On the Reduction of Temperatures by Electricity. 419 



bisecting the angle ACD must pass between BC and CD. Draw 

 this line, and produce AB to meet it. 



As AE and CD are parallel, DCE and AEC are equal (XXIX.), 

 therefore ACE and AEC ai'e equal, therefore AE and AC are 

 equal (VI.), and therefore AC is greater than AB. 



XXVI. If two triangles (BAC, DEF) have two angles, and a 

 side similarly placed with regard to the equal angles, equal, these 

 triangles are equal in every respect. 



Place them so that the bases form one 

 right line, and the equal sides AC and 

 DE are next each other. Produce BA 

 and FE until they meet at G. Join A 

 and E. As the angles ECF and CEF are 

 equal to ACB and CAB, the remaining angles ABC and EFC 

 are equal (XXXII.). Therefore BG and FG are equal (VI.). 

 As AC and CE are equal (Hyp.), the angles DExl and CAE are 

 equal, therefore GAE and GEA are equal, and therefore GA and 

 GE are equal ; taking these from BG and FG, we have AB and 

 EF equal, and therefore (IV.) the triangles are equal in every 

 respect. 



If the angles ABC and EFC are obtuse, the point G will lie 

 at the other side of BF, but the proof will remain the same. 



If, however, ABC and EFC are right angles, a different de- 

 monstration must be adopted. 



Produce AC and EC until the pro- 

 duced parts are each equal to AC or 

 EC. Join BD and FG. In the tri- 

 angles ACB and DCB, the sides AC 

 and CB are equal to DC and CB and 

 the included angles equal, therefore AD forms one continued 

 right line. In a similar manner EG is proved to be one right 

 line. In the triangles ACD and ECG, AC and CD are equal to 

 EC and CG, and the included angles (XV.) arc equal, therefore 

 AD and EG are equal, and therefore their halves AB and EF 

 are equal. 



Queen's College, Cork. 

 Sept. 28, 1852. 



LXVI. On the Reduction of Temperatures by Electricity. 

 By Dr. John Tyndall, F.R.S. 

 [With a Plate.] 

 To the Editors of the Philosophical Magazine and Jonrnal. 

 Gentlemen, 



IN an abstract of Professor William Thomson's Mechanical 

 Theory of Thermo-electric Currents, given in your Supple- 

 mentary Number for July, reference is made to the well-known 



2E2 



