23G 



Prof. R. Clausius on a new Mechanical Theorem 



the complete calculation of the formula? for every station. As 

 the numbers first obtained were not immediately comparable, I 

 have made them more nearly so by trebling the numbers given 

 by theory and doubling those in the preceding Table. The re- 

 sults are as follows : — 



Longi- 

 tudinal 

 ordi- 



Trans- 

 versal 

 ordi- 

 nate, 



a. 



/3. 



Result of T , , . , 



theoretical cal- ,, . , , , 

 , ^ result trebled, 

 culation. j 



Experimental 

 result doubled. 











or p. 







X. 



Y. | X. 



Y. 



X. 



Y. 



00 



226 



O \.o ,! 1 

 161 10 18 40 |- 160 1- 480 



- 432 







1-34 



2-26 



157 15 15 40 - 1681+ 30 j- 504 + 90 



- 480,+ 76| 



2-68 



2 26 



151 0! 13 25 - 208 + 82 - 624 + 246 



- 630+ 240 



402 



2-26 



140 20 11 35- 297+206 



- 891 + 618 



- 900+ 650 



5-36 



2-26 



121 55110 15 - 354+503 



-1062+1509 



-1100+1696 



67 



2-26 



91 0, 9 20 - 38, + 855 



- 114+2565 



- 160+2960 



7-78 



1-70 



58 25 6 10 + 543+771 



+ 1629+2313 



+2020+3260 



8-2 



074 



28 2 35+1417 



j 



+ 688 



+ 4251+2064 



+4960 



+2340 



00 



3-73 



151 29 - 124 







- 372: 



- 368 







1-34 



373 



145 30 24 42 - 128 + 32 



- 384 + 96 



- 378 



+ 82 



2-68 



3-73 



137 2021 30 - 139+ 77 



- 417+ 231 



- 400 



+ 208 



4 02 



3-73 



126 10 18 57 - 150+148 



- 450+ 444 



- 434 



+ 424 



5-36 



3-73 



110 5 16 58 I- 109+243 



- 327 j+ 729 



- 246 



+ 766 



67 



3 73 



91 15 27 - 20+295 



- 60+ 885 



- 114 



+ 848 



7*83 



3-44 



73 13 2 + 80 +308 



+ 240+ 924+ 200 



+ 872 



8-82 



2-8 



54 5 10 + 179+281 



+ 537!+ 843+ 528 



+ 820 



949 



1 82 



34 35 6 10 + 318 +223 



+ 954+ 669+ 950 



+ 676 



97 



0-73 



14 25 2 5 + 456+120 



+ 1368+ 360+1336 



+ 372 



In spite of some discordances in the large forces (which it was 

 impossible to measure with accuracy), there is enough of agree- 

 ment to show that confidence may be placed in the method of 

 theoretically computing the attraction of the galvanic coil. 



XXV. On a new Mechanical Theorem relative to Stationary 

 Motions. By R. Clausius*. 



IN a memoir published in 1870f, I have, for a material point 

 which moves in a closed path, adduced and demonstrated 

 an equation which stands in close connexion with the proposi- 

 tion of least action and with Hamilton J s principle and yet is 

 essentially distinct from them. In the same memoir I then en- 



* Translated from a separate impression, communicated by the Author, 

 having been read before the Niederrheinische Gesellschaft fur Natur- und 

 Heilkunde on June 16, 1873. 



f " On the Reduction of the Second Proposition of the Mechanical 

 Theory of Heat to general Mechanical Principles," Phil. Mag. S. 4. vol. 

 xlii. p. 161. 



