British Association. 309 



a small hole in the centre ; but on inserting into this a glass tube 

 of three inches in length, the effect was reversed, the sound being 

 only heard when the glass was unclosed ; upon increasing this small 

 tube to seven inches, being half the length of the larger one, no 

 sound was produced. Mr. Addams said he would not attempt to 

 explain the cause of this phenomena, but leave it to Professor Wheat- 

 stone and other abler hands. 



Thurmay^ 25f/i August. — 1. Mr. Talbot's Researches on the In- 

 tegral Calculus. — Mr. Talbot had succeeded in assigning an algebrai- 

 cal value to the sura of three or more integrals of functions, whose 

 denominators are not merely quadratic radicals of entire functions of 

 the fifth and higher degree, such as constitute the ultra elliptic 

 integrals furnished by Abel's celebrated theorem, but also of others 

 whose denominators are cubic, and other radicals of similar functions 

 which that theorem does not contemplate ; thus effecting a very 

 great extension of one of the most difficult and interesting depart- 

 ments of the integral calculus. 



2. Dr. Apjohn on the Specific Heat of Gases. — All gases have 

 not, under equal volumes, the same heat, as is conceived by Haycraft, 

 Marcet, De la Rive, and others. Neither is this law true of the 

 simple gases, as supposed by Dulong. The specific heat of hydrogen, 

 under an equal volume, is nearly one and a half that of atmospheric 

 air. The author's numbers come nearer those of De la Roche and 

 Berard than any other. No simple relation appearing to exist, 

 according to the author, between the specific heats of gases and their 

 specific gravities or atomic weights. 



3. Professor Hamilton on the Calculus of Principal Rela- 

 tions. — By this method, the author proposes to reduce all questions 

 in analyses to one fundamental equation or formula. Its principle 

 depends on the fact, that he had discovered the following relation to 

 subsist between all differential functions, no matter how numerous — 



I d s c s 

 h dx~ d x' 



4. The Rev. W. Scoreshy on Two Magnetical Instruments. — 

 The first instrument depends on the influence of an extremely sus- 

 ceptible bar of soft iron, on a magnetic needle ; so susceptible that by 

 merely passing it roughly through the hand, a deviation of many 

 degrees of the needle may be obtained. By means of an appropriate 

 contrivance the bar is set at any given angle to a common compass, 

 and by this the dip may be obtained to within a very small error. 

 The other consists of a needle of about 16 inches long; it is con- 

 structed of several thin lamina? of steel, united at their extremities, 

 and separated in the centre by a block of wood, supporting the agate> 

 upon which it rests ; the weight of this needle, which is not great, 

 is relieved from the point supporting the agate by sus[)ension silk. 

 There are at the extremities silver verniers. It is intended to apply 

 this instrument to the measurement of magnetic powers generally, 

 and to the distances between inaccessible points, as in the case of the 

 thickness of rocks and walls. 



5. Professor Forbes on the ^Ter rest rial Magnetic Intensity at 

 carious heights. — Professor Forbes, in this communication, has gone 



