G. E. Curtis — Theory of the Wind Vane. 45 



meteorological observations, these forms were replaced by sim- 

 ple plane plates, discs, or arrows, designed solely with regard to 

 the mechanical action of the wind upon them. 



The form in general use at present is that of an arrow with 

 a double or spread tail. The first reference I find to the con- 

 struction of a vane of this design is by the elder Parrot, 

 (Yoigt's Magazin, i, 1797). In order to diminish the contin- 

 ual oscillations to which the vane is subject during variable 

 winds, he made a vane of two thin plates joined at one end at 

 an angle of about 45°. This was used by the younger Parrot, in 

 his well known expedition to the Caucasus in 1811, with 

 Engelhardt. Similar vanes were soon introduced in other 

 countries, and by 1840 were in common use by English 

 meteorologists. With respect to the advantages of their use, 

 Jelinek, writing in 1850, makes the following statement : " The 

 English seek to obviate the disadvantages of the complete rota- 

 tions by making the vane of two plane surfaces set at an angle 

 to each other of generally about 22|-°. They say that thereby 

 the oscillations are smaller, and the complete rotations less fre- 

 quent." Stating that experience shows this to be true, Jelinek 

 adopted the same form for a self-recording anemoscope, de- 

 signed as an improvement on that constructed for the Austrian 

 meteorological service by Dr. Kreil in the preceding year, which, 

 consisting of a single plane circular plate, had occasioned much 

 difficulty by its frequent complete rotations. 



While the spread vane has thus grown in favor, the angle of 

 the wings has gradually been reduced. Starting with an angle 

 of 45°, as made bv Parrot in 1800, the angle in 1850 was gen- 

 erally 22ij°, and at present even a smaller angle is frequently 

 used. In practice the surfaces are made with a slight curvature, 

 so that the actual angle made by their tangents increases from 

 zero at the vertex, to 30°, or more, at their extremities. Yoigt's 

 Magazin, in which Parrot's description of his vane appeared, is 

 not accessible to me, and his reasons for adopting 45° are not 

 given by reviewers. Similarly, I have found no explanation 

 of the reason for adopting any of the smaller angles subse- 

 quently used. The following analysis has therefore been 

 made, in order to find definitely what advantages the spread 

 vane possesses, as compared with a straight vane of the same 

 length and shape, and at what angle the wings should be set 

 to secure the greatest efficiency. 



The wind vane, its surfaces assumed to be plane, is a case of 

 a body immersed in a fluid current, whose resultant pressure is 

 normal to the exposed surface, and proportional to some func- 

 tion of the angle of incidence. If a be the angle between the 

 surface normal and the perpendicular to the direction of the 

 current, the old theory of the resistance of fluids made the re- 



