372 RECORD OF SCIENCE FOR 1887 AND 1888. 



Substitutiug this value of G in the general differeDtial equation of 

 motion, Ferrel deduces the following expression for v for the mean 

 temperature condition of the earth where li is the altitude, aud G^ the 

 full gradient at the earth's surface; the last term is negligible as ex- 

 pressing the effect of inertia and friction due to meridioual motions: 



^_ (3.37 (1+0.004 r) ^.,_(>.0U0169O A2 sin j^ dt'^ " 



^~ cos ^ 1 + 0.004 r co¥'^7^7r+¥) 



The coefficient A2 represents the principal term in Ferrel's previous 

 develoi)ment of the solar diurnal variation of temperature in a harmonic 

 series that obtains for the whole year and the whole earth. Instead of 

 attempting to compute the temperature (r) Ferrel has preferred to 

 compile from charts of temperature and pressure the actual average 

 values of temperature and ])ressure and wind velocity for each five de- 

 grees of latitude for January, July and the whole year, for the north- 

 ern and southern hemispheres. The introduction of these observed 

 temperatures and pressures enables him to compute the value of v 

 which on comparison with the observed velocity shows a very excellent 

 agreement. The process is simply a refinement upon the numbers 

 already iiublished by him in 1858, and is, I think, equivalent to the 

 statement that if among the many direct solutions of the equations of 

 motion ijossible when the boundary conditions are given, we, without a 

 previous knowledge of these boundary conditions, select that special 

 solution that we find existing on the earth's surface as indicated by 

 our observed temperatures and pressures, then the resulting computed 

 velocity agrees with the observed velocity of the wind. After explain- 

 ing the annual oscillations of winds and calms, rain and cloud, Ferrel 

 passes to chapter 4 on cyclones. In this is given an elementary me- 

 chanical theory of the gyration of a small portion of the atmosphere 

 near the earth's surface at any latitude, the resulting equations (7) on 

 page 238 being, of course, entirely similar to the general equations 13 

 on page 188 for the general cyclonic motion of the atmosphere about 

 the earth's axis. 



The treatment of these equations is natuially very similar to that for 

 the general motion of the atmosphere, and if Ferrel's methods seem pro- 

 lix and inelegant, as compared with the beautiful work of Oberbeck and 

 Helmholtz, it must be remembered that he expressly states this treatise 

 to have been written for persons who have a slight acquaintance with 

 the mathematical progress of the past thirty years, and that he has 

 therefore adopted such elementary and simpler methods as could be 

 easily comprehended by those who graduate from minor colleges and 

 scientific schools, while at the same time he has also exi)ressly avoided 

 analytical refinements that are not demanded in the present crude state 

 of meteorological knowledge. In fa<'t, like all his other treatises, this 

 ftjso impresses one with the oouvi<''tion that ri'irel aims to bo a pmotiCHl 



