THE SCIENTIFIC LAW 97 



formulae, by aid of which we can classify the relationships 

 and sequences of more and more extensive groups of 

 phenomena. The earlier formulas are not necessarily 

 wrong-/ they are merely replaced by others which in 

 briefer language describe more facts. 



We cannot do better than examine this process very 

 briefly in a special case, namely, the motion of the 

 planetary system. An easily observed part of this 

 motion was the daily passage of the sun, its rising in the 

 East and setting in the West. A primitive description 

 of the motion consisted in the statement that the same 

 sun which set in the West passed, hidden by northern 

 mountains, along the surface of the flat earth and rose 

 again in the East. The description was clearly very 

 insufficient, but it was a first attempt at a scientific 

 formula. An obvious improvement was soon made by 

 limiting the surface of the earth and supposing the sun 

 to go below the solid earth. The motion of the sun 

 taken in conjunction with the motion of the stars led 

 early astronomers to conclude that the earth was fixed 

 in mid-space, and sun and stars were daily carried round 

 it. The description thus improved was still far from 

 complete ; the sun was observed to vary its position 

 with regard to the fixed stars. Gradually and laboriously 

 facts were accumulated, and in time those early astron- 

 omers concluded that the sun went round yearly in the 

 same circle, this circle itself being carried round with the 

 starry heavens once in a day. This formula embraced 

 a wider field of phenomena than the earlier ones, and 

 probably was as exact a description as men's perceptions 

 of earth and sun allowed when it was invented. Hipp- 

 archus improved it by placing the earth not exactly in the 

 centre of the sun's circle, and thus more accurately 

 described certain apparent irregularities in the sun's 

 motion. A still more complete description was adopted 



1 They are what the mathematician would term " first approximations," true 

 when we neglect certain small quantities. In Nature it often happens that 

 we do not observe the existence of these small quantities until we have long 

 had the "first approximation" as our standard of comparison. Then we 

 need a widening, not a rejection of " natural law." 



