SCIENCE. 



[Vol. XXI. Ni.. 520 



In man, there is not, inrleed, a habit, but an organ which has 

 lost its uses, yet is still developed in every child brought into the 

 world. The outer ear was formerly provided with mu cles by 

 which it could be turoed towards any sound for its better recog- 

 nition. These muscles have become obsolete by heriditary disuse, 

 so that in all normal subjects the ear is motionless. That it could 

 formerly be directed so as the better to receive a sound will the 

 less be denied as it survives in certain exceptional individuals. 

 But as it is absent in the great bulk of our species, the question 

 arises, Why does the external ear not gradually cease to he devel- 

 oped ? No one can now contnnd that it is useful. 



J. W. Slateu 



London, England. 



Speed of Flight of Birds. 



I HAVE aUvays been more or less of a sceptic in regard to the 

 high rate of speed in the flight of certain birds, but I have only 

 just obtained a bit of satisfactory evidence from my own observa- 

 tions. Our wild ducks are admitted to be among our strongest 

 flyers, but I am satisfied that the bxifS.e-head ( CJiaritonetta albeola) 

 does not attain a speed of forty miles per hour. While travelling 

 on the Baltimore and Ohio Railway, up the valley of the Potomac, 

 on Jan. 3 I saw a great many ducks, nearly all of which were 

 buffle-heads. Those who are familiar with the road will recall 

 how closely it follows the windings of the river, so that a bird 

 flying up mid-stream would travel just the same distance as the 

 train on the bank. It so happened that, on rounding a sharp 

 curve, my train flushed a pair of buffle-heads, which started up 

 stream at full speed. On watching them I found that, instead 

 of leaving us behind, we were actually beating them, and I am 

 confident that their rate of speed was not equal to that of tlie 

 train. We kept alongside of them for nearly a minute before 

 they turned back down-stream. Careful calculation showed that 

 the train was running at about thirty-seven miles per hour, so 

 that the rate of speed for those wild ducks would be about thirty- 

 six. I hope that others may have some evidence on this question 

 of speed in flight which will throw more light on the subject. 



Hubert Lyman Claek. 



Pittsburgh, Pa. 



Bowser's Trigonometry. 

 As I have learned to admire the mathematical text books of 

 Professor Bowser from the excellent results I have had fro'n their 

 class room use for several years, I was surprised to see the some- 

 what adverse criticism of his Trigonometry in Science of Nov. 25. 

 I disagree with your critic's assertion that the best way to study 

 trigonometry is along the line of its historical development. I 

 beheve that such a course of study would be objectionatile, be- 

 cause of the long time it would require, and because the student 

 would be compelled to unlearn, if I may so phrase it, many things 

 he would necessarily be called upon to learn if he followed the 

 historical method. It is a recognized pedagogical fact that it is 

 easier to teach correct methods to a student who has never used 

 incorrect methods, than to one who has. To acquire a complete 

 knovvledsie of trigonometry would undoubtedly require a study of 

 its development, to acquire the knowledge required for its proper 

 and facile use in its many applications, does not require a studv of 

 its history. 



And accordingly f believe his plan of giving the be?t results and 

 methods of the Ijest studenis and workers in trigonometry is to be 

 preferred to a method which requires a student to test and reject 

 what has long before been tested and rejected. I admire Profes- 

 sor Bowser's plan of giving such definitions of the functions as ap 

 ply to all angles, acute, obtuse or reflex. I think some of the 

 writers on the subject have fallen into a grave error when they 

 give definitions of the functions of acute angles, and afterward 

 modify the definitions to suit obtuse angles. 



In Professor Bowser's development of the theoretical part of 

 the subject, he is especially clear. His book is a rt-adable one. 

 He is precise in his statements, and his demonstrations are such 

 as the average student can readily follow— which cannot be said 

 of every book on the ,=;ubject. 



The collection of exercises and examples is an unusually large 



one, suited to every requirement, while the model solutions are 

 truly model in their methods and arrangement, llis chapter on 

 De Moivre's Theorem is more complete than is usually given in 

 text-books, while his final chapter on the application of spherical 

 trigonometry serves at once to show the student its use, and to 

 give him a glimpse of several fascinating branches of mathe- 

 matics. 



Your critic is hardly justified in bis claim that Professor Bow 

 ser has made several historical mistakes. It is unfortunate that 

 Professor Bowser should imply that Napier was the inventor of 

 what are now called Napierian logarithms; but surely he is right 

 in saying that Briggs introduced the common system in 1615, 

 since it is generally ad mitteii that Briggs lectured on them in that 

 year, though his tables were not pu^lli^hed until two years later. 

 And why your critic should object because Professor Bowser, in 

 speaking of addition and subtraction logarithms, refers to Zech's 

 tables, I fail to understand, since Zech's tables are equal if not su- 

 perior to any others published. 



Of course, only a class-room test can determine the merits of a 

 text-book, but this latest book of Professor Bo" ser is so filled with 

 the many qualities which have made his previous books so suc- 

 cessful that I cannot see any reason why it should not meet with 

 a liue success. H. L. HoDGKiNS, Professor of Mathematics. 



C'olumoiau University, Washington, D. C, Jan. 5. 



Humming-Bird's Food. 



In several recent numbers of Science there have been notices of 

 the habit of Trochilus colubres feeding on the sap of different 

 trees. I have also noticed the fact, and was interested on becom- 

 ing acquainted with T. anna to find that it also made this a staple 

 article of food during the summer and fall. In this part of Cali- 

 fornia there are few trees yielding a sap save the Cottonwood and 

 willow. 



During a mountain trip in August, 1890, 1 found the humming- 

 bird very common in the willows along the creeks, at about 5,000 

 feet elevation ; and was pleased to find that the red-breasted sap- 

 sucker {Sphyrapicus rufer) filled the office of S. varius to the 

 ruby-throat. The willow thickets were very dense and composed 

 mostly of dwarfish shrubs of Salix lariolepis. 1 forced my way 

 into the interior, and watched the birds; sap-suckers, humming- 

 birds, and warblers (Dendroiea auduboni), often waiting turns at 

 a favorite drinking-spot ; though possibly the latter were more 

 interested in the insects attracted by the honey than by the honey 

 itself. There were often three, and even four or five, humming- 

 birds in sight at a time. They were very tame, and very curious; 

 coming within three or four feet of me, poising themselves on 

 their wings and looking me over. I noticed most of these were 

 young, and that the adult males were quite shy. 



Sutisequently, while teaching at Dunlap, at about 3,500 feet 

 elevation, I found the birds as late as December feeding in the 

 same manner. 



Irrigation seems to have an important influence on the habitat 

 of this bird. 



For three years I have lived most of the time in the southern 

 half of Fresno County, in an open plain. For the first two years 

 I saw but very few humming birds, and never saw them feeding 

 on the nitive floivers, no matter how showy they were. 



Meanwhile, the water had formed a pond by sub-irrjgation. on 

 the ranch, and the same variety of willow {Salix lariolepis), which 

 in the valley forms a tree 40-60 feet high and 3-5 feet in diame- 

 ter, had come in thickly and grown to about 15 feet in height. 

 This fall I noticed many humming-birds about the place, and 

 traced them to this pond. 



I have never seen but one or two sap-suckers here, but I found 

 the birds in great numbers feeding on the sap exuding from the 

 wounds caused by a large borer, the moth of which, about two 

 inches across the wings, colored black and white, was flying about 

 in abundance. 



I have not as yet found them feeding upon any tree save this 

 willow. Maples are very scarce in the Sierras of this county, and 

 the sap-suckers prefer willows to any other tree. I have not 

 observed that the squirrels score the bark of trees here as in the 



