PAPER BY MAX MARGULES. 303 



Here, and in the following, we adopt as units the metre, the kilogram, 

 the second of time, the degree of the Centigrade thermometer, and for 

 pressures the barometric scale. For T =273° we have c=279.9. 



The values 7/=4xl0 7 or the circumference of the equator, @= 

 24x60x60 or 1 day and T =273° gives a wave of pressure whose max- 

 imum coincides with the maximum of temperature, and also gives 

 5=1.576 x A. A temperature variation of 1° C. produces a pressure 



p x 1.576 

 variation ° " — or 4.4 millimetres of mercury when p is 760 on 



the barometer scale. 



When we desire to obtain pure horizontal vibrations in a layer of 

 appreciable altitude without neglecting force of gravity we should have 

 to introduce a function (A) of the altitude as we see from the equations 

 (3), tliat shall satisfy the condition 



ldi g L z - c 2 2 

 A dz c 2 I? 



For isothermal vibrations in a vertical column of air the conditions 

 are 



r = 



¥=<> 



and equation (4) becomes 



f £ g d « l f * 



d z* ~ RT d z ~ BT d t 2 



= 0. 



This equation or the corresponding equation in w has recently been 

 discussed at length by Lord Rayleigh (Phil. Mag., Feb., 1890).* 



IV. VIBRATIONS OF THE AIR WHEN A WAVE OF TEMPERATURE AD- 

 VANCES HORIZONTALLY, TAKING INTO CONSIDERATION THE 

 FORCE OF GRAVITY. 



With a constant value of T and putting r = A sin (mx + nt) the dif- 

 ferential equation (4) becomes 



t¥+Tt>- a rz-g-Ji>--gJt>- aT ' ' ' ' (4C) 



[" = wJ 

 The wave of pressure will be of the form e = F (z) sin (mx + nt). 



* [See also No r XVIII of this present collection of Translations.] 



