86 KANSAS Academy of science. 



tangent to the conjugate hyperbola, is the same circle. The whole theory for the 

 hyperbola is, therefore, at once evident, and further details may be omitted. 



The above theory for the ellipse is also capable of another interpretation. We 

 may say that the conjugate ellipse is wholly imaginary, and that the theorems in 

 the above list give us the focal properties of the conjugate ellipse. 



In the case of the parabola, the theory of the imaginary foci is more compli- 

 cated. Since the line at infinity is tangent to the parabola, two of the four tan- 

 gents drawn from / and J coincide, and there are left only three tangents and three 

 points of intersection. Two of these are / and J, and the other is the real finite 

 focus. Thus the circular points at infinity are the imaginary foci of the parobola. 



It would be interesting to know what properties the points / and J have in com- 

 mon with the finite foci of a conic, and especially with the finite focus of a para- 

 bola ; but this question I have not investigated. 



NOTES ON SOME SUMMER BIRDS OF ESTES PARK, COLORADO. 



BX VEBNON L. KELLOGG, LAWBENOE. 



Estes Park is a beautiful little valley at the base of Long's Peak, about seventy 

 miles northwest of Denver, being in latitude 40°24' north, longitude 105°36'' west. 

 The Big Thompson, afflaent of the North Platte, fed by the melting snow of the 

 Front Range, of which Long's Peak and adjacent peaks are a spur, winds through 

 the six miles of the Park's extent, and its many small tributary streams come 

 tumbling out of the surrounding hills and mountains in well-worn gorges, or glide 

 gently down woods-lined valleys. Spreading away from the Big Thompson on either 

 side, for half a mile or more, extends a luxuriant pasture. The Park narrows at its 

 head, and the bounding lateral moraines, covered with ice-worn boulders, approach 

 rapidly, until the Park is no park, but a gorge, which cuts deeply into the great 

 snow-covered range, and is yet as wild and primeval in its aspect and condition as 

 before the first camp-fire smoke ever drifted up from the now fairly civilized meadows 

 along the Big Thompson. 



The altitude of the Park is about 8,000 feet, and of the range from which its 

 massive boulders have been brought about 13,000 feet; while Long's Peak rears its 

 square-capped head to an elevation of 14,271 feet. The peaks and chasms of the 

 range are white with never- melting snow, and in certain places — two, at least — the 

 snow has become so compacted, and the well-marked crevasses and half-proven 

 movements so sure evidences, that Hallet's and Chapin's Glaciers are beginning to 

 attract more than local attention. Great tracts on the range sides are covered with 

 spruce forests, but so many fires have swept over the region that the hills and val- 

 leys are covered with the charred spars of spruce and pine, some standing, others 

 prostrate and entangled in the up-springing new growth. 



The following notes on the avian fauna of the Park are from observations made 

 during the summers of 1886-1889. A brief visit in June of this year (181)0) gave 

 opportunity for some corroborative observation: 

 1.— Anas strepera Linn. Gadwall. 



A pair seen on a small pond in an offshoot of Estes Park, called Horseshoe 

 Park. This duck is not an uncommon summer resident. 

 2. — Actitis maculata (Linn.) Spotted Sandpiper. 



Not uncommon. A few seen along the Big Thompson, and a pair seen August 

 19 at a small pond near timber-line. 



