86 THE PRINCIPLES OF SCIENCE. 



sphere would offer a resistance proportional to the velocity 

 of the moving body, and concluded that the path would 

 have in consequence a logarithmic character. Newton 

 investigated in a general manner the subject of resisting 

 media, and came to the conclusion that the resistance was 

 more nearly proportional to the square of the velocity. 

 The subject then fell into the hands of Daniel Bernouilli, 

 who pointed out the enormous resistance of the air in 

 cases of rapid movement, and calculated that a cannon ball, 

 if fired vertically in a vacuum, would rise eight times as 

 high as in the atmosphere. In more recent times an 

 immense amount both of theoretical and experimental in- 

 vestigation has been spent upon the subject, since it is 

 one of great importance in the art of war. Successive 

 approximations to the true law have been made, but 

 nothing like a complete and final solution has been 

 achieved or even hoped for m . 



It is quite to be expected that the earliest experi- 

 menters in any branch of science will overlook corrections 

 which afterwards become most apparent. The Arabian 

 astronomers determined the meridian by taking the 

 middle point between the places of the sun when at 

 equal altitudes on the same day. They overlooked the 

 fact that the sun has its own motion among the stars 

 in the time intervening between the observations. Newton 

 thought that the mutual disturbances of the planets might 

 be disregarded, excepting perhaps the effect of the mutual 

 attraction of the greater planets, Jupiter and Saturn, near 

 their conjunction n . The expansion of quicksilver was long 

 used as the measure of temperature, in ignorance or dis- 

 regard of the fact that the rate of expansion increases 

 with the temperature. Rumford, in the first experiment 

 leading to a determination of the mechanical equivalent of 



m Button's ' Mathematical Dictionary,' vol. ii. pp. 287-292. 

 n 'Principia/ bk. iii. Prop. 13. 



