W. Harhness — Magnitude of the Solar System. 237 



of the length of the sidereal month, divide the product by 

 four, and take the cube root of the quotient, the result will be 

 the distance from the earth to the moon. To find the length 

 of the seconds pendulum we would rate the watch by means of 

 the railroad transit, and then making a pendulum out of a 

 spherical leaden bullet suspended by a fine thread, we would 

 adjust the length of the thread until the pendulum made 

 exactly 300 vibrations in five minutes by the watch. Then, 

 supposing the experiment to be made here, or in New York 

 City, we would find that the distance from the point of suspen- 

 sion of the thread to the center of the bullet was about 39-§- 

 inches, and dividing that by the number of inches in a mile, 

 viz : 63,360, we would have for the length of the seconds 

 pendulum one sixteen hundred and twentieth of a mile. The 

 next step would be to ascertain the radius of the earth, and the 

 quickest way of doing so would probably be, first to determine 

 the latitude of some point in New York City by means of the 

 railroad transit, next to run a traverse survey along the old 

 Post Road from New York to Albany, and finally to determine 

 the latitude of some point in Albany. The traverse survey 

 should surely be correct to one part in three hundred, and as" 

 the distance between the two cities is about two degrees, the 

 difference of latitude might be determined to about the same 

 percentage of accuracy. In that way we would find the length 

 of two degrees of latitude to be about 138 miles, whence the 

 earth's radius would be 3953 miles. It would then only remain 

 to observe the time occupied by the moon in making a sidereal 

 revolution around the earth, or in other words the time which 

 she occupies in moving from any given star back to the same 

 star again. By noting that to within one-quarter of her own 

 diameter we would soon find that the time of a revolution is 

 about 27*32 days, and multiplying that by the number of sec- 

 onds in a day, viz : 86,400, we would have for the length of 

 the sidereal month 2,360,000 seconds. "With these data the 

 computation would stand as follows; the radius of the earth, 

 3953 miles, multiplied by the length of a sidereal month, 

 2,360,000 seconds, and the product squared, gives 87,060,000,- 

 000,000,000,000. Multiplying that by one-fourth of the length 

 of the seconds pendulum, viz : 1/6480 of a mile, and extracting 

 the cube root of the product, we would get 237,700 miles for 

 the distance from the earth to the moon, which is only about 

 850 miles less than the truth, and is certainly a remarkable result 

 considering the crudeness of the instruments by which it might 

 be obtained. Nevertheless, when all the conditions are rigor- 

 ously taken into account these data are to be regarded as deter- 

 mining the relation between the moon's mass and parallax 

 rather than the parallax itself. 



