320 
PROCEEDINGS OF SOCIETIES. 
" That diffraction and consequent obscurity of microscopic image 
must necessarily increase with increasing amplifications of the image, 
and this, quite independently of any particular construction of the 
instrument, rests as a fact upon a general law which applies to all 
optical instruments, and which was first formularized by La Grange 
for combinations of any kind of infinitely thin lenses. The law has 
apparently remained unknown, perhaps, says Helmholtz, because La 
Grange enunciated it in equations (formulaB) whose coefficients have 
not characters which readily present clear ideas to the mind. In my 
treatise on physiological optics I have given expression to this law in 
a somewhat more general form . . . and have endeavoured to formu- 
larize it in readily intelligible characters." Professor Helmholtz 
here states he has endeavoured to formularize these complicated 
mathematical expressions so as to be readily intelligible. This, in 
plain English, I have expressed " by popularized." And I trust this 
will give no offence to this distinguished and highly gifted savant. 
Dr. Abbe, perhaps, would do me the honour to send a copy of his 
paper to me. But whether it would receive any damage by an 
attempt on my part to popularize his physical reasoning by which he 
arrived at the result (afterwards given by Helmholtz) omitted by Dr. 
Fripp, I must leave him to judge for himself. 
I am, Sir, your obedient servant, 
G. W. KOYSTON-PlGOTT. - 
N.B. — The primary object of connecting mathematical repre- 
sentations of waves with acknowledged dynamical principles formed 
the basis of the investigations of Huyghens, Euler, and D'Alembert 
(Berlin Acts, 1749), and by La Grange (' Turin Memoirs,' 1759), and 
it was soon seen to apply to the case of undulating ether ; a long list 
of worthies have devoted their resplendent talents to the question of 
the wave theory and its phenomena. Our own savant. Sir J. F. 
Herschel, expressly states in his work on ' Light,' " that Fraunhofer 
seems inclined to conclude that an object of less linear diameter than 
X (a wave-length) can never be discerned by microscopes as consisting 
of parts : a conclusion," says Herschel, " which would put a natural 
limit to the magnifying power of microscopes, but which we cannot 
regard as following from the premmises." 
PEOOEEDINGS OF SOCIETIES. 
KoYAL Microscopical Society. 
King's College, November 1, 1876. 
H. C. Sorby, Esq., F.K.S., President, in the chair. 
The minutes of the preceding meeting were read and confirmed. 
A list of presents to the Society was read, and the thanks of the 
meeting were voted to the donors. 
The Secretary called the particular attention of the Fellows to a 
