98 
cation would only be of value where the circumstances of 
locality and distance prevented connexion with the prime 
mover being made by ordinary mechanical means. 
Ordinary Meeting, March 21st, 1882. 
Dr. R. Angus Smith, F.RS., &c., in the Chair. 
“Note on Envelopes and Singular Solutions, continued 
from vol. XVII. p. 15,” by Sir James Cockle, F.RS., 
F.RA.S., Corresponding Member of the Society. 
6. Lagrange ( Legons , 1806, p. 178) observes that singular 
values had presented themselves almost at the birth of the 
calculus ; but since the theory of arbitrary constants was 
scarcely known at the time, these values were not regarded 
as exceptions to general rules. He adds that Euler was the 
first who looked at them in this point of view, and who 
gave rules for distinguishing them from ordinary integrals. 
7. I shall follow Lagrange, and ascribe to Euler the first 
real recognition of singularity. So far as I know there is 
no proof that by a singular solution Taylor meant more 
than a solution obtained by differentiation. 
8. In a letter to me, dated January 15th, 1867, Mr. 
Robert Rawson announced two theorems, which I give in 
a footnote.* I mention this, not as claiming priority for 
Mr. Rawson, but as stating his views. 
* « The condition of equal roots with respect to (C) in the com- 
plete primitive <p (x, y t C)=0 is a singular solution.” 
“(B)” “ The condition of equal roots of <p ( x , y, p) = 0 with respect to 
p, is a singular solution if it satisfies the differential equation.” 
Mr. Eawson adds that the usual infinity tests are consequences of the 
condition, and that if the condition does not lead to a solution of a dif- 
ferential equation it is because the equation has not been derived from a 
