HOW TO OBSERVE THE HEAVENS. 351 



tween two successive returns of the centre of the sun's disk to the summer 

 solstitial point. A single observation, however accurate it be, will only give 

 a rough estimate of this, such a one, for example, as will be liable to an error, 

 say of ten minutes of time, five minutes of the error being ascribed to each of 

 the two observations. Instead of observing two successive solstices, let us 

 now observe two solstices having an interval of ten years between them. It 

 might be objected that to do this we must be supposed to know the length of 

 the year, which is the thing we are in quest of. But to this it is answered, 

 that we only require to be sure that the interval between the two solstices 

 which we observe is not either a greater or a less number of years than ten. 

 Now although we do not yet know the exact length of the year, yet we do 

 know that it is certainly greater that an eleventh of the interval between the 

 phenomena we observe, and consequently that the interval can not be so much 

 as eleven years, and that it is less than a ninth, and that therefore it must be 

 more than nine years. But since, from the nature of the phenomena observed, 

 we are sure that there must be a whole number of years intervening (subject 

 only to ten minutes error, five minutes at each observation), we know that this 

 number must be ten. We then take the entire interval of time between the 

 two observed solstices, and we divide it by ten. The quotient will give the 

 length of the year, subject to an error of a tenth part of ten minutes, that is, 

 subject to an error only of one minute. By this expedient, in fact, the sum of 

 the errors of the two solstitial observations is divided among ten years, and 

 the quantity which falls on a single year is only the tenth part of the whole 

 error. 



This process may be carried further. The error being thus reduced to a 

 single minute, may again be spread over a still greater interval until the length 

 of the years be obtained, even in fractions of a second of time. 



The same method is applicable to all periodical phenomena and among 

 others, to the periodical variations of the stars. By the firs! rough observation 

 of a single period, we are enabled with certainty to recognise the number of 

 complete periods which intervene between two similar phases of the star ob- 

 served with a known interval of time between them. We divide that interval r 

 by the number of periods, and thereby obtain a second approximation, which ' 

 enables us to say with certainty how many complete periods there are between 

 two similar phases separated by a much longer interval than the former one. 

 Dividing this as before by the number of periods, we obtain a still closer ap- 

 proximation, and so on. 



The double stars, which will be fully noticed on another occasion, supply 

 a fruitful and interesting field of employment for the amateur. Nor need he 

 be discouraged from devoting himself to this labor by the consciousness of his 

 inability to submit his raw observations to those processes of calculation called 

 reductions, which are indispensable to render them ultimately available for the 

 high purposes of science. He will not find his labors neglected or con- 

 temned. Others, with better means and opportunities, will take the materials 

 and data which he supplies, and apply all those calculations to them which 

 are requisite to render them valuable. Nor will he lose a particle of the 

 eredit justly due to him ; for to omit the record of the name of the observer, 

 the nature of the instrument, aijd the place where the original record of the 

 observations is to be found, would be to insure the rejection of the results of 

 such observations both abroad and at home. The fundamental observations 

 of double stars are peculiarly pointed out as the most certain field for the pri- 

 vate observer, because they do not require any astronomical clock. The day 

 of the observation is all that is necessary to be known, and accordingly a 

 timepiece, with its necessary accompaniment, a transit instrument, is not 



