ON THE MAGNITUDE OF THE SOLAR SYSTEM. 99 



earth, tlie oeutrit'iigal force at its surface, the eccentricity of its orbit 

 and the mass of the moon, the hiw of gravitation sliows that if we 

 nuiltiply together the lengtli of the seconds pendulum, the square of 

 the radius of the earth, and tlie square of the length of the sidereal 

 month, divide the product by four, and take the cube root of the quo- 

 tient, the result will be the distance from the earth to the moon. To 

 tiiid 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 tiie 

 length of the thread until the pendulum made exactly three hundred 

 vibrations in tive minutes by the watch. Then, supposing the experi- 

 ment to be made here or in ISTew York City, we would find that the 

 distance from the point of suspension of the thread to the center of the 

 bullet was about 39 J inches, and dividing that by the number of inches 

 in a mile, viz, G3,3G0, we would have for the length of the seconds pen- 

 dulum 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 deternune the latitude of some 

 point in New York City by means of the railroad transit; next to run 

 a traverse survey along the old x>ost-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 2° the diflerenee 

 of latitude might be determined to about the same percentage of 

 accuracy. In that way Ave would find the length of 2° of latitude to 

 be about 138 miles, whence the earth's radius would be 3,953 miles. It 

 would then only remain to observe the time occupied by the moon in 

 making a sideieal 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 tune of revolution is about 27.32 days, and 

 multii)lying that by the number of seconds in a day, viz, 86,400, we 

 would have for the length of the sidereal month 2,3(50,000 seconds. 

 With these data the computation would stand as follows: The radius 

 of the earth, 3,953 miles, multiplied by the length of a sidereal month, 

 2,300,000 seconds, and the i)roduct squared gives 87,000,000,000,000,- 

 000,000. IMultiplyiug that by one-fourth of the length of the seconds 

 pendulum, viz, one sixty-four hundred and eightieth 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 certainly a remarkable result consider- 

 ing the crudeness of the instruments by which it might be obtained. 

 Nevertheless, when all the conditions are rigorously taken into account 

 these data are to be regarded as determining the relation between the 

 moon's mass and parallax, rather than the parallax itself. . 



