152 



SCIENCE. 



[Vol. XIII. No. 316 



may readily be large enough to have a vertical component equal to 

 the bird's weight, in which case the resultant force on the bird may 

 be horizontal. 



Let us suppose, now, that a bird is at any instant moving hori- 

 zontally, in the same direction as the wind, and with a small velo- 

 city relative to the earth. Since the resultant force on him may be 

 horizontal, he may continue to move horizontally with increasing 

 speed. As his speed increases, the velocity of the wind relative to 

 him diminishes, and therefore also, probably, the upward force 

 exerted on him by the wind. Although, therefore, the resultant 

 force on the bird may have been initially horizontal, it will not re- 

 main so even for a short time. But it may remain for some time 

 very nearly horizontal ; for, as the magnitude of the relative velo- 

 city diminishes, its inclination to the normal to the plane of the 

 wings will diminish also. During that time the bird will move 

 slightly downwards, and his velocity will increase. When his 

 velocity has become so great, and therefore the velocity of the wind 

 relative to him so small, that the resultant force on him begins to 

 have a direction differing markedly from the horizontal, let the 

 bird wheel and steer upwards to windward. Let us suppose that 

 in wheeling he maintains his velocity relative to the earth as well as 

 his elevation. Then, starting upwards with a considerable velocity, 

 he will clearly be able to rise through a certain height before his 

 velocity has been reduced to its initial value. Let him then wheel 

 again, and he will now be in a position to repeat the cycle with the 

 same starting conditions as before. Whether soaring has been 

 accomplished or not, will depend on whether or not the height 

 gained when moving to windward is or is not greater than that lost 

 in moving to leeward. 



To determine this, consider first the downward part of the cycle. 

 Let 1-Vi be the mean vertical component, and W^ the mean hori- 

 zontal component, of the force exerted by the wind on the bird's 

 wings. Let R be the mean resistance to the relative motion of bird 

 and air (due to friction, etc.), which in this case helps the bird. 

 Let w be the weight of the bird, A the height through which he 

 falls, and d the horizontal distance he traverses. Then the work 

 done on the bird by the vertical and horizontal forces will be 

 (7t> — Wi)A and (i?+ W^d respectively (we may treat i? as a hori- 

 zontal force, because the path is nearly horizontal). Let Hhe the 

 energy expended immediately or ultimately in the production of 

 heat. Then the kinetic energy gained by the bird on the down- 

 ward motion will be — 



(w — W^)/t + {R+ Wi)d—H. 



During the upward motion against the wind, the mean velocity 

 of the wind relative to the bird will be much greater than during 

 the downward motion with the wind ; but while the direction of 

 the relative velocity during the downward motion was upward, 

 during the upward motion it is downward. It seems reasonable, 

 therefore, to suppose that the upward force exerted by the wind 

 may be made by the bird the same as before, and may have, there- 

 fore, the same components, W^ and W„. Let R' be the mean re- 

 sistance of the air due to friction, etc. R', in this case, impedes the 

 motion of the bird. Let w, as before, be the bird's weight ; and let 

 h' be the height through which he rises, and d' the distance trav- 

 ersed horizontally. Then the work done by the bird against the 

 forces acting on him will be — 



{w-lV^)h'+{R'+ lV^)d'. 



If the bird wheels when the energy expended on the upward 

 motion is just equal to that gained on the downward motion, 

 he will be ready to begin his second cycle under the same start- 

 ing conditions as his first, and we shall have, for determining the 

 height to which he has risen, the equation — 



{■w—JVi)/i + {R+ Ws)d — H = (w — Wi)h' + (^R' + W^)d', 



from which it follows that the gain of elevation 



k' ~ k = 



Rd-R'd'+ W^{d — d') — H 



downward motion, R' will be greater than R. But the bird can so 

 steer his course as to give his path a greater inclination to the ho- 

 rizon than his downward path had : hence d' may be made smaller 

 than d ; and thus Rd — R'd' may, by good steering, be made posi- 

 tive. Also, d' being less than d, W^{d—d') will be positive. If 

 these two quantities together are greater than H, h' — h will be 

 positive ; and if, finally, the increase of energy represented by the 

 elevation h' — ^ is greater than the inevitable waste during the 

 turns, the bird will have increased his elevation during the cycle. 



It seems to me possible, therefore, for a bird to soar in a uniform 

 horizontal wind ; because, by falling slowly in the motion to lee- 

 ward, he allows the wind to do a large amount of work on him, 

 and, by rising rapidly in moving to windward, he may regain his 

 former level without having to do so much work against the wind. 

 If it is possible, the bird's path must clearly be a spiral about aline 

 rising in the direction of the wind, not about a vertical line ; and 

 this agrees exactly with observed fact. J. G. MacGregor. 



Dalhousie College, Halifax, N.S., Feb. 5. 



Some Habits of the Omahas. 



In the article entitled " Some Habits of the Omahas," on p. 60 

 of Science for Jan. 25, was a slip of the pen, which I wish to cor- 

 rect. Both Omahas and Ponkas, who speak the same dialect, call 

 the wild honey " bee-dung." The term " bee-gum " was given me 

 in 1872 by a Ponka, my interpreter, who stated that it was not the 

 old name. My Omaha informant, Samuel Fremont, does not wish 

 incorrect statements credited to him. J. Owen Dorsey. 



TakomaPark, D.C., Feb. 13. 



Sawdust Explosion. 



w—W-^ 



Since during the upward motion ag9,inst the wind the mean value 

 of the velocity of the air relative to the bird is greater than in the 



I ENCLOSE you a cutting from the Ottawa /ournal in reference 

 to what is called a " sawdust explosion," as it is a somewhat unique 

 phenomenon. Last winter one occurred in the Ottawa River op- 

 posite this city, near the place referred to in this article, which 

 broke up the thick ice over a large space. The river-channel is 

 deep, but it is filled with a great accumulation of sawdust from the 

 large mills just above. This sawdust generates immense quanti- 

 ties of marsh-gas, and once in a while something seems to start it 

 up suddenly in large volumes. These striking the under side of 

 the ice with great force, burst it up in the manner here described. 

 This is why they are called " explosions." The gas is never ig- 

 nited. 



" Mr. J. de St. Denis Lemoine, sergeant-at-arms of the Senate, 

 was blown up in a sawdust explosion on the Ottawa River, Satur- 

 day, Feb. 9, 1889, at midnight. He escaped with a wetting, and 

 will not snowshoe to Gatineau Point again. It was a jolly party of 

 gentlemen who left the city Saturday evening for a tramp on the 

 ice-bound Ottawa. It included Messrs. Riddington, Lemoine, R. 

 Fleming, J. Travers Lewis, J. W. Pugsley, Charles Elliott, Laurence 

 Taylor, W. Middleton, Bogert, G. A. Henderson, and some others. 



" The snowshoers headed direct to Gatineau Point, where an 

 enjoyable time was spent. They started for home shortly before 

 midnight. Mr. Riddington led the way, the snowshoers following 

 in Indian file at a distance of about ten feet apart. The leader 

 cautiously picked his way, because an ominous crackle here and 

 there gave warning of proximity to cold waters running a few 

 inches beneath. 



" Matters went well for a time, until, some little distance below 

 the Rideau Falls, suddenly the snowshoers were startled by a 

 terrific explosion. An instant later they saw Mr. Lemoine hurled 

 in the air, and as suddenly fall back into a mass of broken ice. It 

 was only the work of a moment to grasp the sash of Mr. Lemoine 

 and haul him on to the firm ice, not much the worse for his partial 

 wetting. There would have been a funeral had the sergeant-at-arms 

 been in the middle of the explosion. 



" Mr. J. Travers Lewis had a narrow escape. Fortunately he 

 stopped for a moment to fix his snowshoe-strings, and, had he con- 

 tinued in the footsteps of Mr. Lemoine, would also likely have ex- 

 perienced a sad fate. 



" The snowshoers say that in their opinion the sawdust question 

 has been solved." Robert Bell, 



Ottawa, Can., Feb. 13, 



