xiii.] MEASUREMENT OF PHENOMENA. 295 



human instruments. The rotation of the earth, too, by 

 variously affecting the apparent velocity of ingress or 

 egress of Venus, as seen from different places, discloses 

 the amount of the parallax. It has been sufficiently 

 shown that by righth' clioosing the moments of obser- 

 vation, the planetary bodies may often be made to reveal 

 their relative distance, to measure their own position, to 

 record their own movements with a high degree of 

 accuracy. With the improvement of astronomical instru- 

 ments, such conjunctions become less necessary to the 

 progress of the science, but it will always remain advan- 

 tatreous to choose those moments for observation when 

 instrumental errors enter with the least eff*ect. 



In other sciences, exact quantitative laws can occasion- 

 ally be obtained without instrumental measurement, as 

 when we learn the exactly equal velocity of sounds of 

 different pitch, by observing that a peal of bells or a 

 nmsical performance is heard harmoniously at any dis- 

 tance to which the sound penetrates ; this could not be 

 the case, as Newton remarked, if one sound overtook 

 the other. One of the most important principles of the 

 atomic theory, was proved by implication before the use 

 of the balance was introduced into chemistry. Wenzel 

 observed, before 1777, that when two neutral substances 

 decompose eacli other, the resulting salts are also neutral. 

 In mixing sodium sulphate and barium nitrate, we 

 obtain insoluble barium sulphate and neutral sodium 

 nitrate. This result could not follow unless the nitric 

 acid, requisite to saturate one atom of sodium, were 

 exactly equal to that required by one atom of barium, 

 so that an exchange could take place without leaving 

 either acid or base in excess. 



An important principle of mechanics may also be 

 established by a simple acoustical observation. When 

 a rod or tongue of metal fixed at one end is set in 

 vibration, the pitch of the sound may be observed to 

 be exactly the same, whether the vil nations be small or 

 great ; lience the oscillations are i^it)chronous, or e([ually 

 rapid, independently of their magnitude. On the ground 

 of theory, it can be shown that such a residt only 

 happens when the flexure is proportional ti) tlie deflecting 

 force. Thus the simple observation that the pitch of 



