Inaugural Address. 27 



"We must strive to discern clearly, understand fully, and report 

 faithfully ; to love truth in things physical as in things moral ; to 

 abjure hasty theories and unsupported conjectures ; where we are 

 in doubt, not to be positive ; to give our brother observer the same 

 measure of credit we take to ourselves ; not striving for mastery, 

 but leaving time for the formation of the judgment which will 

 inevitably be given, whether for or against us, by those who come 

 after us ; contented if we are able to add but one grain to that 

 enduring pyramid which is now in course of erection as the testi- 

 mony of Nature to the truth of Revelation. 



If in this spirit we make progress, in this way our own mental 

 enjoyment will be increased. 



It is a work not only suitable to a Society of humble-minded 

 men who profess to unite for this very end ; but, if carried on 

 earnestly, charitably, with simplicity and faithfulness, is one worthy 

 not only of Royal Patronage, but of Universal Encouragement. 



Aet. I. — On " Non-Linear Coresolvents," ly the Honourable Chief 

 Justice Cockle, F.R.S., President of the Queensland Philoso- 

 phical Society. 



[Bead before the Society, 7th August, 1867, by Martin Gardiner, Esq., C.E.] 



1. Let y denote the root of a quartic whereof the coefficients are 

 regarded as functions of a variable x and let^> and q respectively 

 denote the first and second differential coefficients of y with 

 respect to x, so that 



d y d 2 y __ dp_ _ _ (1 9,\ 



dec dec 2 dx 



also let 



Pi =V (3) 



y 



