240 KANSAS CITY REVIEW OF SCIENCE. 



most important numbers known to mathematicians, and should be committed 

 to memory by all who would learn astronomy or know how celestial measure- 

 ments are determined. Let us examine this matter closely Take a ball one 

 foot in diameter, place it on a standard in front of a telescope provided with a 

 micrometer, and the globe will subtend a certain number of degrees angular meas- 

 urement which, let us assume is four degrees. Now move the standard on 

 a right line away from the telescope, and soon the sphere will only subtend 

 three degrees, then two degrees, until finally its distance becomes so great 

 that its angular diameter shrinks to one degree. An important circumstance 

 follows — we know that the ball is precisely 57.295795139 feet distant from 

 the focus of the objective, because we have seen that radius contain that many 

 circular units. Again, move the standard until the angular diameter of the ball 

 shrinks to one minute, and it is at once known that the globe is distant 3437.- 

 73677 feet. Still bear the sphere away until its diameter subtends one second, a 

 space only visible in a powerful telescope, and we likewise know that the ball is 

 in distance 206,264.80625 feet or 39.0653 miles. 



This is the process of measuring the distance of an object when its linear 

 diameter is known. To reverse the case we will suppose that we have a globe 

 whose diameter is one foot placed on a standard. Let an observer with a tele- 

 scope retire and view the ball at a distance, and telephone to an assistant at the 

 sphere its angular diameter. Then the party at the standard can tell the distance 

 of the telescope. If the message received is : — the apparent diameter is one min- 

 ute, of course the distance traversed is 3,437 feet, if two minutes half that dis- 

 tance. But to avoid calculation sines, cosines and tangents of all angles are made 

 use of to abridge the work. If we divide : 



3.1415926535 by 180 the quotient is .0174532925 



3.1415926535 by 10,800 the quotient is .0002088820867 

 3. 1415926535 by 648,000 the quotient is .00000484813681 



which decimals are ratios of the units of the circumference in terms of the radius, 

 for degree, minute and second respectively, and are termed sines. To determine 

 distances all that is necessary is to use the sines in simple multiplication and di- 

 vision. Thus the diameter of the ball is one foot, and since the observer saw it 

 as one minute, we divide i by .00029088820867 having for a quotient 3437.74677 

 feet distance. 



THE DISTANCE OF THE SUN. 



If the Sun subtended an angle of one second we have seen how many times 

 greater its distance would be, than its diameter, but the actual angular diameter of 

 the Sun as obtained by many measures is 1924 seconds. Therefore 296,264.- 

 80625 divided by 1924 equals 107.20624 which we positively know is the num- 

 ber of times the distance of the Sun exceeds its diameter. But this gives us no 

 clue to the distance in miles, because we have not yet learned the diameter of 

 the Sun in miles. We know its angular diameter to be 1924 seconds of arc, 



