2 ANNUAL RECORD OF SCIENCE AND INDUSTRY. 



These tables give the four theta functions which form the 

 numerators and denominators of the three elliptic functions. 

 The calculations relating to these functions have been carried 

 to ten decimal places, and the printed results will occupy 

 about four hundred pages. 12 A, X., 372. 



NEW FORMULA FOR DETERMINING THE ALTITUDE FROM BARO- 

 METRIC OBSERVATIONS. 



M. St. Robert, of France, has published the concluding vol- 

 ume of his memoirs, among which we notice a new formula 

 for determining the altitude for barometric observations. 

 This formula embodies the results of Glaisher's balloon ob- 

 servations. 



THE REDUCTION OF ELLIPTIC INTEGRALS. 



From a mathematical paper by Meissel, Professor in Kiel, 

 we take the following theorem, whose enunciation will be of 

 interest to mathematicians. He states that in a great num- 

 ber of cases he has been able to represent the complete el- 

 liptic integral of the second order by means of algebraic 

 formulae, and demonstrates, in general, that the complete in- 

 tegral of the second order can be converted into a complete 

 integral of the first order. Archiv der Jfathematlk i 'LVI. i 337. 



THE TRISECTION OF AN ANGLE. 



The problem of the trisection of a circular arc has lately 

 been solved by Dr. Hippauf in a simple manner by means of 

 an auxiliary curve, which may be designated as the conchoid 

 on a circular base. This circular conchoid is the locus of a 

 series of points found by drawing through one extremity of 

 the diameter of a circle a series of lines, and finding, upon 

 each, that point which is at a distance from the circumference 

 of the circle equal to the radius. Having described such a 

 circular conchoid for the circle an arc of which we wish to 

 trisect, we draw the chord beloncjina: to the latter arc, and 

 then through the origin of the conchoid a parallel chord ; 

 this latter is equal to the chord of the third part of the arc 

 to be trisected. Three other methods of effecting this tri- 

 section are also given by Hippauf by the aid of the same 

 curve; and many other curious properties are found by Pro- 

 fessor Sidler, who has shown that this conchoid may also be 



