1816.) Royal Institute of France. 155 
he determines the parallaxes and the apparent places of two stars, 
referred to the equator or the ecliptic. It is then only that he 
endeavours to find the apparent distance, and he obtains it by two 
lineary formulas of the most simple kind, as well as all those 
through which he has successively passed. M. Lagrange, on the 
other -hand, attacks the difficulty at once, and without supposing 
any thing, except what he takes directly from the astronomical 
tables, he expresses the tangent of the apparent distance of the centres. 
But this expression is embarrassed by radicles; the quantities under 
the sign represent values very 'long and very complicated. The author 
to no purpose exhausts all the resources of his art and his genius to 
eradicate from these formulas all the terms, the absence of which 
will produce scarcely any change in the degree of precision. To 
no purpose has he contrived tables of an ingenious construction, in 
order to diminish the length of the calculation; even these tables, 
and the artifices of the calculus, are tacit acknowledgements that 
the problem surpasses the force of analysis, and a disguised imita- 
tion of the practice of astronomers. These tables, in fact, are 
formulas of ‘the parallaxes from which the nonagesimal and its 
height are eliminated, which only makes the use of them more 
troublesome. It is this task, so great and so difficult, that M. Henri 
has accomplished by means quite different. M. Lagrange expressed 
by rectangular co-ordinates the true and apparent positions of two 
stars and those of the observer in space. M. Henri draws the same 
expressions from trigonometry, either plane or spherical. By this 
means he obtains all the formulas of Lagrange; so that the solution 
has gained nothing on the side of facility. To abbreviate, he 
restores the nonagesimal eliminated by Lagrange. Without using 
the name parallax, he introduces what is equivalent, and reduces 
it to tables ; but notwithstanding all these efforts, he acknowledges 
himself that the method is still very troublesome. He does not 
believe that any professed astronomer will ever prefer it; but if the 
method is long and troublesome, this is the only fault with which 
it can be charged. It is neither less precise nor less proper to give 
exactly the difference of longitude between two places where the 
same eclipse shall have been observed. And the new point of view, 
under which M. Henri has presented it, cannot but augment the 
number of its partisans, by increasing the number of calculators 
capable of appreciating it. ‘The methods employed by M. Henri 
deserve to be generally known. Opportunities perhaps of applying 
them more advantageously will occur. And the Class, as well as 
the commissioners, were of opinion, that at at a time when the 
original memoir of Lagrange is printed in the Connoissance des 
Temps for 1817, of which only a German translation had appeared 
in the Ephemerides of Berlin, astronomers would see with plea- 
sure the same formulas demonstrated in a manner quite different, 
which is neither less rigorous nor less easy. 
Annals of Mathematics, pure and mixed; a periodical Work, 
edited by M. I. D. Gergonne, Professor of transcendental Mathe- 
L 2 
