EARTH 355 came more clearly recognized. Voyages north- ward and southward were found to lead to steady rising or sinking of the north pole of the heavens, a circumstance which showed that there must exist a curvature in that direction ; while voyages eastward and westward, being found by careful observation to lead to a short- ening or lengthening of the intervals between noon and noon, proved that in that direction also the earth is curved. We pass over the history of such researches, in order to give more space to the exact investigations of mod- ern times. The measurements made on the assumption that the earth is a true sphere had been conducted to a sufficiently satisfactory issue exactly at the time when Newton's dis- covery of gravitation was about to lead him to the inference that the earth must be somewhat oblate. Picard showed in 1679 that each de- gree of a great circle of the earth contains rath- er more than 69 m., instead of 60 as had been supposed. Soon after Newton pointed out that if the earth were regarded as originally a homo- geneous fluid rotating mass, its shape would not be globular, but so far compressed that the polar diameter would bear to an equatorial di- ameter the ratio 229 to 230. By a singular mis- apprehension the elder Cassini was led to im- agine that if the earth were thus compressed the degrees of latitude must diminish as either pole is approached; an obvious mistake, see- ing that the polar flattening implies diminished polar curvature. But Cassini's actual mea- surements seemed to indicate a diminution of the degrees of latitude toward higher lati- tudes; and when it was pointed out to him that his results were the reverse of what New- ton's theory required, he maintained their ac- curacy, and the inference that the earth is a prolate instead of an oblate spheroid ; in other words, he maintained that the polar diameter exceeds the equatorial. The controversy hence arising led to the famous earth-measuring ex- pedition of 1 735-'45. Bouguer, La Condamine, and Godin left Paris for Peru, where they were joined by Antonio d'Ulloa and Jorge Juan from Spain. Maupertuis with four others sailed to Bothnia, where they were joined by the Swedish astronomer Celsius. The measurements made in both places were most satisfactory, repeated observations leading to results differing only a few feet per mile. The length of the degree in Peru was found to be 362,790 ft., while the estimated length of a degree in Sweden amount- ed to 365,744 ft. The difference was far too great to be ascribed to errors of measurement, and it was justly regarded as demonstrative of the general accuracy of Newton's reasoning. However, the value actually ascribed to the compression by Newton (on a certain hypothe- sis as to the earth's structure) was not confirmed by these observations ; on the contrary, it ap- peared that the compression was 1 in about 300, instead of 1 in about 230. Subsequent observations, as well as considerations founded on the attraction exerted by the moon upon the bulging equatorial parts of the earth, have shown that the compression has not so great a value as Newton's hypothesis required; nor need we wonder at this when we remember that under the influence of attraction the interior parts of an originally fluid earth would necessarily be much denser than the outer parts, and that Newton himself only introduced the hypothesis of homogeneity to simplify his calculations. The following list of measurements of degrees in different latitudes indicates what has been done since such labors were first undertaken, and serves to show how satisfactorily all obser- vations agree in pointing to an increase of the length of a degree with increase of latitude, whether north or south of the equator : COUNTRY. Latitude of mid- die of arc. Arc measured. Mean length of a degree at the mid- dle latitude In feet. Sweden 66 20' 10-0" N 1 87' 19'6" 365 711 Sweden 66 19 87 57 80-4 367'086 Kussia Eussia Prussia Denmark Hanover 58 17 37 56 8 55-5 54 58 26-0 54 8 18-7 52 32 16 - 6 8 85 5-2 8 2 28-9 1 30 29-0 1 81 53-8 2 57 - 4 365^368 865,291 365,420 865,087 865 800 England 52 35 45 8 57 13-1 864 971 England 52 2 19-4 2 50 28-5 864'951 France 46 52 2 8 20 0-3 864872 France 44 51 2-5 12 22 12-7 364572 Rome .... 42 59 2 9 47 364'262 United States India... 89 12 16 8 21-5 1 28 45-0 15 57 40-7 363,786 863044 India 12 32 20-8 1 84 56-4 862 956 Peru Cape of GM Hope. Cape of G'd Hope. 1 31 0-4 8. 33 18 80 35 43 20-0 8 7 8-5 1 13 7-5 8 84 84-7 362,790 364,718 364,060 These measurements are due to the following mathematicians and observers: The two Swe- dish to Svanbergand Maupertuis; the two Rus- sian to Struve and Tenner; the Prussian to Bessel and Bayer ; the Danish to Schumacher ; the Hanoverian to Gauss ; the two English mea- surements to Eoy and Kater ; the two French to Lacaille, Cassini, Delambre, and Mechain; the Roman to Boscovich; the American to Mason and Dixon ; the Indian to Lambton and Everest ; the Peruvian to La Condamine and Bouguer ; and lastly, the two measurements at the Cape of Good Hope to Lacaille and Maclear. Later measurements made in India by Sir George Everest give 363,606 ft. for the length of a meridional degree in lat. 26 49', and 363,- 187 ft. for the length in lat. 21 5'. Combining all the observations, and attributing minor irre- gularities either to errors of observation or to local peculiarities of the earth's surface, we de- duce the following table of the lengths of de- grees of latitude in feet for every tenth degree : LATITUDE. Length of degree in ft. LATITUDE. Length of degree in ft
862734 50 864,862 10 862,843 160 865,454 20 363158 i70 365,937 30 863641 '80 866,252 40 864,233
- 90
366,361
