300 MK. N. BOHE ON THE DETERMINATION OF THE 



The jet in question, which had a mean radius a = 0'0675 cm. and a velocity 

 c = 425 cm./sec., was so stable that the wave-length could be measured with great 

 exactness up to a distance of about 35 cm. from the orifice. We will now examine 

 such a jet at a distance of 30 cm. from the orifice. 



The viscosity will firstly have the effect that an original difference in velocity at 

 different points of the cross-section of the jet is rapidly extinguished. 



The calculation on p. 298 shows that the differences mentioned must decrease 

 approximately as e~'\ where e = /A//O (7rl'2197/a) 2 . Let, now, a = 0'0675 and 

 = Q'0125 (temperature 1 1 '8 C.), we get e = 40 '3. Let, further, t = -ffg, and we get 



e~ li = e~ 2 '"" = 0'0582. We see from this that the differences in velocity at the place 

 in question must be about 17 times smaller than close by the orifice. 



The viscosity will furthermore have the effect that also the waves on the surface 

 of the jet tend to be of single types. We found above that the general form of the 

 surface of the jet, considering the vibrations as infinitely small, can be expressed by 



r = a + $& cos (n5 + T n ) cos (k n z + y M ) e 



where with approximation we have 



_ /u, 2n(nl) 



"" 1 



" p ca* 



Let now a = 0'OG75, p/p = 0'0125, c = 425 and z = 30, we get e~ v = 0'461, 

 e -'* = 0-098, -*'-" = 0-0096, e~ v = 0'00043, e~ f " : = 0'000009, &c. 

 If now the form of the surface of the jet is close to the orifice, 



r a + b 2 cos 23 cos k 2 z + b 3 cos 35 cos k 3 z + b t cos 4$ cos k 4 z + ... , 



the form of the surface will therefore be at a distance of 30 cm. from the orifice, 

 approximately, 



r = a + (6 2 cos 25 cos k 2 z + }b 3 cos 35 cos A- 3 2 



+ -foh cos 45 cos l\z + TcroU^s cos 55 cos & 5 z +...). 



For the jet used, the term with cos 25 cos k a z was already at the orifice quite 

 predominant, and especially the quantities b 3 , b 6 , ..., were very small in proportion to 

 b 2 , as the jet at the examination mentioned was found to be very nearly symmetrical 

 about two perpendicular planes through its axis. 



We thus see that the jet in the experiment mentioned at a distance of 30 cm. 

 from the orifice rmist have executed exceedingly pure vibrations. 



In the experiments ordinary tap-water was used. 



For the sake of the investigation it was important to get a jet which could run 

 without variation (same velocity and temperature) as long as wanted. In order to 

 give the water a suitable constant temperature, it was led from the tap through a 

 long leaden spiral tube, placed in a water-bath, and a regulator connected with the 



