ASTRONOMY. 243 



diameter of the earth. What we are searching for is the meaning equatorial hori- 

 zontal parallax of the Sun, or what is the same thing, the angle that would be sub- 

 tended by the mean equatorial radius of the earth if viewed by a micrometer 

 placed on the Sun. Radii drawn from all the observing stations to the centre of 

 the earth of course are not equatorial, since observers are placed in all latitudes, 

 hence they must be expressed in terms of equatorial radii by computation. 



Again, the mean distance of the earth from the Sun is equal to i, but at the 

 time of the last transit, December 9, 1874, and at the next December 6, 1882, 

 the earth was not, and will not be at mean distance; being near perihelion, with 

 distance less than unity. And due allowance must be made for this fact in cal- 

 culating parallax, also an allowance must be noted arising from the motions of 

 the earth and Venus during the time of transit, which complicate matters, making 

 it necessary to introduce algebraic formulas wholly inconsistent with a note like 

 this, only intended to give general ideas. However, when all corrections are 

 made, it is found that at transits of Venus under refined micrometrical manipula- 

 tion, the space between the chords on the solar disc corresponding to a distance 

 on the earth equal to its mean equatorial radius, is 22.96 seconds of arc. But 

 we have seen that this is 2.61 times greater than the line that would be subtended 

 by the semi-diameter of the earth at the same distance. Whence 22.96 divided 

 by 2.16 equals 8.8 seconds, the long sought number, \ht parallax oi ^^ Sun. 

 That is if we stand on the Sun and look this way with a powerful telescope and 

 micrometer, the earth will appear as a little ball whose radius subtends an angle 

 of only 8.8 seconds. 



Now since the mean equatorial radius of the earth is known to be 3962.72 

 miles we are nearing the end of a search kept up for centuries, and will soon know 

 the value of i second in miles, at the earth's distance from the Sun. Dividing 

 3962 72 by 8.8 gives a quotient of 450.30909 the number of miles in one second 

 of arc subtended on the circumference of a circle whose radius is the distance 

 separating the earth and Sun. 



But we saw that the sine of i second is .00000484813681, which multiplied 

 by 8.8 equals .000042663603928 the sine of 8.8 seconds, since the sines of min- 

 ute arcs vary directly with the arcs themselves. 



In any triangle the sides are in the ratio of the sines of opposite angles ; 

 therefore 3962.72 divided by .000042663603928 equals 92,882,917 the number of 

 miles from the centre of the earth to the centre of the Sun. Or the result may 

 be thus obtained: 1 divided by 000042663603928 equals 23,439.18253337 which 

 is the number of times the distance of the Sun is greater than the mean equatorial 

 semi-diameter of the earth, and being multiplied by 3962.72 gives 92,882,917, as 

 before. If this is not clear to beginners, the case may be presented in a still 

 more elementary form. For when we know the value of i second, the circum- 

 ference can be found by multiplying the value by the number of seconds in a 

 circle. Thus: 450.30909 multiplied by 1,296,000 equals 583,600,580 miles in 

 the orbit of the earth which divided by 6.283185307 the ratio of a circumference 

 to its radius gives as in other methods, — 92,882,917. 



