position of the tangent to the curve at its origin from the pole S.

When the two poles which give rise to the magnetic curves are of the same, instead of being of different, denominations, a different system of curves is produced, which have been termed the divergent, in contradistinction to the former, which are convergent to the poles. The divergent curves preserve, with slight modifications, the same geometrical relations to the axis as the convergent curves, and admit of a similar mode of mechanical description. Instead of the south pole S, in the preceding figures, let another north pole N' be substituted; that is, let the north poles N, N', Fig. 7, of two different mag

Fig. 7.

T

nets, be placed so as to front each other; and let the actions. of their remote south poles be neglected. In the former case, where the actions of the two poles of the magnet were of an opposite kind, the resultant of their joint action, or the line CT, Figs. 1 and 3, passed in a direction intermediate between NC prolonged, and SC (the former line being the direction of the repulsion, and the latter that of the attraction): it therefore cut the axis NX at some point in the prolongation of NS. But in the present case, the two magnetic poles being of the same kind, their action is similar, and their resultant is a force, of which the direction is intermediate to the lines CN and C N', Fig. 7.; and this line produced, must cut the axis somewhere between N and N'. The angle CN'T being reversed from the situation with respect to C N', which it had in the former case, the sign of its cosine must be changed, and the equation becomes

VOL. I.

c + x = C.

FEB. 1831.

Y

This applies to the case, in which the angle formed by CN' with the produced axis is acute, and its cosine positive. When it is obtuse (or CN' N acute), its cosine being negative, the equation is

When the two poles are similar, and consequently the curves divergent, the two radii, which, during their revolution, generate them by their intersections, revolve in opposite directions; and the points in each which preserve the same perpendicular position with relation to one another, will be found to lie on opposite sides of the axis. The intersections of N n are made with that portion of the line Ss, which is produced on the other side of the pole S. This is shown in Fig. 8,

n

n

P

Fig. 8.

where N, P, are the two similar poles, and Nn, Pp, the two revolving radii; the latter being produced beyond P to q. In this position, when N n coincides with the axis, Pq is the direction of the tangent to the divergent curve at the pole P. In their positions N n' and Pp', the radii intersect one another at the point c'; when they arrive at n" and p", they intersect at c"; and so on; P, c', c", &c., being so many successive points of the curve. When Nn and Pp become parallel, they direction of the curve.

indicate the ultimate

The divergent magnetic curves are capable of being described by an instrument of a similar construction to the one already explained; only the ruler Bn, Fig. 6, must be of twice the length of the former; and in order to obtain a sufficient extent of curve, the revolving rulers, Nn, and Ss, must be prolonged in those parts where the intersections are to take place.

ON THE FIRST INVENTION OF

TELESCOPES, COL

LECTED FROM THE NOTES AND PAPERS OF THE

LATE PROFESSOR VAN SWINDEN.

BY DR. G. MOLL, OF UTRECHT.

[Communicated by Professor Moll.]

THE late Professor Van Swinden had been at considerable pains to illustrate some important points in the history of natural philosophy. The first invention of telescopes in Holland attracted a considerable share of his attention, and he had the good fortune to meet with some official documents, which are calculated to throw some light on the mystery in which the early history of this celebrated invention is involved.

Mr. Van Swinden exposed the result of his labours in several public lectures, and he intended to publish a paper on the subject: his death prevented the accomplishment of this purpose. He left, however, the sketches of his lectures, together with extensive notes, and abstracts from various writers, which he had collected with great industry. These papers were committed to my hands, and the result of what I collected from them has been ordered to be printed by the Royal Institute of the Netherlands.

The little which is known of the first invention of telescopes in this country has been principally derived from two sources: first, from the book which the French physician, Pierre Borel, wrote on the subject in 1655, probably at the request, and certainly with the assistance, of William Boreel, at that time ambassador of the States at the court of France*. The second

* De vero Telescopii inventore, cum brevi omnium Conspicilliorum historia, authore Petro Borello, Regis Christianissimi consiliario et medico ordinario; Haga Comit. ex typogr. Adriani Vlacq. 4to., 1655.

source from which information is generally derived, is a passage in Descartes's Dioptrics*, in which he attributes the invention to a citizen of Alkmar, called James Metiús. Both the versions of Borel and Descartes are usually given in books written on this part of natural philosophy, and very recently they were repeated in the very excellent account of the life of Galileo published in England, and in the still more recent and capital work of Professor Littrow on Dioptrics.

The real name of this Metiús, of whom Descartes speaks, and who is also mentioned by Huygens, was Jacob Adriaansz. His father Adriaan Anthonisz was a man of considerable knowledge for his time; he possessed a great influence, and took a principal part in the struggle with Spain. In consequence, he was banished by the Duke of Alva, and his property confiscated. He contributed very essentially to the glorious defence of his native town against the Spaniards in 1592. He was created afterwards inspector of fortifications, and many towns were fortified on his plans. As a mathematician he is celebrated for his expression of the ratio of the diameter and circumference of the circle, by the numbers 113 and 355. At that time Ludolf van Ceulen had not given his celebrated number, and the ratio of Archimedes, of 7 and 22, was in general use. The numbers of Anthonisz have the merit of being easily kept in memory, and of being as accurate as almost any purpose requires. If no logarithms are used, it is easier to calculate than Ludolf's number.

There is another problem remaining of this Anthonisz, which shows his ability as a mathematician: it is recorded in one of the writings of his son Adrian, and Delambre notices it in his history of astronomy. The problem was solved by Nicholas des Muliers of Bruges, then professor of mathematics in Groningen.

All the four sons of Adriaan Anthonisz were mathematicians like their father. The eldest, Dirk or Theodore, was an engineer and surveyor in the service of the States. He sailed in

Pierre Borel was a native of Chartres, and author of several other books: he died 1689. A copy of this very rare tract has been recently added to the library of the Royal Institution. It contains a portrait of Lippershey. Cartesii Dioptrica, p. 49.

that capacity in the expedition against the Spanish colonies in the West Indies and the coast of Africa, sent out under Admiral Peter Van der Does in 1599. He died in that ill-fated expe dition.

The second son, Adrian, whilst at the University, had the nickname of Metiús given to him by his fellow-students, on account of his propensity to mathematics. He became generally known under that name, and wore it through life. His father sent him to Hueen to study astronomy under the celebrated Tycho, and afterwards he visited several universities of Germany. He filled the astronomical chair at the university of Franeker with great credit, and died in that place in 1635. His works were very numerous and celebrated in their time, being considered the best elementary works then extant. Delambre seems to have known only one of Metiús's books, of which a complete catalogue is to be found in Vriemoet*.

The fourth son, Anthony, did not rise to such extensive fame however, he also served his country as an engineer.

The third son is the person whom Descartes designates as the inventor of the telescope. His name was Jacob Adriaansz; and sometimes the name of Metiús, which properly belonged to his brother, was given to him. This Jacob, or James, died between 1624 and 1631. Contemporary writers describe him as a person of eccentric and fanciful habits, buried incessantly in deep meditations, and of a temper so little communicative, that he very seldom spoke to any one about the subject of his studies. It is well known that such an eccentric turn of mind is not incompatible with mechanical genius, and in England and elsewhere the most consummate skill has often been blended with most singular habits. It appears, from the evidence of writers of that time, that this Jacob had acquired considerable skill in working glass, and excelled, amongst other things, in the construction of large burning lenses. It is said that he once placed a large lens on the walls of Alkmar, and predicted that at a certain hour of the day it would set fire to a tree standing at a great distance on the other side of the At the request of Prince Maurice of Nassau, who was

* Athena Frisiacæ.