which is now at 817 miles deep from the surface; and
that the greatest density may not be much more than the mean of 5·66
times that of water ascribed to it by astronomers.
(3) That the inner surface of the shell of the hollow globe cannot be
much over or under 2000 to 2200 miles from the outer surface.
(4) That the hollow part of the globe must be filled by an atmosphere
consisting possibly in part of vapours of the chemical elements, and by
gases at a very high degree of pressure.
(5) That the region of greatest density, and the position of the
interior surface of the shell, may be expressed with very approximate
accuracy as follows:--The former must be at 0·7939 of the mean radius
of the earth, and the latter at 0·5479 of the same; both counted from
the centre.
(6) That if the earth is a hollow sphere, the same must be the case
with all the major planets and their satellites, the sun, and all the
suns, or stars, that are seen in the heavens; and that their interior
proportions and form must be in much the same ratios to their radii as
those we have found for the earth.
CHAPTER XI.
PAGE
197 The Earth. The idea entertained by some celebrated men,
and others.
199 Difficulties of forming a sphere out of a lens-shaped nebula.
200 Various studies of the earth's interior made for special purposes.
Difficulty some people find in conceiving how the average
density of little over 5·66 can be possible, the earth being
a hollow sphere.
201 What is gained by its being a hollow shell.
202 Geological theories of the interior discussed. Volcanoes and
earthquakes in relation to the interior.
206 Liquid matter on the interior surface of the shell, and gases
in the hollow, better means for eruptions than magma layers.
207 Focal depths of earthquakes within reach of water,
but not of lavas.
209 Minute vesicles in granite filled with gases, oxygen and hydrogen,
but not water.
211 The Moon. A small edition of the earth.
212 Rotation stopped. Convulsions and cataclysms caused thereby.
Air, water, vapour driven off thereby to far off hemisphere.
Liquid matter in hollow interior would gravitate to the inside
of the nearest hemisphere.
213 Form and dimensions during rotation. Altered form after
it stopped.
214 Agreeing very closely with Hansen's "curious theory."
CONSEQUENCES OF THE EARTH AND MOON BEING HOLLOW BODIES.
_The Earth._--The idea that bodies such as those of the solar system,
even of the whole universe, have their greatest density where the
greatest mass is and are hollow spheres, is so natural and logical,
more especially if it is supposed that they have all been formed out of
some kind of nebulæ, that it seems strange it has never been brought
forward prominently before. We say prominently because we know that the
earth has been considered to be a hollow sphere by very eminent men,
such as Kepler, Halley, Sir John Leslie, and by others of less name
long after them. In support of this last remark, we shall make a few
extracts--with comment on them--from an article on the "Interior of
the Earth" in "Chambers's Journal" for February 1882, which have some
interest in connection with our work.
1. "The great astronomer Kepler, for instance, in seeking to account
for the ebb and flow of the ocean tides, depicted the earth as a
living monster, the _earth animal_, whose whalelike mode of breathing
occasioned the rise and fall of the ocean in recurring periods of
sleeping and waking, dependent on solar time. He even, in his flights
of fancy, attributed to the earth animal the possession of a soul
having the faculties of memory and imagination."
If it could be believed that Kepler had any idea of the earth being
formed out of a nebula, whether hollow, or solid to the centre, the
idea of a breathing animal was almost a consequence, because the
attraction--a thing he is supposed to have known nothing about--of
the original nebula for the earth one, on matter so light as nebulous
matter, would raise enormous tides and make the earth, in its then
state, not far from like an enormous primitive bellows made out of
goatskins. No one knows what dreams may have passed through his brain.
The last part of his notion was altogether fanciful.
2. "Halley was opposed to the idea of the globe being solid, 'regarding
it as more worthy of the Creator that the earth, like a house of
several storeys, should be inhabited both without and within.' For
light, too, in the hollow sphere, he thought provision might in some
measure be contrived." This notion appears to be altogether fanciful,
the fruit of an enthusiastic, exuberant imagination, leaving no trace
of scientific thought upon the subject.
3. "Sir John Leslie, like Halley, conceived the nucleus of the world
to be a hollow sphere, but thought it filled, not with inhabitants,
but with an assumed 'imponderable matter having an enormous force of
expansion.'" It would be interesting to know on what bases he formed
his ideas, as the filling of the hollow with imponderable matter seems
to show more method than the former cases, but we have never seen
any allusion made to his theory anywhere, except in the article we
are quoting from. There may have been some reasons given for such a
supposition in his "Natural Philosophy," but when we began to read that
work in times long past, a more modern one was recommended to us, and
we lost the chance, never to return.
There are other theories referred to in the article, but we shall take
notice of one more only.
4. "A certain Captain Symmes, who lived in the present century, was
strongly convinced of the truth of Leslie's theory. He held that near
the North Pole, whence the polar light emanates, was an enormous
opening, through which a descent might be made into the hollow sphere,
and sent frequent and pressing invitations to A. von Humboldt and Sir
Humphrey Davy to undertake this subterranean expedition! But these
imaginative conceptions must one and all be set aside, and the subject
treated on more prosaic, though not less interesting, lines."
This conception of Captain Symmes will probably be looked upon as the
most absurd of the whole lot, but to us it seems to give evidence of
more thought than any one of them. One would think that he must have
formed some notion of how a hollow sphere, with an opening out to the
surface at each one of its two poles, could be formed. We must note
that he lived in, possibly after, the time of Laplace.
We doubt whether anyone has ever studied out thoroughly how even a
solid sphere could be ultimately elaborated from a nebula. It has
always been a very general idea that a condensing and contracting
nebula would, under the areolar law, assume the form of a lens rather
than of a sphere. If this be so in reality, we may ask: How can the law
of attraction produce a sphere out of a lens-shaped mass of rotating
vaporous or liquid matter? It seems evident that to bring about
such a result attraction must cease to act altogether in the polar
directions, and only continue to draw in the matter from the equatorial
directions of the lens, till the desired sphere was formed; and, How
were the action and inaction of the law of attraction to be regulated
meanwhile? Or, when the time came that a sphere of a pre-arranged
diameter could be formed, a goodly part of the lens must have been
cut off and abandoned; in which case we have again to ask: What was
done with the surplus, the cuttings? No doubt they could be used up in
meteor swarms, comets, or something; but Captain Symmes's theory has
opened up a field for a good deal of thought, and our present knowledge
of polar matters prevents us from being sure that strange discoveries
may not be made as to the condition of the earth at the poles, although
there may not actually be holes into the hollow interior. With regard
to the last sentence of the quotation, we fully agree and are doing our
best to comply with it. And in so doing, we shall have to return to
the formation of globes out of nebulæ, elaborated into something more
advanced than even lens-shaped discs.
There is no doubt that the reasons assigned by most, if not all, of
the authors of the notions above cited are very fanciful, but one can
hardly believe that the true reason--why the earth must be hollow--has
not occurred to some of them; and that they did not follow it out
because it involved too much work, and they did not feel inclined to
undertake it, or had not time. On the other hand, modern astronomers
and physicists have been so fascinated by the discoveries they have
made, and in following them up, that the temptation to go on in the
same course has been too great to allow them to spend time on the
investigation of sublunary and subterranean affairs. Some of them
have indeed studied the interior of the earth for special purposes,
such as the thickness of the crust, solidity or liquidity, stability,
precession of the equinoxes, the action of volcanoes, etc., etc.; but
they never, apparently, examined into any of these features to the
very end, otherwise, we believe, they would have come long ago to the
same conclusion as we have. And withal it seems wonderful how near
some of them have come to it. To most people it would appear absurd
to think that any part of the earth of any great magnitude can be
hollow, if in order to make up its mass its average specific gravity
must be 5·66--more especially, if we tell them that the greatest
specific gravity at any place need hardly exceed 5·66--forgetting that
weight or mass can be taken from the interior where the volume per
mile in diameter is small, and be distributed near the exterior where
the volume per mile in diameter is comparatively immensely greater.
But in whatever light we look upon the conclusions we have arrived
at, a change in the construction of the bodies in space from solid to
hollow spheres must produce changes in our ideas of them, and have
consequences of great importance, too numerous to be all taken account
of; we shall, therefore, only take notice of the most prominent.
Looking at the earth as a hollow sphere, we get rid of the difficulty
of conceiving that matter can be compressed to three or four times less
than the volume it has as known to us; and also of the misplacement of
metals to the incredible degree we have shown to be necessary to make
up its whole mass according to the sorting-out theory. And if we can
only be bold enough to look upon gases as ponderable matter that can be
compressed to great density, and so added to the weight of the whole
mass, we may not be under the necessity of compressing the known matter
composing it to even the half of its volume.
Somewhere in the first quarter of this century (see "Edinburgh Review,"
January 1870) Mr. Hopkins argued that the solid crust of the earth
must be at least 800 to 1000 miles thick, in order to account for the
precession of the equinoxes and nutation, but about a quarter of a
century afterwards M. Delaunay demonstrated before the French Academy
by actual experiment that the thickness of the crust had no bearing
whatever on the problem. And about the same time Lord Kelvin inferred
from the same thickness of crust that "no continuous liquid vesicle at
all approaching to the dimensions of a spheroid 6000 miles in diameter
could possibly exist in the earth's interior without rendering the
phenomena of precession and nutation sensibly different from what they
are"; and that the earth, as a whole, must be far more rigid than glass
and probably more rigid than steel, "while the interior must be on
the whole more rigid, probably many times more rigid, than the upper
crust." With the theory of a hollow shell, a better foundation is
given for Mr. Hopkins's argument than a solid crust at about the same
depth as he assumed, while at the same time the liquid vesicle of 6000
miles in diameter is removed, which Lord Kelvin showed would change
the phenomena of precession and nutation. We have seen that imprisoned
gases may have a high degree of density, and consequently rigidity, and
may in some measure supply what was required by Lord Kelvin, who knows,
also, very well that a structure with some degree of elasticity in it
is stronger than one that is absolutely rigid. Moreover, the shell of
the earth, composed of solid materials at a very high temperature, and
consequently so far plastic, could not fail to accommodate itself to
any variation of centrifugal force that could take place. Variations
in rotation of the earth could only have come on extremely slowly, and
even the most rigid matter we know will gradually yield to extreme
pressure long continued. But this subject of the plasticity of the
most solid part of the interior was discussed and, it may be said,
demonstrated during the meeting of the British Association of 1886, as
reported in "Nature" from July to September of that year. Any way, the
possibility of plasticity is most patently shown by the hollow-sphere
construction of the earth.
We do not know what were M. Delaunay's proofs that the thickness of
the crust has no bearing whatever on precession and nutation, but if
they were complicated with the fluidity, or even viscosity, of a liquid
interior beyond a depth of 800 to 1000 miles, they must be entirely
changed under the notion of a hollow sphere where there could be no
really liquid molten matter, except near the inner surface. One thing
we may be certain of, and that is, there must be something to account
for precession and nutation, and we believe that the hollow shell,
with the greatest density where the mass is greatest, is a much more
rational cause for these phenomena than the bulging out of the earth to
the extent of 13 miles or so at the equator.
It is very difficult to find out what geologists consider to be the
nature of the interior of the earth in its details, but for our
purpose no particular knowledge is required. However, it is necessary
to allude to the principal features of their theories in order to
note and remark how far they will agree to, or be facilitated, or the
reverse, when applied to a hollow sphere. It would seem that almost
all geologists are agreed that the central part is solid, and possibly
extremely rigid owing to the enormous pressure of superincumbent
matter; that it has a solid crust of several hundreds of miles in
thickness; and that under this there is a sub-crust divided into two
or more layers of different densities, partially liquid or at all
events plastic, extending all over the solid interior matter; the chief
purpose for which it is required being apparently to supply matter for
volcanic action and surface movements.
Under the theory we are advocating, the place of greatest density of
the interior is calculated to be at 817 miles from the surface, and
its greatest approach to solidity will be there also; consequently,
if geologists consider that it will have sufficient plasticity there
to provide matter for volcanic eruptions, they will be at one with us
so far. But should they consider that they require, for volcanoes,
matter more liquid than is likely to be found at that depth, they
will have to place their magma layers either much deeper or somewhere
between that depth and the surface, in which case they will encroach
on the requirements of astronomers, without liberating themselves from
a difficulty in which they must find themselves involved under their
present ideas. They say that these plastic layers exist under the solid
crust all round the interior of the earth, so that if one of the duties
they have to perform is to keep the various chains of volcanoes in
communication with each other, their lateral movements must extend to
some hundreds of miles in the cases of the enormous volumes of matter
that are sometimes thrown out in even modern eruptions, and they have
to provide the means for procuring that lateral motion. Shrinkage from
cooling, or falling in of part of the solid crust, might bring about
these enormous outbursts of lava, but they would be more likely to
produce simple overflows than the explosive ejection of such masses
as are now being recorded from time to time. We have brought into
remembrance, page 148, that water cannot penetrate into the interior
of the earth to a greater depth than 9 miles, more or less, as water,
and that beyond that depth it can only exist in the form of steam, or
dissociated into its elements of hydrogen and oxygen. As long as it
continued in the form of water it could be suddenly flashed into steam,
of not far from two thousand times its volume, by relief from pressure
or sudden application of heat, and thus be converted into a violent
explosive almost instantaneously; but when it came to have the form of
a gas, it could only be heated gradually the same as any other gas. It
is clear, therefore, that water cannot be looked to for producing the
force, explosive or otherwise, that is required to raise even molten
matter from depths of hundreds of miles to overflow from the summits or
outlets of volcanoes.
A pressure of 400 atmospheres would be required to balance a column of
average rock of _one mile_ high. A mass of water, through shrinkage
of the crust, might get introduced to the vent of a volcano, or some
cavity connected with it, a few miles under the surface of the earth
and cause an earthquake--it might be introduced by an earthquake--or
eruption or both, abundantly formidable and destructive, no doubt, but
only comparatively superficial, such as those of Naples and Charleston,
where the extreme depth was calculated to be only a few miles; but it
seems to us to be totally inadequate to produce those outpours that
last for days and weeks, covering leagues of land, and filling up bays
of the sea, with floods of lavas. It may be the principal agent or ally
in producing the horrors and devastation of a grand eruption that has
invaded the regions of water, but it is not to be conceived as possible
that it can be the prime cause. The volumes of steam, water, and mud
thrown out on such occasions, only tend to distract our attention from
looking deeper for the true cause of the eruption. Geologists are
therefore thrown back upon their magma layers to look for the motive
power for producing these grand eruptions, and they cannot get water
down deep enough to do it.
Tides produced by the sun and moon cannot be appealed to, otherwise the
eruptions would be more or less uniform in their periods of occurrence.
Sudden evolution of gases in the magma layers could not be accounted
for in any way known to us, and accumulation of gases would involve
the idea of immense cavities, to serve as reservoirs to be gradually
filled till the pressure was sufficient to force a way out, and would
imply a formation of the interior in compartments specially adapted for
particular purposes, and altogether too fanciful to be entertained.
Where could such enormous masses of matter, as those thrown out, come
from at only a few miles from the surface? The great eruption at the
Sandwich Islands, of about a century ago, after flowing over a distance
of many miles of land, on which it left enormous quantities of lava,
filled up a bay of the sea twenty miles long, and ran out a promontory
of three or four miles into the sea; and we cannot conceive it to
be possible that such a quantity of matter could be blown out from
something less than 9 miles deep by water suddenly flashed into steam.
The critical temperature of water--that temperature at which it changes
into steam under any pressure however great--being 412°, its pressure
in the state of steam will be somewhere about 7150 lb. per square inch,
let us say 500 atmospheres; then, if 400 atmospheres are required to
balance 1 mile in depth of average rock, as we have stated above, the
pressure of steam just cited would balance only 1-1/4 miles of rock.
We can, therefore, see how inadequate it would be to force a column of
lava up from even the depth of 9 miles. At that depth 3600 atmospheres
of pressure are required to balance a column of lava, and there are
only 500 available. It has been said that the downward pressure of
steam would force up the lava through the vent of a volcano, but an
arrangement of that kind would require a downcast shaft as well as
the upcast one of the vent like as there are in collieries; but the
downcast would have to go very deep to compress the steam--a gas
now--to the required number of atmospheres. Far more likely that the
steam itself would put an end to any increase of water, by driving it
back through the channels by which it was descending; for if they are
supposed to exist under a solid crust of 800 miles thick the pressure
required would be 320,000 atmospheres, and with a crust of only 100
miles thick 40,000 would be required. The only way, therefore, in which
volcanic eruptions can be produced in the earth, if solid or liquid,
or partially solid and partially liquid, to the centre--in other
words, from magma layers--is by the shrinking of the crust squeezing
out the lava. With a hollow earth and shell of more or less 2200
miles in thickness, liquid to some depth on the interior surface the
difficulty becomes very much less. The communication between the vents
of volcanoes would be complete and simple, without any lateral forcing
of the lava through magma layers made expressly for the purpose; it
would be an open and natural flow from one place to another. That
there are such volcano vents connected with each other has been very
generally believed, and even almost proved by observation of eruptions
taking place in two or more almost simultaneously, or at the least
showing signs of violent agitation, the motive forces for which would
be the gases which we have concluded must be imprisoned in the hollow
centre. When their pressure came to be sufficient to blow or force out
the liquid, or semiliquid matter, bubbling and boiling in the vents in
constant activity, there would be an eruption, during and after which
the gases would escape till their pressure was greatly reduced, when
the volcanoes would return to their semi-active state. The gases would
naturally be those of the many kinds that are found in eruptions, by
reason of their being generated in the earth, mixed with steam and
water in the manner we have already shown.
Let it not be supposed that the gases would require to have force
enough to raise lavas from depths of over 2000 miles from the surface.
According to our arguments for a hollow earth, at 817 miles from the
surface the two halves--outer and inner--of the matter composing it
meet and balance each other, so that all the pressure required would be
what is necessary to overcome the inertia, viscosity, or cohesion of
the matter in the vents. What that would be we do not pretend to be
able to calculate, but we believe that it would be very much inferior
to that required to balance a column of lava of even 100 miles high. We
have seen that gas compressed to 4835 atmospheres would be 6-1/4 times
more dense than water, and of equal specific gravity to the heaviest
matter required in any part of the earth to make up its average density
to 5·66 that of water, and we cannot assume any greater pressure than
this, without diminishing that maximum. If that, or any lesser degree
of compression, would supply the necessary force, then all difficulty
is removed further than pointing out the means of keeping the volcano
vents open or openable; and the quality of openable may be facilitated
by the contraction of the interior from cooling. If a greater pressure
be necessary, we need not be afraid of greatly increasing it, for the
only consequence would be to diminish the maximum density of solid
matter required in any part of the earth, to make up the general
average to 5·66, which means less compression of the matter. If the
idea of the accumulation of gases in the hollow centre, or of the
hollow centre itself, is inadmissible, then scientists in general can
continue as before with their magma layers--aqueo-igneous if they
like--but they must abandon the notion of lavas being expelled from
them by steam pressure. We repeat that steam could never get down in
the form of steam to the depths they require. The temperature there
would be more than sufficient to resolve it into its elements of oxygen
and hydrogen, and it would behave very much like the gases we have
supposed to be in the hollow; there might be accumulation, but there
could be no sudden flashing into existence like steam from water.
In support of our observation--if it needs support--that water as
water cannot penetrate into the earth to a greater depth than where it
meets a temperature of 412° we may refer to reports on earthquakes of
comparatively recent occurrence. We learn from the "London Quarterly
Review" of January 1869, that in the Neapolitan earthquake of 1857, Mr.
Mallett found the greatest focal depth to have been 8-1/8 geographical,
or 9·35 statute miles, which agrees very well with the depth to which
water could penetrate and be suddenly flashed into steam. (We say
nothing, for the present at least, about how the water and the heat
managed to meet so instantaneously.) The shock of the instantaneous
generation of steam might be felt much lower, but it would tend to
interrupt, not to produce, the eruption of lavas. In speaking of the
pressure on the walls of the cavity, where the shock was produced,
being 640,528 millions of tons, the reviewer says, "it may have been
greater because the steam might be supposed to have acquired the
temperature of the lava," and that is 2000°F.; but that could not well
be. In order to meet lava of that temperature the steam would have
to descend to from 20 to 25 miles deep; on the other hand, if the
lava is assumed to have entered the cavity, it could only do so at a
comparatively low velocity and would not reach more than a fraction
of the steam at a time, and even for that reason there could be no
flashing, as steam is only a gas, and cannot be heated otherwise
than as a gas. Here the spirit of facilitating the meeting of the
lava and the steam, is as apparent as in bringing about the meeting
of the water and the lava noticed above. On the whole, therefore, we
think that we were right in saying that steam or water cannot be the
cause of volcanic eruptions, but that the invasion of the domains of
water by the lavas may be the cause, in the main, of the explosive
part of eruptions, and of the most disastrous effects of earthquakes.
Moreover, the focus of the Neapolitan earthquake was 75 miles distant
from Vesuvius, and therefore far removed from anything like direct
connection with the vent of the volcano, so that water from it in any
form could have no effect upon the magmas of scientists.
"The Scientific American" of July 16, 1887, tells us that Captain E.
D. Dalton has calculated that the depth of the Charleston earthquake
was 12 miles; statute miles, it is to be supposed, as nothing is said
to the contrary. To reach the temperature of 412° this would give
an increase of 1° in 45 metres in depth, which is a considerably
greater depth than what we have estimated, but does not invalidate our
reasoning, as it has always been known that the gradient of increase
of heat varies considerably from one place to another. Besides, and
more especially, Charleston being a seaport, and, consequently, not
far from the level of the sea, it is to be supposed that, owing to the
presence of water, the cooling of the earth has penetrated to a greater
depth there than in the heart of Italy. The same authority states that
in the formidable Yokohama earthquake of 1880, the mean depth was only
3-1/4 miles. The mention of mean depth here makes us notice that the
12 miles may have been the extreme depth to which the earthquake, or
shock, was felt at Charleston, and that the focal depth may have been
considerably higher up than that. Be that as it may, there is no proof
existing that water or even steam can penetrate into the earth more
than a very few miles, much less to hundreds of miles.
Having referred pretty freely to the aqueo-igneous magmas, supposed by
some scientists to exist deep down in the interior of the earth, it is
but fair to give our reasons for refusing to believe that there can be
any such mixture in any part of it, or anywhere else. In order to do
so, we shall first cite some of the bases upon which such ideas have
been founded. In "Nature" of December 12, 1889, we find what follows:--
"Let us now consider the alternative theory suggested by Mr. Fisher. He
claims that geologists furnish him with a certain amount of positive
evidence for the idea that water is an essential constituent of the
liquid magma from which the igneous rocks have been derived. Passing
over the proofs of the existence of water in the crystals of volcanic
rocks, and in the materials of deep-seated dykes, let us come at once
to the granite, a rock which can only have been formed at great depths
and under great pressures, and which often forms large tracts that are
supposed to have been subterranean lakes or cisterns of liquid matter
in direct communication with still deeper reservoirs. Now, all granites
contain crystals of quartz, and these crystals include numerous minute
cavities which contain water and other liquids; and the quartz of some
granites is so full of water-vesicles that Mr. Clifton Ward has said:
'A thousand millions might easily be contained within a cubic inch of
quartz, and sometimes the contained water must make up at least 5 per
cent. of the whole volume of the containing quartz.' This amount only
represents the water that has been as it were, accidentally shut up in
the granite, for some was doubtlessly given off in the form of steam
which made its way through the surrounding rocks."
We cannot follow Mr. Fisher in "passing over the proofs of the
existence of water in the crystals of volcanic rocks and in the
materials of deep-seated dykes"; because the presence of water in
these crystals when examined in a laboratory is no proof that water
was present in them when they were liquid, and before they put on the
form of crystals. There is no analogy between them and General Wade's
read. Any crystals that a man can pick up anywhere, even from the
mouth of a volcano, are quite capable of absorbing vapour of water
from the atmosphere before he can carry them to his laboratory. All
matter is supposed to be pervaded, more or less, by the ether, and
there is always an open road for it, i.e. the vapour of water to enter
by. Nature dives more rapidly into a piece of rock than a man can walk
or drive down from the summit of a volcano, so that getting water out
of it when he is in his laboratory, is no proof that the water was
there when the piece of rock was at the bottom, not the mouth, of the
volcano. The minute so-called water-vesicles in granite have only
served the purpose of a snare to facilitate his deceiving himself,
by the help of Mr. Clifton Ward, to further his speculations. For we
think it would have been far more natural for him to have supposed that
these vesicles were originally filled with the all-pervading ether.
Or, are we to prohibit the ether from being present anywhere, except
where it suits us? Even the dimensions given to the vesicles of a
thousand millions of them being contained in a cubic inch makes us at
once think of something more ethereal than water. And the whole object
of Mr. Fisher's argument is to show how the depth of the ocean may be
increased by water expelled from such magmas.
A hollow planet, with compressed gases in the centre, raises the idea
of the possibility of explosion. It would have furnished Olbers, or
any follower of his, with the bursting force to shatter into fragments
the planet, out of which he supposed the asteroids to have been made.
It need not cause any alarm with respect to the earth, whose shell is
very much thicker than that of the exploded planet, seeing that its
whole mass has been estimated not to have exceeded one-fourth of that
of the earth (see Table I.). The 5000 atmospheres of pressure we have
spoken of could have no such effect on so thick a shell as the earth's;
and we cannot increase the number without diminishing its average
density, as we have shown. When we see Mars blown up, whose diameter,
and consequent thickness of shell, are not much more than half those of
the earth, we may begin to think of getting out of the way.
THE MOON.
This satellite is supposed, according to the nebular hypothesis, to
have been at one time neither more nor less than a smaller edition
of the earth itself, endowed with atmosphere, plains, mountains,
volcanoes, rivers, seas, rotary motion, etc.; previous to which it had
passed through the same stages of gasiform, molten-liquid, and solid as
its parent had done. One would think that its almost perfectly round
form proves to demonstration that it must have rotated rapidly on its,
or an, axis at one time; but there are some astronomers who think that
it has never rotated at all, an opinion in which we cannot concur by
any means. When it arrived at the stage of having seas, the tides
raised in them by the attraction of the earth must have acted like a
brake on its rotation--in the same manner as its attraction is supposed
to be now doing on the earth--and gradually reduced it until it ceased
altogether; from which time forward it must have always presented the
same side to the earth. It has been thought that the tides raised in it
by the earth would be so tremendous that they would prevent anything
like rotation having ever existed; but everything requires to be
accounted for, and the only way to account for its perfectly circular
form is by its having rotated.
Considering, then, the moon as having been dispossessed, absolutely,
of rotation and reduced to the single motion of revolution round the
earth--as far as we are at present concerned, at least--we can go back
to the period when this change came over it, and consider what would
happen about the time, and immediately after the rotation came to an
end.
When a fly-wheel is made to revolve rapidly and is then allowed to run
until it stops, it very seldom comes to rest all at once, and generally
swings backwards and forwards something like a pendulum, until it
finally stops; because it is always a little heavier on one side than
the opposite, even should the difference of weight be only that of
the handle by which it was set in motion; so we may suppose it would
be with the moon when at last it failed to turn the centre, as it is
called--the tides, the retarding cause, giving origin to the difference
of weight on opposite sides--and we can conceive what commotions
would be created on its surface by the wobbles it would make. We can
imagine how the seas would rush backwards and forwards over the lower
land and hills, levelling them down to the flat plains that are seen
spread abroad among the innumerable volcanoes which cover the side
turned towards the earth, until it finally came to rest. When the
commotions ceased and the centrifugal force of the moon's revolutionary
motion round the earth--which is over 38 miles per minute-came to act
freely, we know that the atmosphere and seas, being the mobile parts
of it, would be pretty nearly all driven off very quickly to the side
farthest from the earth, perhaps even before it came to the final
state of comparative rest, whose translation would involve mighty
rushings of waters there as well. Also, that all the liquid matter in
its interior, being so much heavier and more difficult to be moved by
centrifugal force, would gravitate towards the side nearest the earth,
whose attractive force would soon put an end to anything in the form of
interior tides of molten matter, which very probably existed up till
that period. If the moon came to a stop without any wobbling, then the
transference of atmosphere and seas to the farthest off hemisphere,
and the gravitation of the liquid matter of the interior to the side
nearest to us, might be more gradual but would finally and certainly
come to pass. And here we must specially note that if it made one
rotation for each revolution, or one rotation in any length of time or
under any circumstances whatever, these transferences of matter from
one hemisphere to the other could not have taken place, because there
would be no stationary region to which they could be transferred by
centrifugal force, as each part of its circumference would in its turn
occupy that region. And above all--be it specially marked--because the
moon would not, in that case, always present its same side to the earth.
Looking upon the moon as a hollow sphere of somewhat the same
proportions as we have made out for the earth, the region of greatest
density would be at about 234 miles deep from the outer surface, the
interior surface of the shell at the depth of 692 miles, and the
hollow centre 776 miles in diameter, as long as it continued to rotate
upon its axis. When that motion ceased and the seas were transferred
to the hemisphere farthest off from the earth, and the liquid matter
in the interior had gravitated towards the nearest, as we have just
said above, its conditions would be very materially altered. Lest it
should be supposed that with a very thin crust, nearly its whole mass
would gravitate to the side nearest to the earth, let us always bear
in mind that the moon would be virtually solid to not far from the
inner surface of the shell, through the pressure of superincumbent
matter, both from without and from within, in the same manner as we
have considered the earth to be. Whatever water had been absorbed by
the crust when it was still rotating on its axis--which, at most,
could have penetrated only a few miles--and even whatever lakes or
inland seas might have been left on the surface always seen by us,
would be soon evaporated by the internal heat, and the heat radiated
by the sun--which Sir John Herschel has calculated to be greater than
boiling water--and driven off in the shape of vapour in the same
manner as the atmosphere had been. These transferences would lead to
two consequences, each one of its own nature, which we must not fail
to notice particularly, as in great measure they explain to us the
constitution, or rather the construction, of the moon. (1) All air and
vaporous matter being translated to the unseen hemisphere would tend to
cool it more rapidly and deeply than the other, not only on account of
the cooling powers of the water, but from the atmosphere and vapours
preventing the heat of the sun from acting so powerfully upon it. (2)
On the other hand, owing to the accumulation of melted, or liquid,
matter in the interior of the side now turned permanently towards the
earth, the formerly solid part of that side would tend to increase in
temperature, which, joined to the heat from the sun not intercepted by
any atmosphere, and continuing without interruption for a fortnight at
a time, would produce a great difference in the temperatures of the two
hemispheres. Thus it is natural to suppose that the thicker and cooler
solid shell on the one side would tend to weaken and drive down the
volcanic forces to a greater depth; while the greater temperature and
thinner solid shell on the other, the down side--the one next to the
earth--would have an exactly opposite tendency and would bring them
nearer to the surface. In this manner we seem to find a very plausible
reason for the great exuberance of the volcanic forces displayed on the
surface of the moon always presented to us.
Both the interior construction and exterior form of the moon, as
modified by losing its rotary motion, would no doubt be very different
to that of a hollow sphere rotating on its axis; but Hansen's "curious
theory" has prepared us for this, by showing that some anomaly in its
construction had been noted and commented upon, although the existence
of the anomaly was not attributed to the atmosphere on its having been
driven away to the far-off hemisphere. But with this subject we have
dealt pretty fully already in Chapter II., which may be referred to for
further explanation if required.
CHAPTER XII.
PAGE
215 Some of the results arising from the sun's being a hollow sphere.
216 Repetition of the effects of condensation on the temperature of
the nebula.
217 Ideas called up by the apparently anomalous increase
of temperature.
218 How heat is carried from the sun to the earth.
219 The sun supposed to radiate heat only to bodies that can receive
and hold it, and not to all space. The heat of the sun
accumulated in a hot box to considerably beyond the boiling
point of water.
220 The heat accumulated in this way supposed to be due to a peculiar
function of the ether, as it is a fact that heat can be
radiated from a cold to a hot body.
221 The sun must be gaseous, or rather gasiform, throughout.
No matter in it solid or even liquid. Divisions and
densities of shell.
222 The hollow centre filled with gases, whose mass naturally
diminishes the mean density of the whole body.
223 The amount of this reduction so far defined. The presence of
gases or vapours in the hollow a natural result
of condensation.
223 The hollow centre filled with gases not incompatible with
the sun's being a hollow sphere. The temperature at the
centre may be anything, not depending on any law of gases.
224 Further exposition of hollow-sphere theory put off till after
further development of the construction of the sun.
In the last chapter we have endeavoured to point out how much our
knowledge of the interior construction of the earth and moon has been
increased, and how many difficulties in the comprehension of their
construction are overcome by the fact demonstrated in previous parts
of our work that they are hollow bodies; and we now proceed to show
some part of what may be learned from studying the sun under the same
conception of its being a hollow body. We say part of what may be
learned, because the whole seems to us to be so great that it would
take much more time and space, not to speak of knowledge, than we can
devote to the subject to make even a proper beginning to such a study.
To our sight it takes away the necessity for guessing in the dark at
what the construction may be, which is all that has hitherto been done;
and furnishes the means of discovering, with intelligent study and
investigation, what most probably is the actual constitution of the sun.
In Chapters V. and VII. we have followed up the contraction and
condensation of the residue of the original nebula, after it had thrown
off all the known planets; first, to the diameter of 58,000,000 miles,
with density of 1/274th of an atmosphere and temperature of -273°,
or _one degree_ of absolute temperature; second, to about 9,000,000
miles diameter, with density equal to air at atmospheric pressure, and
temperature represented by zero of the centigrade scale, or what has
been hitherto called 274° of absolute temperature; third, to 4,150,000
miles diameter, with density equal to ten atmospheres and temperature
of 2740° of actual, or 2742° of absolute temperature; and fourth, to
972,895 miles diameter, with density equal to water and temperature
which we do not venture to express. All these stated densities and
temperatures are understood to be average, the temperatures being those
the various stages would have had, had no heat been radiated into space
by them.
Here, then, we might go on to set forth what might be the interior
dimensions, various densities, and conditions of each one of the four
stages, under the conception of their being all hollow spheres, and
afterwards carry on a _résumé_ of the whole of them and apply it to the
sun as it is at the present day; but this, in addition to involving
an immense deal of difficult work, subject to errors and omissions in
operation, would not do much towards enabling us to explain in a more
simple way what may be, most probably is, its interior construction. We
shall, therefore, look upon the four stages as represented by a model
having the diameter and other known measurements of the sun in its
present state.
To begin what we propose to do we believe it is necessary to repeat,
as a thing that has to be borne in mind, that when we had contracted
the original nebula from 6,000,000,000 miles in diameter to
58,000,000 miles, its density was only equal to a barometric pressure
of _one-ninth_ of an inch of mercury, and its mean temperature had
been increased only _one degree_, that is, from -274° to -273°; and
we can add that, although we had given the original nebula ten times
that diameter, the result both in density and temperature would have
been the same when it was condensed to 58,000,000 miles in diameter.
Then, again, we believe it necessary to repeat that by contracting the
nebula from 58,000,000 to 9,000,000 miles in diameter its mean density
was raised from 1/274th to full atmospheric pressure, and its mean
temperature from -273° to zero of the ordinary centigrade scale, i.e.
to the temperature of freezing water. These two results strike us,
at first sight, as somewhat remarkable, seeing that what looks like
almost unlimited condensation to 58,000,000 miles diameter produced
only one degree of temperature, while the comparatively insignificant
condensation of from 58,000,000 to 9,000,000 miles in diameter produced
273° of heat, _in the way we are accustomed to measure heat_.
Following up these two facts gives rise to ideas that have been borne
in upon us ever since we stumbled upon them when making the analysis
of the nebular hypothesis. One of these notions was that, were it
practicable, the most effectual mode of liquefying gases would be by
putting any one of them into a sealed vessel, and confining it in
another vessel in which a vacuum of 1/274th part of an atmosphere could
be produced; no difficult matter as far as the vacuum is concerned,
for a good exhausting air-pump would be all that is required. But
the practicability? The vessel in which the vacuum is produced would
have to be protected so that no extraneous heat could be conveyed or
conducted into it in any way whatever. How this could be, or is, done
without cutting off every possibility of manipulating the enclosed
vessel, we do not see; but it seems evident that some method is
available because something presenting the same difficulties has been
actually done, as everybody knows. The only degree of vacuum of any use
in the exterior vessel would be about one-ninth of an inch of mercury,
because that would as we have just said, furnish a temperature of
-273°. There would be no necessity for applying pressure to the gas
experimented upon. In fact pressure would be an obstacle to the
experiment, according to the theory of the air thermometer; and could
only be of use by furnishing a larger quantity of liquid to be handled
and examined.
Another idea is that there can be no such condition as absolute zero of
temperature of what we are accustomed to think of as a gas, as far as
science is concerned; as on arriving at that condition, perhaps long
before, any gas would slip out of its hands altogether. But there is a
much more rational reason than this, which we have brought forward on
a former occasion. We are taught that heat is a mode of motion, which
means that as long as there is heat there will be motion to account for
it, so that motion would have to be annihilated on the earth before
absolute zero of temperature could be reached. We have, then, to come
back to what we said when treating of the heat of space, and look upon
the temperature of the vibration of the ether as being the lowest that
can be measured by science. We said then that it must be far below
-225°. Since then a temperature has been reached of within 23° or 24°
of absolute zero, according as that condition is measured by 273 or 274.
This, of course, leads us to think of the ether as a carrier of light,
heat, etc., and of how it can carry heat to the earth without becoming
heated itself, as there can be no doubt about its being a material
substance. How it can bring what may be called considerable heat to
the earth and still have little or no heat in itself; even should it
turn out, which we do not believe possible, that the estimates of the
heat of space of -150° and -142°, made about the beginning of this
century by Sir John Herschel and Pouillet, turn out to be near the
truth. We have seen, in "Nature" of July 15, 1886, a monograph by
Captain Ericsson, in which he shows that the heat radiated by the sun
to where his rays strike our atmosphere is somewhere about 83°F., and
it is not easy to see how radiated heat can be transmitted through 90
million miles of space at a temperature of much lower than -225°, and
reach the confines of our atmosphere with the heat of 83°F. There is
one supposition that occurs to us under which this can happen, and that
is, that the sun only radiates heat to bodies which can receive it,
and does not radiate it into all space where there is nothing but the
ether to hold it. This, of course, implies that the ether acts the same
part--the part for which it was really invented--with respect to heat
that a telegraph wire does with respect to electricity; in which case,
we could imagine that it starts from the sun with the maximum heat
radiated by him, and that this goes on decreasing in the ratio of the
square of the distance it travels through, the same as is understood
to be the case with all radiated heat; and that the part of space not
occupied, for the time necessary, by these connexions might be supposed
to form the return current which we believe must exist, just the same
as the earth does for electricity. For that there is a return current
is demonstrated by the fact that the earth radiates heat into space
when the sun is not shining upon it. Again, even in this case, we
have another difficulty thrown upon us, over and above that cited by
Captain Ericsson, of the heat delivered at the bounds of our atmosphere
being about 83°F., by our being informed in "Engineering" of December
4, 1885, that: "A hot box, contrived to observe the temperature which
could be attained by the unconcentrated solar rays, was used on Mount
Whitney, 12,000 feet above the sea"--well within the limits of our
atmosphere--"and that the enclosed thermometer rose to 233·3°F. on
September 9, 1 p.m., 1881, the shade thermometer then reading 59·8°F."
How are we to comprehend these two facts? We have seen a way of
getting over part of the first fact as far as to the boundary of our
atmosphere, but from there we have to carry 83°F. to the top of Mount
Whitney, through the atmosphere there and present it along with the
other lot in the hot box at 233·3°F.