OF ARTS AND SCIENCES. 



225 



mula (7 = ^ log I -\- .75. The close agreement shows that t =z 



m 



length. 



v/, or that the time is jDroportional to the square root of the 



The observations given in Table II. were 



2. Force of Magnetism 

 made by Professor Mayer (Amer. Jour. Sci., Sept. 1870), to determine 

 the effect of a coil on a galvanometer needle placed at different distances. 



TABLE II. 



The first column gives the distance, the second its logarithm, and the 

 third the logarithm of the force produced, or the tangent of the angle 

 of deflection. To see if f= in d'"', a curve was constructed, with col- 

 umns 2 and 3 as co-ordinates, and appeared to coincide very closely 

 with the line y = — 2.76 a; -|- 2.545. Column 4 gives the values of 

 log f thus computed, which shows a close agreement with observation. 

 The result found by Professor Mayer was « = 2.7404 ; but the last 

 two figures should be omitted, as they alter the result by only about 

 one or two hundredths as much as the accidental errors. 



3. Resistance of Air. Another excellent example is found in the 

 resistance of air to projectiles. Newton assumed that the resistance 

 was proportional to the square of the velocity, or R = m v- ; but 

 this result is not sustained experimentally. The agreement with the 

 cube of the velocity is, in fact, more exact ; but neither is the true law. 

 A more careful exammation shows that the law alters for velocities 

 above and below that of sound, or about 1,100 feet per second ; since 

 above that velocity the air cannot flow in rapidly enough to fill the 

 space behind the shot, but leaves a vacuum. To show this, a series of 

 observations with the Bashforth chronograph were examined, and 

 showed in a marked manner the change when i = 1,100. No part of 

 the curve, however, for either spherical or elongated shot becomes a 

 straight line ; and therefore no power of the velocity will give the cor- 

 rect value of the resistance. 



4. Conic Sections. It often happens, especially in astronomy, that 

 VOL. I, 29 



