380 M. J. Nicklés on a New System of Electro-magnets, 
quently P in the formula (a) cannot be a constant accelerating 
orce. . 
Lastly, if any variable accelerating force P, act continually 
upon a body 4, it will give to that body at the end of the indefi- 
nitely small time dit, a velocity dV and momentum dm. An 
use the effect or momentum is proportional to its cause, viz: 
to the force P multiplied by the time of its action dt, we have 
- dma dtP. AG 
And because the momentum of a body is that body multiplied 
by its velocity, we have dm=bdV. k 
By substituting for dm in (i) its value as found in (k), we have 
P : 
bdV cc dtP or dV o and because 6 is a constant quantity, we 
aiP : 
have Voc Lak, whence by substituting for 5 its value VDS, re- 
| | 3 v 
ducing, and regarding S constant, we derive Ve a and 
consequently VDS « oe (1) 
D 
Now it is obvious that this formula (1) cannot be identical with 
(a), unless P be a constant quantity ; but in that case the formula 
(1) will reduce to (h), which it has been shown cannot be identi- 
cal with (a), therefore the formula (1) cannot be identical with 
(a). Consequently P in the formula (a) is necessarily a moment 
ary force, and therefore the velocity induced thereby must be 
uniform. But Mr. Blake has shown independently of the formula 
(a), that in the flow of elastic fluids, the velocity increases as the 
fluid approaches the orifice, therefore the formula (a) which he 
employs in his investigation is not applicable to the case he is 
pei S and consequently his determinations are not necessé 
y true. 
Auburn, Ind., Feb, 14, 1853. 5 
ee 
Arr, XLIV.—On a New System of Electro-Magnets ; bY M. 
betes J. Nicxuis.* 
“Tur discrepancy pointed out by me between the conclusion of 
M. Dub, and tha oe M. Muller ps MM. Lenz and Jacobi, as ' 
the in nence of the length of the arms of an electro-magie 
the weight carried by them, is only apparent; each of te 4 
Opinions is based on a special case. ‘The elongation of the arm 
has in fact Some influence*(as M. Dub asserts,) when, (as se 
* An addition to the former paper at page 104 of this volume. 
